Articles in RIA

On the two-dimensional rotational body of maximal Newtonian resistance

Gouveia, P.D.F., Plakhov, A.Y., Torres, D.F.M.

Springer Verlag

We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that the bodies are moving forward and at the same time slowly rotating. A two-dimensional geometric shape that confers to the body a resistance very close to the theoretical supremum value is obtained, which improves previous results. © 2009 Springer Science+Business Media, Inc. CEOC FCT ECF FEDER/POCI 2010 PTDC/MAT/72840/2006 ECF PRODEP III/5.3/2003

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Two-dimensional body of maximum mean resistance

Gouveia, P.D.F., Plakhov, A., Torres, D.F.M.

Elsevier

A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, [Alexander Yu. Plakhov, Paulo D.F. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271-2287], shapes of nonconvex bodies were sought which would maximize the braking force of the medium on their movement. Giving continuity to this study, new investigations have been undertaken which culminate in an outcome which represents a large qualitative advance relative to that which was achieved earlier. This result, now presented, consists of a two-dimensional shape which confers on the body a resistance which is very close to its theoretical supremum value. But its interest does not lie solely in the maximization of Newtonian resistance; on regarding its characteristics, other areas of application are seen to begin to appear which are thought to be capable of having great utility. The optimal shape which has been encountered resulted from numerical studies, thus it is the object of additional study of an analytical nature, where it proves some important properties which explain in great part its effectiveness. © 2009 Elsevier Inc. All rights reserved.

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Optimal control of Newton-type problems of minimal resistance

Torres, D.F.M., Plakhov, A.Yu.

Rosenberg & Sellier

We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessary and sufficient condition. Solutions are then computed for concrete situations, including the new case when the flux of particles is non-parallel.

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Newton's aerodynamic problem in media of chaotically moving particles

Plakhov, A.Yu., Torres, D.F.M.

Institute of Physics (IOP Publishing)

The problem of minimum resistance is studied for a body moving with constant velocity in a rarefied medium of chaotically moving point particles in the Euclidean space R. The distribution of the velocities of the particles is assumed to be radially symmetric. Under additional assumptions on the distribution function a complete classification of the bodies of least resistance is carried out. In the case of dimension three or more there exist two kinds of solution: a body similar to the solution of the classical Newton problem and a union of two such bodies 'glued together' along the rear parts of their surfaces. In the two-dimensional case there exist solutions of five distinct types: (a) a trapezium; (b) an isosceles triangle; (c) the union of an isosceles triangle and a trapezium with a common base; (d) the union of two isosceles triangles with a common base; (e) the union of two triangles and a trapezium. Cases (a)-(d) are realized for an arbitrary velocity distribution of the particles, while case (e) is realized only for some distributions. Two limit cases are considered: when the average velocity of the particles is large and when it is small in comparison with the velocity of the body. Finally, the analytic results so obtained are used for the numerical study of a particular case: the problem of the motion of a body in a rarefied homogeneous monatomic ideal gas of positive temperature in ℝ2 and in ℝ3. © 2005 RAS(DoM) and LMS. CEOC

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Retroreflecting Curves in Nonstandard Analysis

Almeida, R, Neves, V, Plakhov, A

National Academy of Sciences of Ukraine

We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve. CEOC FCT FEDER/POCTI

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Explicit optimality conditions for problems of convex semi-infinite programming

Kostyukova, O. I., Chemisova, T. V., Ermolinskaya, S. A.

Belaruskaya Navuka

Resumo não disponível...

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An implicit optimality criterion for problems of convex Semi-Infinite Programming

Kostyukova, O. I., Tchemisova, T. V., Yermalinskaya, S. A.

State University of Grodno

Resumo não disponível...

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On a special nonlinear problem arising in the study of convex SIP problems

Kostyukova, O. I., Tchemisova, T. V., Yermalinskaya, S. A.

University of Aveiro

We continue a study of convex problems of Semi-In¯nite Programming (SIP) started in [6, 7]. In the Implicit Optimality Criterion from [6], we formulated the optimality conditions for convex SIP problem in terms of such the conditions for a special Nonlinear Programming (NLP) problem. In the present paper, we study some speci¯c properties of this nonlinear problem and obtain e±cient optimality conditions for it. We show that in the case when the constraint function of the initial SIP problem is analytical, the optimality conditions take the form of criterion.

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Discrete time and continuous time formulations for a short sea inventory routing problem

Agra, Agostinho, Christiansen, Marielle, Delgado, Alexandrino

Universidade de Aveiro

We consider a fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The production/consumption rates are given and assumed to be constant. We provide two alternative mixed integer formulations: a discrete time model adapted from the case where the production/consumption rates are varying and a classical continuous time formulation. We discuss different extended formulations and valid inequalities that allow us to reduce the linear gap of the two initial formulations. A computational study comparing the various models accordingly to their size, linear gap and running time, was conducted based on real small-size instances, using a commercial software.

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On a constructive approach to optimality conditions for convex SIP problems with polyhedral index sets

Cordeiro, Tatiana Tchemisova, Olga, Kostyukova

Taylor & Francis

In the paper,we consider a problem of convex Semi-Infinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new optimality conditions with other known results is provided.

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A fundamental theorem on initial value problems by using the theory of reproducing kernels

Castro, L. P., Rodrigues, M. M., Saitoh, S.

Springer

We introduce a new method for solving general initial value problems by using the theory of reproducing kernels. The results are depending on the specific structure of each problem. Here, we give the general principle of the method and illustrate it with simple prototype examples. On the basis of the process, we have certain integral transforms, which are generated by each specific initial value problem, and need to be analysed. In view of this, we shall establish the basic relations among initial value problems for linear operator equations, eigenvalues and eigenfunctions in the related operator equations, integral transforms and associated reproducing kernels. Within this process, we will realize a general theory for operator equations and incorporate a time dependence in view to consider an associated regularization method.

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Whittaker transform on distributions

Rodrigues, M. M., Vieira, N.

Springer

The aim of this paper is to construct a testing function space equipped with the topology generated by the L_{v,p}-multinorm of the differential operator Bx = -4x^2 d^2/dx^2- 1 + x^2 -ux, where u < 1/2, v>0, p in [1, infinity[, and its k-iterates B^k_x where k = 0, 1,..., and B^0_x phi=phi. We also introduce the correspondent dual space for the index Whittaker transform on distributions. The existence, uniqueness, imbedding and inversion properties are investigated.

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A heat conduction problem of 2D unbounded composites with imperfect contact conditions

Castro, L. P., Kapanadze, D., Pesetskaya, E.

Wiley

We consider a steady-state heat conduction problem in 2D unbounded doubly periodic composite materials with temperature independent conductivities of their components. Imperfect contact conditions are assumed on the boundaries between the matrix and inclusions. By introducing complex potentials, the corresponding boundary value problem for the Laplace equation is transformed into a special R-linear boundary value problem for doubly periodic analytic functions. The method of functional equations is used for obtaining a solution. Thus, the R-linear boundary value problem is transformed into a system of functional equations which is analysed afterwards. A new improved algorithm for solving this system is proposed. It allows to compute the average property and reconstruct the temperature and the flux at an arbitrary point of the composite. Computational examples are presented.

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Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications

Almeida, Alexandre, Caetano, António

Elsevier

In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spaces. Some other properties, like Sobolev embeddings, are also obtained via atomic representations.

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Classification of regular maps with prime number of faces and the asymptotic behaviour of their reflexible to chiral ratio

Azevedo, António Breda d', Fernandes, Maria Elisa

Elsevier

In this paper we classify the reflexible and chiral regular oriented maps with faces of valency, and then we compute the asymptotic behaviour of the reflexible to chiral ratio of the regular oriented maps with faces. The limit depends on and for certain primes we show that the limit can be 1, greater than 1 and less than 1. In contrast, the reflexible to chiral ratio of regular polyhedra (which are regular maps) with Suzuki automorphism groups, computed by Hubard and Leemans (2014), has produced a nill asymptotic ratio.

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String C-groups as transitive subgroups of $S_n$

Cameron, Peter J., Fernandes, Maria Elisa, Leemans, Dimitri, Mixer, Mark

Elsevier

If $Gamma$ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of is at most n/2+1, with nitely many exceptions (which are classi ed). It is conjectured that only the symmetric group has to be excluded.

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Regularization with maximum entropy and quantum electrodynamics: the MERG(E) estimators

Macedo, Pedro, Scotto, Manuel, Silva, Elvira

Taylor & Francis

It is well-known that under fairly conditions linear regression becomes a powerful statistical tool. In practice, however, some of these conditions are usually not satisfied and regression models become ill-posed, implying that the application of traditional estimation methods may lead to non-unique or highly unstable solutions. Addressing this issue, in this paper a new class of maximum entropy estimators suitable for dealing with ill-posed models, namely for the estimation of regression models with small samples sizes affected by collinearity and outliers, is introduced. The performance of the new estimators is illustrated through several simulation studies.

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Effective conductivity of a composite material with stiff imperfect contact conditions

Castro, L. P., Kapanadze, D., Pesetskaya, E.

Wiley

We present an analytic and numerical analysis of several properties of a composite material with stiff imperfect interface conditions. Spaces of functions are identified where we can guarantee existence and uniqueness of solutions. In particular, formulas for the temperature distribution and flux are exhibited. Numerical calculations of the material characteristics such as temperature, flux and the effective conductivity are also performed and interpreted.

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Spontaneous baroreceptor reflex sensitivity for risk stratification of heart failure patients: optimal cut-off and age effects

Gouveia, Sónia, Scotto, Manuel G., Pinna, G. D., Maestri, R., La Rovere, M. T., Ferreira, Paulo J.

Portland Press

Baroreflex sensitivity (BRS) is an important prognostic factor as a reduced BRS has been associated with an adverse cardiovascular outcome. The threshold for “reduced” BRS was established by the ATRAMI study at BRS <3 ms/mmHg in patients with a previous myocardial infarction and has shown to improve risk assessment in many other cardiac dysfunctions. The successful application of this cutoff to other populations suggests that it may reflect an inherent property of baroreflex functioning. Hence, our goal is to investigate whether it represents a “natural” partition of BRS values. Since reduced baroreflex responsiveness is also associated with aging, we also investigate whether a BRS estimate below 3 ms/mmHg can be the result of a process of physiologic senescence besides a sign of BRS dysfunction. This study involved 228 chronic heart failure (CHF) patients and 60 age-matched controls. Our novel method combines transfer function BRS estimation and automatic clustering of BRS probability distributions to define indicative levels of different BRS activities. The analysis produced a fit clustering (cophenetic coefficient 0.9 out of 1) and identified one group of homogeneous patients (well separated from the remaining by 3 ms/mmHg) with increased BRS based mortality risk (HR: 3.19 [1.73,5.89], p<0.001). The age dependent BRS cutoff, estimated by 5% quantile regression of log(BRS) with age (considering the age-matched controls), provides a similar mortality value (HR: 2.44 [1.37,4.43], p=0.003). In conclusion, the 3 ms/mmHg cutoff identifies two large clusters of homogeneous HF patients, thus supporting the hypothesis of being a natural cutoff in the HF population. Furthermore, age was found to have no statistical impact on risk assessment, thus suggesting that there is no need to establish age-based cutoffs as 3 ms/mmHg optimally identifies patients at high mortality risk.

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Laplacian spread of graphs: lower bounds and relations with invariant parameters

Andrade, Enide, Cardoso, Domingos, Robbiano, Maria, Rodriguez, Jonnathan

Elsevier

The spread of an $ntimes n$ complex matrix $B$ with eigenvalues $beta _{1},beta _{2},ldots ,beta _{n}$ is defined by begin{equation*} sleft( Bright) =max_{i,j}leftvert beta _{i}-beta _{j}rightvert , end{equation*}% where the maximum is taken over all pairs of eigenvalues of $B$. Let $G$ be a graph on $n$ vertices. The concept of Laplacian spread of $G$ is defined by the difference between the largest and the second smallest Laplacian eigenvalue of $G$. In this work, by combining old techniques of interlacing eigenvalues and rank $1$ perturbation matrices new lower bounds on the Laplacian spread of graphs are deduced, some of them involving invariant parameters of graphs, as it is the case of the bandwidth, independence number and vertex connectivity.

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Upper bounds on the Laplacian spread of graphs

Andrade, Enide, Gomes, Helena, Robbiano, Maria, Rodrigues, Jonnathan

Elsevier

The Laplacian spread of a graph $G$ is defined as the difference between the largest and the second smallest eigenvalue of the Laplacian matrix of $G$. In this work, an upper bound for this graph invariant, that depends on first Zagreb index, is given. Moreover, another upper bound is obtained and expressed as a function of the nonzero coefficients of the Laplacian characteristic polynomial of a graph.

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Some new considerations about double nested graphs

Andelic, M., Andrade, E., Cardoso, D. M., Fonseca, C. M. da, Simic, S. K., Tosic, D. V.

Elsevier

In the set of all connected graphs with fixed order and size, the graphs with maximal index are nested split graphs, also called threshold graphs. It was recently (and independently) observed in [F.K.Bell, D. Cvetkovi´c, P. Rowlinson, S.K. Simi´c, Graphs for which the largest eigenvalue is minimal, II, Linear Algebra Appl. 429 (2008)] and [A. Bhattacharya, S. Friedland, U.N. Peled, On the first eigenvalue of bipartite graphs, Electron. J. Combin. 15 (2008), #144] that double nested graphs, also called bipartite chain graphs, play the same role within class of bipartite graphs. In this paper we study some structural and spectral features of double nested graphs. In studying the spectrum of double nested graphs we rather consider some weighted nonnegative matrices (of significantly less order) which preserve all positive eigenvalues of former ones. Moreover, their inverse matrices appear to be tridiagonal. Using this fact we provide several new bounds on the index (largest eigenvalue) of double nested graphs, and also deduce some bounds on eigenvector components for the index. We conclude the paper by examining the questions related to main versus non-main eigenvalues.

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On the Π-operator in Clifford analysis

Blaya, Ricardo Abreu, Reyes, Juan Bory, Adán, Alí Guzmán, Kähler, Uwe

Elsevier

In this paper we prove that a generalization of complex Π-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism.

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Discrete Hilbert boundary value problems on half lattices

Cerejeiras, Paula, Kähler, Uwe, Ku, Min

Taylor and Francis

We study discrete Hilbert boundary value problems in the case of the upper half lattice. The solutions are given in terms of the discrete Cauchy transforms for the upper and lower half space while the study of their solvability is based on the discrete Hardy decomposition for the half lattice. Furthermore, the solutions are proved to converge to those of the associated continuous Hilbert boundary value problems.

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Time-dependent operators on some non-orientable projective orbifolds

Krausshar, R. S., Rodrigues, M. M., Vieira, N.

Wiley

In this paper we present an explicit construction for the fundamental solution of the heat operator, the Schrödinger operator and related first order parabolic Dirac operators on a class of some conformally flat non-orientable orbifolds. More concretely, we treat a class of projective cylinders and tori where we can study parabolic monogenic sections with values in different pin bundles. We present integral representation formulas together with some elementary tools of harmonic analysis that enable us to solve boundary value problems on these orbifolds.

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Testing General Relativity with Present and Future Astrophysical Observations

Berti, Emanuele, Barausse, Enrico, Cardoso, Vitor, Gualtieri, Leonardo, Pani, Paolo, Sperhake, Ulrich, Stein, Leo C., Wex, Norbert, Yagi, Kent, Baker, Tessa, Burgess, C. P., Coelho, Flávio S., Doneva, Daniela, De Felice, Antonio, Ferreira, Pedro G., Freire, Paulo C. C., Healy, James, Herdeiro, Carlos, Horbatsch, Michael, Kleihaus, Burkhard, Klein, Antoine, Kokkotas, Kostas, Kunz, Jutta, Laguna, Pablo, Lang, Ryan N., Li, Tjonnie G. F., Littenberg, Tyson, Matas, Andrew, Mirshekari, Saeed, Okawa, Hirotada, Radu, Eugen, O'Shaughnessy, Richard, Sathyaprakash, Bangalore S., Van Den Broeck, Chris, Winther, Hans A., Witek, Helvi, Aghili, Mir Emad, Alsing, Justin, Bolen, Brett, Bombelli, Luca, Caudill, Sarah, Chen, Liang, Degollado, Juan Carlos, Fujita, Ryuichi, Gao, Caixia, Gerosa, Davide, Kamali, Saeed, Silva, Hector O., Rosa, João G., Sadeghian, Laleh, Sampaio, Marco, Sotani, Hajime, Zilhão, Miguel

IOP Publishing

One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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Duality for the left and right fractional derivatives

Caputo, M. Cristina, Torres, Delfim F. M.

Elsevier

We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operators is useful to obtain results for the left operators from analogous results on the right operators and vice versa. We illustrate the usefulness of our duality theory by proving a fractional integration by parts formula for the right Caputo derivative and by proving a Tonelli-type theorem that ensures the existence of minimizer for fractional variational problems with right fractional operators. (C) 2014 Elsevier B.V. All rights reserved.

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Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions

Debbouche, Amar, Torres, Delfim F. M.

Springer Verlag

We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given.

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Generalized fractional operators for nonstandard Lagrangians

Taverna, Giorgio S., Torres, Delfim F. M.

Wiley

In this note, we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems, and the corresponding Euler-Lagrange and Hamilton equations are analyzed. The dependence of the equation of motion on the generalized kernel permits to obtain a wide range of different configurations of motion. Some examples are discussed and analyzed.Copyright (c) 2014 John Wiley & Sons, Ltd.

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Szegö Kernel for Hardy space of matrix functions

He, Fuli, Ku, Min, Kähler, Uwe

Elsevier

By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szegö projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.

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Linear spanning sets for matrix spaces

Micheli, G., Rosenthal, J., Vettori, P.

Elsevier

Necessary and sufficient conditions are given on matrices $A$, $B$ and $S$, having entries in some field $F$ and suitable dimensions, such that the linear span of the terms $A^iSB^j$ over $F$ is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of $F[A]SF[B]$ when $F$ is a finite field.

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Numerical solution for fractional variational problems using the Jacobi polynomials

Khosravian-Arab, Hassan, Almeida, Ricardo

Elsevier

We exhibit a numerical method to solve fractional variational problems, applying a decomposition formula based on Jacobi polynomials. Formulas for the fractional derivative and fractional integral of the Jacobi polynomials are proven. By some examples, we show the convergence of such procedure, comparing the exact solution with numerical approximations.

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Variational problems for Hölderian functions with free terminal point

Almeida, Ricardo, Martins, Natália

Wiley

We develop the new variational calculus introduced in 2011 by J. Cresson and I. Greff, where the classical derivative is substituted by a new complex operator called the scale derivative. In this paper we consider several nondifferentiable variational problems with free terminal point: with and without constraints, of first and higher-order type.

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Caputo derivatives of fractional variable order: numerical approximations

Tavares, Dina, Almeida, Ricardo, Torres, Delfim F. M.

Elsevier

We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is obtained in terms of standard (integerorder) derivatives only. Estimations for the error of the approximations are also provided. We then compare the numerical approximation of some test function with its exact fractional derivative. We end with an exemplification of how the presented methods can be used to solve partial fractional differential equations of variable order.

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The braid and the Shi arrangements and the Pak–Stanley labelling

Duarte, Rui, Guedes de Oliveira, António

Elsevier

In this article we study a construction, due to Pak and Stanley, with which every region RR of the Shi arrangement is (bijectively) labelled with a parking function λ(R). In particular, we construct an algorithm that returns R out of λ(R). This is done by relating λ to another bijection, that labels every region S of the braid arrangement with r(S), the unique central parking function f such that λ−1(f)⊆S. We also prove that λ maps the bounded regions of the Shi arrangement bijectively onto the prime parking functions. Finally, we introduce a variant (that we call “s-parking”) of the parking algorithm that is in the very origin of the term “parking function”. S-parking may be efficiently used in the context of our new algorithm, but we show that in some (well defined) cases it may even replace it.

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Maximum principle for the regularized Schrödinger operator

KrauBhar, R. S., Rodrigues, M. M., Vieira, N.

Springer International Publishing

In this paper we present analogues of the maximum principle and of some parabolic inequalities for the regularized time-dependent Schrödinger operator on open manifolds using Günter derivatives. Moreover, we study the uniqueness of bounded solutions for the regularized Schrödinger-Günter problem and obtain the corresponding fundamental solution. Furthermore, we present a regularized Schrödinger kernel and prove some convergence results. Finally, we present an explicit construction for the fundamental solution to the Schrödinger-Günter problem on a class of conformally flat cylinders and tori.

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Second-order differential equations in the Laguerre-Hahn class

Branquinho, A., Moreno, A. Foulquié, Paiva, A., Rebocho, M. N.

Elsevier

Laguerre–Hahn families on the real line are characterized in terms of second-order differential equations with matrix coefficients for vectors involving the orthogonal polynomials and their associated polynomials, as well as in terms of second-order differential equation for the functions of the second kind. Some characterizations of the classical families are derived.

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Orthogonal polynomial interpretation of Delta-Toda equations

Branquinho, A., Moreno, A. Foulquié, Godoy, E., Area, I.

IOP Publising

The correspondence between dynamics of Delta-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. A method to solve inverse problem - integration of Delta-Toda equations - based on Padé approximates and continued fractions for the resolvent function is proposed. The main ingredient are orthogonal polynomials which satisfy an Appell condition, with respect to the forward difference operator Delta. Two examples related with Jacobi and Laguerre orthogonal polynomials and Delta-Toda equations are given.

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Characterizations of Δ-Volterra lattice: a symmetric orthogonal polynomials interpretation

Area, I., Branquinho, A., Moreno, A. Foulquié, Godoy, E.

Elsevier

In this paper we introduce the Δ-Volterra lattice which is interpreted in terms of symmetric orthogonal polynomials. It is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like (1+x2)1−tμ(x)(1+x2)1−tμ(x) where μ is a given positive Borel measure. Moreover, the Δ-Volterra lattice is related to the Δ-Toda lattice from Miura or Bäcklund transformations. The main ingredients are orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ and the characterization of the point spectrum of a Jacobian operator that satisfies a Δ-Volterra equation (Lax type theorem). We also provide an explicit example of solutions of Δ-Volterra and Δ-Toda lattices, and connect this example with the results presented in the paper.

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Newton's problem of minimal resistance under the single-impact assumption

Plakhov, Alexander

IOP Publishing

A parallel flow of non-interacting point particles is incident on a body at rest. When hitting the body’s surface, the particles are reflected elastically. Assuming that each particle hits the body at most once (the single impact condition (SIC)), the force of resistance of the body along the flow direction can be written down in a simple analytical form. The problem of minimal resistance within this model was first considered by Newton (Newton 1687 Philosophiae Naturalis Principia Mathematica) in the class of bodies with a fixed length M along the flow direction and with a fixed maximum orthogonal cross section , under the additional conditions that the body is convex and rotationally symmetric. Here we solve the problem (first stated in Buttazzo et al 1995 Minimum problems over sets of concave functions and related questions Math. Nachr. 173 71–89) for the wider class of bodies satisfying the SIC and with the additional conditions removed. The scheme of solution is inspired by Besicovitch’s method of solving the Kakeya problem (Besicovitch 1963 The Kakeya problem Am. Math. Mon. 70 697– 706). If is a disc, the decrease of resistance as compared with the original Newton problem is more than twofold; the ratio tends to 2 as M 0 and to 20.25 as M . We also prove that the infimum of resistance is 0 for a wider class of bodies with both single and double reflections allowed.

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On the kernels of Wiener-Hopf-Hankel operators on variable exponent Lebesgue spaces

Castro, L. P., Silva, A. S.

Cambridge Scientific Publishers

We investigate properties of the kernels (and cokernels) of Wiener-Hopf plus and minus Hankel operators on variable exponent Lebesgue spaces. Constructive operator identities are used in view to describe those kernels upon the consideration of auxiliary operators. Moreover, a Coburn-Simonenko type theorem is obtained for Wiener-Hopf plus and minus Hankel operators in the framework of variable exponent Lebesgue spaces.

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On 2-microlocal spaces with all exponents variable

Almeida, Alexandre, Caetano, António

Elsevier

In this paper we study various key properties for 2-microlocal Besov and Triebel–Lizorkin spaces with all exponents variable, including the lifting property, embeddings and Fourier multipliers. We also clarify and improve some statements recently published.

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A unified matrix approach to the representation of Appell polynomials

Aceto, L., Malonek, H. R., Tomaz, G.

Taylor and Francis

In this paper, we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix – a special matrix which has only the natural numbers as entries and is closely related to the well-known Pascal matrix. By this means, we stress the arithmetical origins of Appell polynomials. The approach also allows to derive, in a simplified way, the properties of Appell polynomials by using only matrix operations.

ria.ua.pt

A characterization of the weighted version of McEliece-Rodemich-Rumsey-Schrijver number based on convex quadratic programming

Luz, Carlos J.

World Scientific

For any graph $G,$ Luz and Schrijver cite{LuzSchrijver} introduced a characterization of the Lov'{a}sz number $vartheta(G)$ based on convex quadratic programming. A similar characterization is now established for the weighted version of the number $vartheta^{prime}(G),$ independently introduced by McEliece, Rodemich, and Rumsey cite{McElieceetal} and Schrijver cite{Schrijver1}. Also, a class of graphs for which the weighted version of $vartheta^{prime}(G)$ coincides with the weighted stability number is characterized.

ria.ua.pt

On the C-determinantal range for special classes of matrices

Guterman, Alexander, Lemos, Rute, Soares, Graça

Elsevier

Let A and C be square complex matrices of sizen, the C-determinantal range of A is the subset of the complex plane{det(A−UCU^∗): UU^∗=In}. If A, C are both Hermitian matrices, then by a result of Fiedler (1971)[11] this set is a real line segment. In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning theC-numerical range of a Hermitian matrix, see Condition 5.1 (a) in Li, (1994)[20]. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et al. (2008)[21], Theorem 3.3).

ria.ua.pt

Properties of a composite material with mixed imperfect contact conditions

Castro, L. P., Pesetskaya, E.

Taylor & Francis

We present an analytical solution of a mixed boundary value problem for an unbounded 2D doubly periodic domain which is a model of a composite material with mixed imperfect interface conditions. We find the effective conductivity of the composite material with mixed imperfect interface conditions, and also give numerical analysis of several of their properties such as temperature and flux.

ria.ua.pt

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

Ferreira, Milton, Vieira, Nelson

Springer International Publishing

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $Delta_+^{(alpha,beta,gamma)}:= D_{x_0^+}^{1+alpha} +D_{y_0^+}^{1+beta} +D_{z_0^+}^{1+gamma},$ where $(alpha, beta, gamma) in ,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+alpha}$, $D_{y_0^+}^{1+beta}$, $D_{z_0^+}^{1+gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $Delta_+^{(alpha,beta,gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

ria.ua.pt

Proof theory for hybrid(ised) logics

Neves, Renato, Madeira, Alexandre, Martins, Manuel A., Barbosa, Luis S.

Elsevier

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. In a series of papers this process has been detailed and taken as a basis for a speci cation methodology for recon gurable systems. The present paper extends this work by showing how a proof calculus (in both a Hilbert and a tableau based format) for the hybridised version of a logic can be systematically generated from a proof calculus for the latter. Such developments provide the basis for a complete proof theory for hybrid(ised) logics, and thus pave the way to the development of (dedicated) proof support.

ria.ua.pt

A numerical method to solve higher-order fractional differential equations

Almeida, Ricardo, Bastos, Nuno R. O.

Springer

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

ria.ua.pt

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

Caetano, António, Opic, Bohumír, Gogatishvili, Amiran

Cambridge University Press; Royal Society of Edinburgh

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(Rn)$, $1 leq p < infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(Rn)$, $0 ria.ua.pt


Self-exciting threshold binomial autoregressive processes

Möller, Tobias, Silva, M. Eduarda, Weiss, Christian, Scotto, Manuel González, Pereira, Isabel

Springer

We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645–650, 1985. doi:10.1111/j.1752-1688.1985. tb05379.x). Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany.

ria.ua.pt

Fractional variational problems depending on indefinite integrals and with delay

Almeida, Ricardo

Springer

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example, where we nd analytically the minimizer.

ria.ua.pt

A Caputo fractional derivative of a function with respect to another function

Almeida, Ricardo

Elsevier

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

ria.ua.pt

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

Castro, L. P., Saitoh, S., Yamada, A.

Springer; Birkhäuser

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

ria.ua.pt

Invertibility characterization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces via even asymmetric factorization

Castro, L. P., Silva, A. S.

De Gruyter

We obtain invertibility and Fredholm criteria for the Wiener-Hopf plus Hankel operators acting between variable exponent Lebesgue spaces on the real line. Such characterizations are obtained via the so-called even asymmetric factorization which is applied to the Fourier symbols of the operators under study.

ria.ua.pt

A lower bound for the energy of symmetric matrices and graphs

Andrade, Enide, Robbiano, María, Martín, B. San

Elsevier

The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2sqrt{m}$, where $m$ is the number of edges of the graph.

ria.ua.pt

Census of quadrangle groups inclusions

d’Azevedo, António Breda, Catalano, Domenico A., Karabáš, Ján, Nedela, Roman

Springer

In a classical result of 1972 Singerman classifies the inclusions between triangle groups. We extend the classification to a broader family of triangle and quadrangle groups forming a particular subfamily of Fuchsian groups. With two exceptions, each inclusion determines a finite bipartite map (hypermap) on a 2-dimensional spherical orbifold that encodes the complete information and gives a graphical visualisation of the inclusion. A complete description of all the inclusions is contained in the attached tables.

ria.ua.pt

Preface of the “2nd Symposium on Modelling and Simulation in Computer Sciences and Engineering”

Miranda, Francisco, Abreu, Carlos

AIP Publishing

The 2nd Symposium on Modelling and Simulation in Computer Sciences and Engineering was held in the 13th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2015), Rhodes, Greece, 23-29 September 2015. (...)

ria.ua.pt

Stabilization of model-based networked control systems

Miranda, Francisco, Abreu, Carlos, Mendes, Paulo M.

AIP Publishing

A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtain an optimal feedback control is also presented.

ria.ua.pt

An exercise on the generation of many-valued dynamic logics

Madeira, Alexandre, Neves, Renato, Martins, Manuel A.

Elsevier

In the last decades, dynamic logics have been used in different domains as a suitable formalism to reason about and specify a wide range of systems. On the other hand, logics with many-valued semantics are emerging as an interesting tool to handle devices and scenarios where uncertainty is a prime concern. This paper contributes towards the combination of these two aspects through the development of a method for the systematic construction of many-valued dynamic logics. Technically, the method is parameterised by an action lattice that defines both the computational paradigm and the truth space (corresponding to the underlying Kleene algebra and residuated lattices, respectively).

ria.ua.pt

Adaptive and context-aware detection and classification of potential QoS degradation events in biomedical wireless sensor networks

Abreu, Carlos, Miranda, Francisco, Mendes, Paulo M.

AIP Publishing

The use of wireless sensor networks in healthcare has the potential to enhance the services provided to citizens. In particular they play an important role in the development of state-of-the-art patient monitoring applications. Nevertheless due to the critical nature of the data conveyed by such patient monitoring applications they have to fulfil high standards of quality of service in order to obtain the confidence of all players in the healthcare industry. In such context vis-à-vis the quality of service being provided by the wireless sensor network this work presents an adaptive and context-aware method to detect and classify performance degradation events. The proposed method has the ability to catch the most significant and damaging variations on the metrics being used to quantify the quality of service provided by the network without overreacting to small and innocuous variations on the metric’s value.

ria.ua.pt

Evaluation and optimization of the performance of frame geometries for lithium-ion battery application by computer simulation

Miranda, D., Miranda, F., Costa, C. M., Almeida, A. M., Lanceros-Méndez, S.

AIP Publishing

Tailoring battery geometries is essential for many applications as geometry influences the delivered capacity value. Two geometries frame and conventional have been studied and for a given scan rate of 330C the square frame shows a capacity value of 305,52 Ahm−2 which is 527 times higher than the one for the conventional geometry for a constant the area of all components.

ria.ua.pt

Higher pain intensity, depression, and being 75 Years or Older are associated with lower Levels of self-reported physical activity in older adults with pain attending primary care

Silva, Anabela G., Queirós, Alexandra, Sá-Couto, Pedro, Rocha, Nelson P.

Taylor & Francis

Objective: This study investigated whether pain characteristics (intensity, frequency, duration and number of pain sites), depression, age, sex and comorbidities are associated with lower levels of selfreported physical activity in older adults with pain at the primary healthcare setting.Methods: A total of 504 participants aged 60 years of age and over were assessed for: socio-demographics, comorbidities, pain, depression, and physical activity. Associations between these variables were investigated using ordinal logistic regression.Results: Reporting severe pain or worst imaginable pain, being older (≥ 75 years), and feeling depressed were significantly associated with lower physical activity in the univariate (OR = 2.33, 2.93, 2.31, and 2.23, respectively) and multivariate models (Adj OR = 2.21, 2.47, 2.49, and 1.97, respectively).Conclusions: Interventions aiming to increase physical activity for older adults in primary care should consider the needs of those reporting higher pain intensity, feeling depressed and who are 75 years or older.

ria.ua.pt

A method for rigorous design of reconfigurable systems

Madeira, Alexandre, Neves, Renato, Barbosa, Luís S., Martins, Manuel A.

Elsevier

Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system’s reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements. In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.

ria.ua.pt

Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph

Agra, Agostinho, Doostmohammadi, Mahdi, Souza, Cid C. de

Elsevier

In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0–1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of the vertex packing set simultaneously are introduced. In particular, the well-known mixed integer rounding inequality is generalized to the case where incompatibilities between binary variables are present. Exact and heuristic algorithms are designed to solve the separation problems associated to the proposed valid inequalities. Preliminary computational experiments show that these inequalities can be useful to reduce the integrality gaps and to solve integer programming problems.

ria.ua.pt

Lifted euclidean inequalities for the integer single node flow set with upper bounds

Agra, Agostinho, Constantino, Miguel Fragoso

Elsevier

In this paper we discuss the polyhedral structure of the integer single node flow set with two possible values for the upper bounds on the arc flows. Such mixed integer sets arise as substructures in complex mixed integer programs for real application problems. This work builds on results for the integer single node flow polytope with two arcs given by Agra and Constantino, 2006a. Valid inequalities are extended to a new family, the lifted Euclidean inequalities, and a complete description of the convex hull is given. All the coefficients of the facet-defining inequalities can be computed in polynomial time. We report on some computational experimentations for three problems: an inventory distribution problem, a facility location problem and a multi-item production planning model.

ria.ua.pt

Two infinite families of Archimedean maps of higher genera

D’Azevedo, António Breda, Catalano, Domenico A., Karabás, Ján

The Charles Babbage Research Centre

The well known infinite families of prisms and antiprisms on the sphere were, for long time, not considered as Archimedean solids for reasons not fully understood. In this paper we describe the first two infinite families of Archimedean maps on higher genera which we call “generalized” prisms and “generalized” antiprisms.

ria.ua.pt

Quadrangle groups inclusions

D’Azevedo, António Breda, Catalano, Domenico A., Karabáš, Ján, Nedela, Roman

Springer Verlag

In this paper we generalise Singerman’s results on triangle group inclusions to the broader class of generalised quadrangle groups, that is, Fuchsian groups with signature of genus 0 and generated by three or four elliptic generators. For any possible inclusion P ria.ua.pt


Highly symmetric hypertopes

Fernandes, Maria Elisa, Leemans, Dimitri, Weiss, Asia

Springer

We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a property of orderly asymmetry occurring frequently in nature as a natural phenomenon. The main result in this paper is that automorphism groups of regular and chiral thin residually connected geometries need to be C-groups in the regular case and C+-groups in the chiral case.

ria.ua.pt

Complex function with GeoGebra

Breda, Ana Maria d’Azevedo, Santos, José Manuel dos Santos dos

Oxford University Press

Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from to through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software.

ria.ua.pt

Paediatric automatic phonological analysis tools (APAT)

Saraiva, Daniela, Lousada, Marisa, Hall, Andreia, Jesus, Luis M. T.

Taylor & Francis

Purpose: To develop the pediatric Automatic Phonological Analysis Tools (APAT) and to estimate inter and intrajudge reliability, content validity, and concurrent validity. Method: The APAT were constructed using Excel spreadsheets with formulas. The tools were presented to an expert panel for content validation. The corpus used in the Portuguese standardized test Teste Fon etico-Fonol ogico – ALPE produced by 24 children with phonological delay or phonological disorder was recorded, transcribed, and then inserted into the APAT. Reliability and validity of APAT were analyzed. Results: The APAT present strong inter- and intrajudge reliability (>97%). The content validity was also analyzed (ICC¼0.71), and concurrent validity revealed strong correlations between computerized and manual (traditional) methods. Conclusions: The development of these tools contributes to fill existing gaps in clinical practice and research, since previously there were no valid and reliable tools/instruments for automatic phonological analysis, which allowed the analysis of different corpora.

ria.ua.pt

Caputo–Hadamard fractional derivatives of variable order

Almeida, Ricardo

Taylor & Francis

In this article, we present three types of Caputo-Hadamard derivatives of variable fractional order and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained and an estimation for the error is given. At the end, we compare the exact fractional derivative of a concrete example with some numerical approximations.

ria.ua.pt

Approximated analytical solution to an Ebola optimal control problem

Hincapié-Palacio, Doracelly, Ospina, Juan, Torres, Delfim F.M.

Taylor & Francis

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler–Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods. © 2016 Taylor & Francis Group, LLC.

ria.ua.pt

Decoding of 2D convolutional codes over an erasure channel

Climent, Joan-Josep, Napp, Diego, Pinto, Raquel, Simões, Rita

American Institute of Mathematical Sciences

In this paper we address the problem of decoding 2D convolutional codes over an erasure channel. To this end we introduce the notion of neighbors around a set of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main idea is to reduce the decoding problem of 2D convolutional codes to a problem of decoding a set of associated 1D convolutional codes. We first show how to recover sets of erasures that are distributed on vertical, horizontal and diagonal lines. Finally we outline some ideas to treat any set of erasures distributed randomly on the 2D plane. © 2016 AIMS.

ria.ua.pt

Two new convolutions for the fractional Fourier transform

Anh, P. K., Castro, L. P., Thao, P. T., Tuan, N. M.

Springer Verlag

In this paper we introduce two novel convolutions for the fractional Fourier transforms (FRFT), and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish a necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in L^1(R) and L^2(R) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper.

ria.ua.pt

Heisenberg uncertainty principles for an oscillatory integral operator

Castro, L. P., Guerra, R. C., Tuan, N. M.

American Institute of Physics

The main aim of this work is to obtain Heisenberg uncertainty principles for a specific oscillatory integral operator which representatively exhibits different parameters on their sine and cosine phase components. Additionally, invertibility theorems, Parseval type identities and Plancherel type theorems are also obtained.

ria.ua.pt

Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights

Anh, P. K., Castro, L. P., Thao, P. T., Tuan, N. M.

American Institute of Physics

This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.

ria.ua.pt

Odd asymmetric factorization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces

Castro, L. P., Silva, A. S.

American Institute of Physics

The main goal of this paper is to obtain an invertibility criterion for Wiener-Hopf plus Hankel operators acting between variable exponent Lebesgue spaces on the real line. This is obtained by a so-called odd asymmetric factorization which is applied to the Fourier symbols of the operators under study.

ria.ua.pt

Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations

Castro, L. P., Simões, A. M.

American Institute of Physics

The purpose of this paper is to study different kinds of stability for a class of Hammerstein integral equations. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of Hammerstein integral equations. The consequent different cases of a finite interval and an infinite interval are considered, and some concrete examples are included to illustrate the results.

ria.ua.pt

Some operational properties of the Laguerre transform

Rodrigues, M. M., Huy, V. N., Tuan, N. M.

American Institute of Physics

This paper is devoted to the study of some properties of the Laguerre transform. We define new properties of the Laguerre transform in a weighted $L_2-$space. Moreover, we present some results concerning the action of this integral transform over some class of polynomials.

ria.ua.pt

Fischer Decomposition and Cauchy-Kovalevskaya extension in fractional Clifford analysis: the Riemann-Liouville case

Vieira, N.

Cambridge University Press

In this paper we present the basic tools of a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville derivatives. A Fischer decomposition, Almansi decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers will be constructed. Moreover, we establish the fractional Cauchy-Kovalevskaya extension ($FCK$-extension) theorem for fractional monogenic functions defined on $BR^d$. Based on this extension principle, fractional Fueter polynomials, forming a basis of the space of fractional spherical monogenics, i.e. fractional homogeneous polynomials, are introduced. We studied the connection between the $FCK$-extension of functions of the form $x ~P_l$ and the classical Gegenbauer polynomials. Finally we present an example of an $FCK$-extension.

ria.ua.pt

Two-sided hypergenic functions

Eriksson, S. L., Orelma, H., Vieira, N.

Springer

In this paper we present an analogous of the class of two-sided axial monogenic functions to the case of axial $kappa-$hypermonogenic functions. In order to do that we will solve a Vekua-type system in terms of Bessel functions.

ria.ua.pt

Compact mixed integer linear programming models to the Minimum Weighted Tree Reconstruction problem

Fortz, Bernard, Requejo, Cristina, Oliveira, Olga

Elsevier

The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes. This problem has applications in several areas, namely, the inference of phylogenetic trees, the modeling of traffic networks and the analysis of internet infrastructures. In this paper, we investigate the MWTR problem and we present two compact mixed-integer linear programming models to solve the problem. Computational results using two different sets of instances, one from the phylogenetic area and another from the telecommunications area, show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes.

ria.ua.pt

The Static Maxwell System in Three Dimensional Axially Symmetric Inhomogeneous Media and Axially Symmetric Generalization of the Cauchy–Riemann System

Bryukhov, Dmitry, Kähler, Uwe

Birkhaeuser

In this paper we discuss different generalizations of the Cauchy–Riemann system and their connection with the static Maxwell system. In particular, this allows us to present relations between slice-monogenic functions and hypermonogenic functions, as well as to provide a physical interpretation of slice-monogenic functions. Furthermore, we present an explicit and complete set of basic solutions of a new class of axial-hypermonogenic functions in R^3. In the end we determine the symmetry operators for the class of axial-hypermonogenic functions.

ria.ua.pt

Ridge regression and generalized maximum entropy: an improved version of the Ridge-GME parameter estimator

Macedo, Pedro

Taylor & Francis

In this paper, the Ridge-GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. A serious concern with the visual inspection of the ridge trace to define the supports for the parameters in the Ridge-GME parameter estimator is the misinterpretation of some ridge traces, in particular where some of them are very close to the axes. A simulation study and two empirical applications are used to illustrate the performance of the improved estimator. A MATLAB code is provided as supplementary material.

ria.ua.pt

Fischer decomposition in generalized fractional ternary Clifford analysis

Cerejeiras, P., Fonseca, A., Vajiac, M., Vieira, N.

Springer Verlag

This paper describes the generalized fractional Clifford analysis in the ternary setting. We will give a complete algebraic and analytic description of the spaces of monogenic functions in this sense, their analogous Fischer decomposition, concluding with a description of the basis of the space of fractional homogeneous monogenic polynomials that arise in this case and an explicit algorithm for the construction of this basis.

ria.ua.pt

Error Estimates for the Coupling of Analytical and Numerical Solutions

Legatiuk, Dmitry, Gürlebeck, Klaus, Kähler, Uwe

Birkhaeuser

In this paper we present error estimates for a continuous coupling of an analytical and a numerical solution for a boundary value problem with a singularity. A solution of the Lamé–Navier equation with a singularity caused by a crack is considered as an example. The analytical solution near a singularity is constructed by using complex function theory and coupled continuously with the finite element solution. The objective of this paper is to estimate the coupling error, which cannot be covered by the classical theory of the finite element method.

ria.ua.pt

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives

Ferreira, M., Vieira, N.

Taylor & Francis

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator ${}^C!Delta_+^{(alpha,beta,gamma)}:= {}^C!D_{x_0^+}^{1+alpha} +{}^C!D_{y_0^+}^{1+beta} +{}^C!D_{z_0^+}^{1+gamma},$ where $(alpha, beta, gamma) in ,]0,1]^3$ and the fractional derivatives ${}^C!D_{x_0^+}^{1+alpha}$, ${}^C!D_{y_0^+}^{1+beta}$, ${}^C!D_{z_0^+}^{1+gamma}$ are in the Caputo sense. Applying integral transform methods we describe a complete family of eigenfunctions and fundamental solutions of the operator ${}^C!Delta_+^{(alpha,beta,gamma)}$ in classes of functions admitting a summable fractional derivative. The solutions are expressed using the Mittag-Leffler function. From the family of fundamental solutions obtained we deduce a family of fundamental solutions of the corresponding fractional Dirac operator, which factorizes the fractional Laplace operator introduced in this paper.

ria.ua.pt

Testing Einstein-dilaton-Gauss-Bonnet gravity with the reflection spectrum of accreting black holes

Zhang, H., Zhou, M. L., Bambi, C. M., Kleihaus, B., Kunz, J., Radu, E. G.

American Physical Society

Einstein-dilaton-Gauss-Bonnet gravity is a theoretically well-motivated alternative theory of gravity emerging as a low-energy four-dimensional model from heterotic string theory. Its rotating black hole solutions are known numerically and can have macroscopic deviations from the Kerr black holes of Einstein's gravity. Einstein-dilaton-Gauss-Bonnet gravity can thus be tested with observations of astrophysical black holes. In the present paper, we simulate observations of the reflection spectrum of thin accretion disks with present and future x-ray facilities to understand whether x-ray reflection spectroscopy can distinguish the black holes in Einstein-dilaton-Gauss-Bonnet gravity from those in Einstein's gravity. We find that this is definitively out of reach for present x-ray missions, but it may be achieved with the next generation of facilities.

ria.ua.pt

Effect of Chern-Simons dynamics on the energy of electrically charged and spinning vortices

Navarro-Lerida, F, Radu, E, Tchrakian, DH

American Physical Society

We study the effect of a Chern-Simons term on the electrically charged and spinning solitons of several U(1) gauged models in 2 + 1 dimensions. These are vortices of complex scalar field theories, both with and without symmetry breaking dynamics, and the O(3) Skyrme model. In all cases the gauge decoupling limits are also considered. It is well known that the effect of the Chern-Simons dynamics is to endow vortices with electric charge Q(e) and spin J, but our main aim here is to reveal a new feature: that the massenergy E of the electrically charged vortex can be lower than that of the electrically neutral one, in contrast to the usual monotonic increase of E with Q(e) and J. These effects of Chern-Simons dynamics were observed previously in 3 + 1 dimensional systems, and the present results can be viewed as corroborating the latter. We carry out a detailed quantitative analysis of azimuthally symmetric vortices and describe their qualitative features by constructing the solutions numerically.

ria.ua.pt

An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings

Kuijper, M., Pinto, R.

Springer Verlag

The construction of shortest feedback shift registers for a finite sequence S1,…,SN is considered over finite chain rings, such as Zpr. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers S1,…,SN, thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with S1, and constructs at each step a particular type of minimal basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reverse sequence SN,…,S1. The complexity order of the algorithm is shown to be O(rN2).

ria.ua.pt

On the dominating induced matching problem:spectral results and sharp bounds

Andrade, Enide, Cardoso, Domingos M., Medina, Luis, Rojo, Oscar

Elsevier

A matching M is a dominating induced matching of a graph if every edge is either in M or has a common end-vertex with exactly one edge in M. The extremal graphs on the number of edges with dominating induced matchings are characterized by its Laplacian spectrum and its principal Laplacian eigenvector. Adjacency, Laplacian and signless Laplacian spectral bounds on the cardinality of dominating induced matchings are obtained for arbitrary graphs. Moreover, it is shown that some of these bounds are sharp and examples of graphs attaining the corresponding bounds are given.

ria.ua.pt

Highest rank of a polytope for An

Cameron, Peter, Leemans, Dimitri, Mixer, Mark, Fernandes, Maria Elisa

London Mathematical Society

We prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n = 5; 4 if n = 9; 5 if n = 10; 6 if n = 11; and the floor of of (n-1)/2 if n>=12. Moreover, if n = 3; 4; 6; 7 or 8, the group An is not a string C-group. This solves a conjecture made by the last three authors in 2012.

ria.ua.pt

Gleason’s problem associated to the fractional cauchy-riemann operator, fueter series, drury-arveson space and related topics

Alpay, Daniel, Cerejeiras, Paula, Kähler, Uwe

American Mathematical Society

In this paper we present the building blocks for a function theory based on fractional Cauchy-Riemann operators. We are going to construct basic monogenic powers and Fueter series. With these tools we are going to study Gleason’s problem and reproducing kernel spaces, like the Drury- Arveson space and de Branges-Rovnyak spaces. We end with a statement on Schur multipliers in this setting.

ria.ua.pt

Riemann–Hilbert Problems for Monogenic Functions on Upper Half Ball of R^4

Ku, Min, Wang, Ying, He, Fuli, Kähler, Uwe

Birkhaeuser

In this paper we are interested in finding solutions to Riemann– Hilbert boundary value problems, for short Riemann–Hilbert problems, with variable coefficients in the case of axially monogenic functions defined over the upper half unit ball centred at the origin in four-dimensional Euclidean space. Our main idea is to transfer Riemann– Hilbert problems for axially monogenic functions defined over the up- per half unit ball centred at the origin of four-dimensional Euclidean spaces into Riemann–Hilbert problems for analytic functions defined over the upper half unit disk of the complex plane. Furthermore, we extend our results to axially symmetric null-solutions of perturbed generalized Cauchy–Riemann equations.

ria.ua.pt

Discrete time and continuous time formulations for a short sea inventory routing problem

Agra, Agostinho, Christiansen, Marielle, Delgado, Alexandrino

Springer

We consider a fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. Inventory management considerations are taken into account at the demand side only, and consumption rates are given and assumed to be constant. We provide two alternative mixed integer formulations: a discrete time model adapted from the case where the consumption rates are varying and a classical continuous time formulation. We discuss different extended formulations and valid inequalities that allow us to reduce the linear gap of the two initial formulations. A computational study comparing the various models accordingly to their size, linear gap and running time, was conducted based on real small-size instances, using a commercial software.

ria.ua.pt

A country-wide probability sample of public attitudes toward stuttering in Portugal

Valente, Ana Rita S., St. Louis, Kenneth O., Leahy, Margereth, Hall, Andreia, Jesus, Luis M. T.

Elsevier

Background: Negative public attitudes toward stuttering have been widely reported, although differences among countries and regions exist. Clear reasons for these differences remain obscure. Purpose: Published research is unavailable on public attitudes toward stuttering in Portugalas well as a representative sample that explores stuttering attitudes in an entire country. This study sought to (a) determine the feasibility of a country-wide probability samplingscheme to measure public stuttering attitudes in Portugal using a standard instrument (the Public Opinion Survey of Human Attributes–Stuttering [POSHA–S]) and (b) identify demographic variables that predict Portuguese attitudes. Methods: The POSHA–S was translated to European Portuguese through a five-step process. There after, a local administrative office-based, three-stage, cluster, probability sampling scheme was carried out to obtain 311 adult respondents who filled out the questionnaire. Results: The Portuguese population held stuttering attitudes that were generally within the average range of those observed from numerous previous POSHA–S samples. Demographicvariables that predicted more versus less positive stuttering attitudes were respondents’age, region of the country, years of school completed, working situation, and number of languages spoken. Non-predicting variables were respondents’ sex, marital status, and parental status. Conclusion: A local administrative office-based, probability sampling scheme generated a respondent profile similar to census data and indicated that Portuguese attitudes are generally typical.

ria.ua.pt

Area burned in Portugal over recent decades: an extreme value analysis

Scotto, M. G., Gouveia, S., Carvalho, A., Monteiro, A., Martins, V., Flannigan, M. D., San-Miguel-Ayanz, J., Miranda, A. I., Borrego, C.

CSIRO Publishing

Forest fires are a major concern in Europe, particularly in Portugal where large forest fires are responsible for negative environmental, social and economic effects. In this work, a long time series of daily area burned in 18 Portuguese districts (north, coastal areas and inner-south) from 1980 to 2010 are analysed to characterise extreme area burned and regional variability. The analysis combines the peak-over-threshold method and classification techniques to cluster the time series on the basis either of their corresponding tail indices or their predictive distributions for 5- and 15-year return values, that is, the level that is exceeded on average once every 5 or 15 years. As previously reported in other wildfire studies, the results show that the distributions of area burned (1980-2010) are heavy tailed for all Portuguese districts, with considerable density in the tail, indicating a non-negligible probability of occurrence of days with very large area burned. Moreover, clustering based on tail indices identified three distinct groups with spatial pattern closely related to the percentage of shrub cover within each district. Finally, clustering based on return values shows that the largest return levels of area burned are expected to occur in districts located in the centre and south of Portugal.

ria.ua.pt

Interpolation in variable exponent spaces

Almeida, Alexandre, Hästö, Peter

Springer

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale.

ria.ua.pt

Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces

Almeida, Alexandre, Samko, Stefan

Elsevier

We prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces). In particular, we obtain embeddings into a new Stummel class of functions with some vanishing property at infinity. We also partially improve a known result on the coincidence of Stummel spaces with a modification of Morrey spaces where the supremum norm is replaced by an integral Lp-norm.

ria.ua.pt

Multiwavelength observations of nova SMCN 2016-10a - one of the brightest novae ever observed

Aydi, E., Page, K. L., Kuin, N. P. M., Darnley, M. J., Walter, F. M., Mróz, P., Buckley, D., Mohamed, S., Whitelock, P., Woudt, P., Williams, S. C., Orio, M., Williams, R. E., Beardmore, A. P., Osborne, J. P., Kniazev, A., Ribeiro, V. A. R. M., Udalski, A., Strader, J., Chomiuk, L.

Royal Astronomical Society

We report on multiwavelength observations of nova Small Magellanic Cloud Nova 2016-10a. The present observational set is one of the most comprehensive for any nova in the Small Magellanic Cloud, including low-, medium-, and high-resolution optical spectroscopy and spectropolarimetry from Southern African Large Telescope, Folded Low-Order Yte-Pupil Double-Dispersed Spectrograph, and Southern Astrophysical Research; long-term Optical Gravitational Lensing Experiment V- and I-bands photometry dating back to 6 yr before eruption; Small and Moderate Aperture Research Telescope System optical and near-IR photometry from ˜11 d until over 280 d post-eruption; Swift satellite X-ray and ultraviolet observations from ˜6 d until 319 d post-eruption. The progenitor system contains a bright disc and a main sequence or a sub-giant secondary. The nova is very fast with t2 ≃ 4.0 ± 1.0 d and t3 ≃ 7.8 ± 2.0 d in the V band. If the nova is in the SMC, at a distance of ˜61 ± 10 kpc, we derive MV, max ≃ -10.5 ± 0.5, making it the brightest nova ever discovered in the SMC and one of the brightest on record. At day 5 post-eruption the spectral lines show a He/N spectroscopic class and an Full Width at Half Maximum of ˜3500 km s-1, indicating moderately high ejection velocities. The nova entered the nebular phase ˜20 d post-eruption, predicting the imminent super-soft source turn-on in the X-rays, which started ˜28 d post-eruption. The super-soft source properties indicate a white dwarf mass between 1.2 and 1.3 M in good agreement with the optical conclusions.

ria.ua.pt

Positive solutions for parametric nonlinear nonhomogeneous Robin problems

Aizicovici, S., Papageorgiou, N. S., Staicu, Vasile

Mathematical Society of Japan

We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. Using variational tools together with suitable truncation and perturbation techniques, we prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. in publication

ria.ua.pt

Stationary scalar clouds around a BTZ black hole

Ferreira, H. R. C., Herdeiro, C. A. R.

Elsevier

We establish the existence of stationary clouds of massive test scalar fields around BTZ black holes. These clouds are zero-modes of the superradiant instability and are possible when Robin boundary conditions (RBCs) are considered at the AdS boundary. These boundary conditions are the most general ones that ensure the AdS space is an isolated system, and include, as a particular case, the commonly considered Dirichlet or Neumann-type boundary conditions (DBCs or NBCs). We obtain an explicit, closed form, resonance condition, relating the RBCs that allow the existence of normalizable (and regular on and outside the horizon) clouds to the system's parameters. Such RBCs never include pure DBCs or NBCs. We illustrate the spatial distribution of these clouds, their energy and angular momentum density for some cases. Our results show that BTZ black holes with scalar hair can be constructed, as the non-linear realization of these clouds. (C) 2017 The Author(s). Published by Elsevier B.V.

ria.ua.pt

Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons

Sanchis-Gual, N., Degollado, J. C., Font, J. A., Herdeiro, C., Radu, E.

IOP Publishing

Recent numerical relativity simulations within the Einstein-Maxwell(charged-) Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordstrm black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these unstable solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordstrm BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.

ria.ua.pt

Fundamental photon orbits: Black hole shadows and spacetime instabilities

Cunha, P. V. P., Herdeiro, C. A. R., Radu, E.

American Physical Society

The standard black holes (BHs) in general relativity, as well as other ultracompact objects (with or without an event horizon) admit planar circular photon orbits. These light rings (LRs) determine several spacetime properties. For instance, stable LRs trigger instabilities and, in spherical symmetry, (unstable) LRs completely determine BH shadows. In generic stationary, axisymmetric spacetimes, nonplanar bound photon orbits may also exist, regardless of the integrability properties of the photon motion. We suggest a classification of these fundamental photon orbits (FPOs) and, using Poincare maps, determine a criterion for their stability. For the Kerr BH, all FPOs are unstable (similar to its LRs) and completely determine the Kerr shadow. But in non-Kerr spacetimes, stable FPOs may also exist, even when all LRs are unstable, triggering new instabilities. We illustrate this for the case of Kerr BHs with Proca hair, wherein, moreover, qualitatively novel shadows with a cuspy edge exist, a feature that can be understood from the interplay between stable and unstable FPOs. FPOs are the natural generalization of LRs beyond spherical symmetry and should generalize the LRs key role in different spacetime properties.

ria.ua.pt

Constructing fading histograms from data streams

Sebastião, Raquel, Gama, João, Mendonça, Teresa

Springer

The ability to collect data is changing drastically. Nowadays, data are gathered in the form of transient and finite data streams. Memory restrictions preclude keeping all received data in memory. When dealing with massive data streams, it is mandatory to create compact representations of data, also known as synopses structures or summaries. Reducing memory occupancy is of utmost importance when handling a huge amount of data. This paper addresses the problem of constructing histograms from data streams under error constraints. When constructing online histograms from data streams there are two main characteristics to embrace: the updating facility and the error of the histogram. Moreover, in dynamic environments, besides the need of compact summaries to capture the most important properties of data, it is also essential to forget old data. Therefore, this paper presents sliding histograms and fading histograms, an abrupt and a smooth strategies to forget outdated data.

ria.ua.pt

On the dominating induced matching problem: Spectral results and sharp bounds

Andrade, Enide, Cardoso, Domingos M., Medina, Luis, Rojo, Oscar

Elsevier

A matching M is a dominating induced matching of a graph if every edge is either in M or has a common end-vertex with exactly one edge in M. The extremal graphs on the number of edges with dominating induced matchings are characterized by its Laplacian spectrum and its principal Laplacian eigenvector. Adjacency, Laplacian and signless Laplacian spectral bounds on the cardinality of dominating induced matchings are obtained for arbitrary graphs. Moreover, it is shown that some of these bounds are sharp and examples of graphs attaining the corresponding bounds are given.

ria.ua.pt

Improving Entrepreneurial Skills in Portugal Higher Education - a case study in Alto Minho Region

Rodrigues, Helena Sofia, Barreto, Luis

Grupo Lusófona

The entrepreneurship topic is identified as a switch gear to enhance the economic growth and as an important driver for the society transformation. In particular, it should be used as a counter response strategy to the current crisis and as a means to combat apathy, inertia, and the lack of entrepreneurial initiative. It is known that entrepreneurship education increase self-reported intentions to begin a business. The biggest challenge in higher education is the breaking of traditional studies methods, where students and their families think in create new employees for other companies and not to create a new employer. Entrepreneurship education aims to produce graduates with a set of skills and an entrepreneurial mindset, in order to come up with original ideas in response to identified market shortfalls and needs. At Business School of the Polytechnic Institute of Viana do Castelo, an integrated set of projects and activities are trying to contribute to the improvement of entrepreneurial skills of the region: since workshops open to community, to individual projects of students to prepare a startup company, they have been contribute to enhance new capacities and a better entrepreneurial identity of students. Some of the objectives of these integrated initiatives refer to: develop the ability to apply concepts and theories covered during the graduation in an integrated manner and providing them the opportunity to confront the theories studied with existing professional practices aimed at consolidation experience and professional performance; fill specific gaps in areas considered relevant to the progression and development of their future professional activity; provide a practical view of business reality through the ideas with potential formulation for the preparation of business plans and marketing; provide students tools for implementation, monitoring and proper business management; encourage the entrepreneurial spirit and an ethical culture and proactive by implementing projects that lead to the solution of problems and improvements of organizational processes.

ria.ua.pt

The effect of drivers gender on the perception of Portuguese road safety communication campaigns

Rodrigues, Helena Sofia, Fonseca, Manuel José, Cardoso, Paulo Ribeiro

IISES

The road safety campaigns use a range of media and marketing communication techniques to alert drivers to take appropriate behavior on the road. The aim of this study was to investigate how gender differences influence the behavior and attitude of the Portuguese drivers regarding driving as well as the attitude toward the road safety campaigns. In Portugal, there are no studies that analyze the gender difference related to road safety, which reinforces its relevance. To implement this purpose, firstly it was described the profile of drivers by gender regarding a set of behavioral variables. The attitude of drivers toward the road safety communication campaigns was analyzed and drivers were grouped by clusters, aiming its characterization as possible targets of communication actions for road safety marketing.

ria.ua.pt

Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials

Branquinho, A., Moreno, Ana Foulquié, Mendes, A.

Taylor & Francis

In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, generalized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattice

ria.ua.pt

General fractional-order anomalous diffusion with non-singular power-law kernel

Yang, X. -J., Srivastava, H. M., Torres, D. F. M., Debbouche, A.

VINCA Institute of Nuclear Sciences

In this paper, we investigate general fractional derivatives with a non-singular power-law kernel. The anomalous diffusion models with non-singular power-law kernel are discussed in detail. The results are efficient for modelling the anomalous behaviors within the frameworks of the Riemann-Liouville and Liouville-Caputo general fractional derivatives. © 2017 Society of Thermal Engineers of Serbia.

ria.ua.pt

A study to understand the acceptance of DICOM Structured Reports on Breast Imaging

Tribuna, Liliana, Silva, Augusto, Sa Couto, Pedro, Bastião, Luís

Elsevier

Purpose: To create a Digital Imaging and Communication in Medicine Structured Reports (DICOM-SR) Repository and compare the acceptance of Free Text (FT) versus Structured Reports (SR) in communication of Breast Imaging findings. Materials and Methods: It was conceptualized the MamoCatalogue to the structuring of the Reports and the SR were converted into DICOM-SR and integrated with Dicoogle. After that, seven representative Breast Imaging Reports were selected and evaluated by a group of 25 Physicians. Each Physician evaluated the seven Reports, in FT and SR with a 3 months timelag, about their, Structure, Clarity and assertiveness, Diagnostic/Recommendations, Easiness of reading, Full reading, Partially reading with Breast Imaging Reporting and Data System (BI-RADS) focus and Ambiguity. Results: A DICOM-SR Repository was created and the assessment of the acceptance of the FT vs. SR revealed that there is a global trend favoring FT. Nevertheless, a group wise analysis revealed that for Gynaecologists and General Practitioners (GP) the differences between FT and SR weren't significant, unlike what happens with Radiologists. Conclusion: The DICOM-SR Repository allows the query/retrieve data for Reports and the communication with Gynaecologists and GP by SR was satisfactory. Although, Radiologists acceptance must be reinforced upon global communication and management strategy.

ria.ua.pt

Detection of C2-singularities using uniform spline approximations

Nagler, Johannes, Kaehler, Uwe

Wiley

For the detection of C2-singularities, we present lower estimates for the error in Schoenberg variation-diminishing spline approximation with equidistant knots in terms of the classical second-order modulus of smoothness. To this end, we investigate the behaviour of the iterates of the Schoenberg operator. In addition, we show an upper bound of the second-order derivative of these iterative approximations. Finally, we provide an example of how to detect singularities based on the decay rate of the approximation error.

ria.ua.pt

Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

Wang, M. J., Herdeiro, C. A. R., Jing, J. L.

American Physical Society

We study Dirac quasinormal modes of Schwarzschild–anti–de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015).].

ria.ua.pt

Light-Ring Stability for Ultracompact Objects

Cunha, P. V. P., Berti, E., Herdeiro, C. A. R.

American Physical Society

We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e., they have a light ring) must have at least two light rings, and one of them is stable. It has been argued that stable light rings generally lead to nonlinear spacetime instabilities. Our result implies that smooth, physically and dynamically reasonable ultracompact objects are not viable as observational alternatives to black holes whenever these instabilities occur on astrophysically short time scales. The proof of the theorem has two parts: (i) We show that light rings always come in pairs, one being a saddle point and the other a local extremum of an effective potential. This result follows from a topological argument based on the Brouwer degree of a continuous map, with no assumptions on the spacetime dynamics, and, hence, it is applicable to any metric gravity theory where photons follow null geodesics. (ii) Assuming Einstein’s equations, we show that the extremum is a local minimum of the potential (i.e., a stable light ring) if the energy-momentum tensor satisfies the null energy condition.

ria.ua.pt

Dynamical Formation of Kerr Black Holes with Synchronized Hair: An Analytic Model

Herdeiro, C, Radu, E

American Physical Society

East and Pretorius have successfully evolved, using fully nonlinear numerical simulations, the superradiant instability of the Kerr black hole (BH) triggered by a massive, complex vector field. Evolutions terminate in stationary states of a vector field condensate synchronized with a rotating BH horizon. We show that these end points are fundamental states of Kerr BHs with synchronized Proca hair. Motivated by the “experimental data” from these simulations, we suggest a universal (i.e., field-spin independent), analytic model for the subset of BHs with synchronized hair that possess a quasi-Kerr horizon, applicable in the weak hair regime. Comparing this model with fully nonlinear numerical solutions of BHs with a synchronized scalar or Proca hair, we show that the model is accurate for hairy BHs that may emerge dynamically from superradiance, whose domain we identify.

ria.ua.pt

Recent Trends in Differential Equations, Aveiro June 27–29, 2016

Staicu, V

The article describe the international conference RECENT TRENDS IN DIFFERENTIAL EQUATIONS, Aveiro, June 27-29, where we celebrated the 75th birthday of Arrigo Cellina and the 60th birthday of Alberto Bressan and includes shorth biografies of the two celebrated mathematicians

ria.ua.pt

O Papel das Revistas Científicas na Internacionalização da Matemática

Kharlamova, Vera Ivanovna, Malonek, Helmuth R., Santos, Sandrina Rafaela Andrade

Sociedade Brasileira de História da Matemática

As primeiras revistas científicas de indole geral surgiram para dar resposta à necessidade de comunicação e estreitamento de relações entre as diversas comunidades intelectuais científicas da Europa que se formaram a partir do Século XVI. Muitas vezes estas revistas tornaram-se um meio de gestão do conhecimento científico, quer como compilações de informação e apresentações de resultados produzidos, quer como catálogos bibliográficos. A partir do início do Século XIX, as revistas especializadas em Matemática e, em particular, revistas de resenhas tiveram um papel importante na internacionalização da comunidade matemática. Já ao nível superior de especialização, serviram como fonte de classificão das diversas áreas em categorias e subareas. O artigo pretende de apresentar um panorama desta evolução, incluindo alguns detalhes menos conhecidos sobre o papel do Jornal de Teixeira, manifestado no Jahrbuch über die Fortschritte der Mathematik, com grande influência na inclusão de matemáticos portugueses no processo da internacionalização.

ria.ua.pt

Matrix approach to hypercomplex Appell polynomials

Aceto, Lídia, Malonek, Helmuth R., Tomaz, Graça

Elsevier

Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a suitable first order initial value problem. The paper aims to confirm that the unifying character of this approach can also be applied to the construction of homogeneous Appell polynomials that are solutions of a generalized Cauchy–Riemann system in Euclidean spaces of arbitrary dimension. The result contributes to the development of techniques for polynomial approximation and interpolation in non-commutative Hypercomplex Function Theories with Clifford algebras.

ria.ua.pt

Approximate confidence intervals for a linear combination of binomial proportions: A new variant

Escudeiro, S., Freitas, A., Afreixo, V.

Taylor & Francis

We propose a new adjustment for constructing an improved version of theWald interval for linear combinations of binomial proportions, which addresses the presence of extremal samples. A comparative simulation study was carried out to investigate the performance of this new variant with respect to the exact coverage probability, expected interval length, and mesial and distal noncoverage probabilities. Additionally, we discuss the application of a criterion for interpreting interval location in the case of small samples and/or in situations in which extremal observations exist. The confidence intervals obtained from the new variant performed better for some evaluation measures.

ria.ua.pt

Predicting and controlling the Ebola infection

Rachah, A., Torres, D.F.M.

Wiley

We present a comparison between two different mathematical models used in the description of the Ebola virus propagation currently occurring in West Africa. In order to improve the prediction and the control of the propagation of the virus, numerical simulations and optimal control of the two models for Ebola are investigated. In particular, we study when the two models generate similar results. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

ria.ua.pt

Chain rules and inequalities for the BHT fractional calculus on arbitrary timescales

Torres, Delfim F. M., Nwaeze, Eze R.

Springer

We develop the Benkhettou–Hassani–Torres fractional (noninteger order) calculus on timescales by proving two chain rules for the α-fractional derivative and five inequalities for the α-fractional integral. The results coincide with well-known classical results when the operators are of (integer) order α = 1 and the timescale coincides with the set of real numbers.

ria.ua.pt

On a Fractional Oscillator Equation with Natural Boundary Conditions

Guezane-Lakoud, Assia, Khaldi, Rabah, Torres, Delfim F. M.

Natural Science Publishing

We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann–Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the problem into an equivalent lower order fractional boundary value problem followed by the use of an upper and lower solutions method. To succeed with such approach, we first prove a result on the monotonicity of the right Caputo derivative.

ria.ua.pt

Generalized weighted Ostrowski and Ostrowski-Gruss type inequalities on time scales via a parameter function

Kermausuor, Seth, Nwaeze, Eze R., Torres, Delfim F. M.

Ele-Math

We prove generalized weighted Ostrowski and Ostrowski–Gr ¨uss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalities

ria.ua.pt

Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences

Abdeljawad, Thabet, Torres, Delfim F. M.

Elsevier

A discrete version of the symmetric duality of Caputo–Torres, to relate left and right Riemann–Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators. As an application, we derive right fractional summation by parts formulas and left fractional difference Euler–Lagrange equations for discrete fractional variational problems whose Lagrangians depend on right fractional differences.

ria.ua.pt

On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales

You, Xuexiao, Zhao, Dafang, Torres, Delfim F. M.

International Scientific Research Publication

We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and monotone convergence theorems.

ria.ua.pt

New convolutions for quadratic-phase Fourier integral operators and their applications

Castro, L. P., Minh, L. T., Tuan, N. M.

Springer

We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann-Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.

ria.ua.pt

Reviving trinification models through an E6-extended supersymmetric GUT

Morais, A. P., Pasechnik, R., Wessén, J., Ordell, A., Sampaio, M., Camrgo-Molina, J. E.

American Physical Society

We present a supersymmetric (SUSY) model based on trinification [SU(3)]^3 and family SU(3)_F symmetries embedded into a maximal subgroup of E8, where the sectors of light Higgs bosons and leptons are unified into a single chiral supermultiplet. The common origin of gauge trinification and of the family symmetry from E8 separates the model from other trinification-based GUTs, as it protects, in particular, the Standard Model fermions from gaining mass until the electroweak symmetry is broken. Furthermore, it allows us to break the trinification symmetry via vacuum expectation values in SU(3)-adjoint scalars down to a left-right symmetric theory. Simultaneously, it ensures the unification of the gauge and Yukawa couplings as well as proton stability. Although the low-energy regime (e.g., mass hierarchies in the scalar sector determined by a soft SUSY-breaking mechanism) is yet to be established, these features are one key to revive the once very popular trinification-based GUTs.

ria.ua.pt

Atitudes em relação à Estatística de alunos do 8.º ano

Carvalho, Maria José, Freitas, Adelaide, Fernandes, José António

Universidade da Coruña; Universidade do Minho

Neste estudo apresenta-se um instrumento de avaliação de atitudes face à Estatística de estudantes portugueses do 8.º ano, o qual resultou de uma adaptação da escala de Estrada (2002). A escala adaptada é constituída por 23 itens usando uma escala de Likert e foi analisada em 332 alunos do 8.º ano, com idade média de 14,4 anos, no ano letivo de 2014/15. Constata-se que a escala adaptada é confiável (alfa de Cronbach=0,910) e com boa adequação dos dados ao modelo fatorial (KMO =0,918). A análise fatorial identificou quatro fatores de atitude: Disposição/Valorização, discernimento/Conceção, Utilidade e Dificuldades.

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Problems of Minimal Resistance and the Kakeya Problem

Plakhov, Alexander

SIAM

Here we solve the problem posed by Comte and Lachand-Robert in [8]. Take a bounded domain R2 and a piecewise smooth nonpositive function u : ¯ ! R vanishing on @ . Consider a flow of point particles falling vertically down and reflected elastically from the graph of u. It is assumed that each particle is reflected no more than once (no multiple reflections are allowed); then the resistance of the graph to the flow is expressed as R(u; ) = 1 | | R (1 + |ru(x)|2)−1dx. We need to find inf ,u R(u; ). One can easily see that |ru(x)| < 1 for all regular x 2 , and therefore one always has R(u; ) > 1/2. We prove that the infimum of R is exactly 1/2. This result is somewhat paradoxical, and the proof is inspired by, and partly similar to, the paradoxical solution given by Besicovitch to the Kakeya problem

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Speech and language therapy service delivery: overcoming limited provision for children

Jesus, Luís Miguel Teixeira de, Martinez, Joana, Valente, Ana Rita, Costa, Maria da Conceição

Elsevier

Objectives: To test an alternative Speech and Language Therapy (SLT) service delivery model based on partnerships between a University and local schools and charities, and to report on the impact and feasibility of intervention based on long-term outcome measures and three case studies with individual analysis of Reliable Change. Study design: The following six-step model was tested: 1—establishing partnerships; 2—flagging children; 3—pre-treatment SLT assessment; 4—reporting and discussion with parents and teachers; 5—treatment; 6—post-treatment assessment. Case studies are presented. Methods: A partnership was established with one kindergarten in a pre-test and a total of 25 kindergartens during the second phase of the process. A group of 139 children were then flagged and assessed. The following long-term outcomes (18 months post-therapy) were investigated: phonetic-phonological standardised test percentiles and raw scores; receptive and expressive language percentiles and raw scores according to a standardised language test; percentage of syllables stuttered; duration of stuttering moments; academic achievement in norm-tests’ core areas (mathematics, Portuguese language and social studies). Case studies and a 95% credible interval analysis to assess Reliable Change are presented. Results: Seventy five (54%) children needed SLT support. Fifty (67%) of those children returned to the clinic for long-term assessments and the analysis of all outcome measures showed significant improvements in their performance, 18 months post-therapy. Case Studies Reliable Change analysis revealed a statistically significant improvement, which also clearly shows the feasibility and the positive impact of the intervention. Conclusions: This specialised and differentiated care network constitutes an alternative delivery system of SLT services that addresses the lack of support currently experienced by children and their families. The long-term outcome measures and the 95% credible interval analysis are reliable methods to determine the impact of interventions.

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Survival Rate of Dental Implants in Patients with History of Periodontal Disease: A Retrospective Cohort Study

Correia, F., Gouveia, S., Felino, A. C., Costa, A. L., Almeida, R. F.

Wiley

Purpose – To evaluate the differences between the survival rates of implants placed in patients with no history of periodontal disease (NP) and in patients with history of chronic periodontal disease (CP). Materials and Methods – A retrospective cohort study was conducted in which all consenting patients treated with dental implants in a private clinic in Oporto, Portugal, from November 2, 2002 through February 11, 2011 were included. All patients were treated consecutively by the same experimental operator. This study aimed to analyze how the primary outcomes (presence of disease, time of placement and time of loading) and the secondary outcomes (severity generalized periodontitis, brand, implant length, prosthesis type, prosthesis metal-ceramic (PFM) extension) influence the survival rate of dental implants. The survival analysis was performed through the Kaplan-Meier method and the equality of survival distributions for all groups was tested with the log-rank test with a significance level of 0.05 for all comparisons. Results - The sample consisted of 202 patients (47% NP and 53% CP) and 689 implants (31% NP and 69% CP). The survival rate in NP and CP groups showed no statistically significant differences (95.8% versus 93.1%, p>=0.05). Implants were lost before loading in 54.9% of the cases. The majority of the implants were lost in the first year and stabilized after the second year. Survival rates in NP and CP patients showed no statistically significant differences when comparing the following factors: sub-classification of the disease, implant brands, implant length (short/standard), type of prosthesis, extension of the PFM and time of placement and loading (p>=0.05). Conclusions –This work disclosed no statistically significant differences in terms of survival rates when compared to the control group. Placing implants in patients with a history of periodontal disease appears to be viable and safe.

ria.ua.pt

Orthogonal polynomial interpretation of q-Toda and q-Volterra equations

Área, Ivan, Branquinho, Amílcar, Godoy, Eduardo, Moreno, Ana Foulquié

Springer Singapore

The correspondences between dynamics of q-Toda and q-Volterra equations for the coefficients of the Jacobi operator and its resolvent function are established. The orthogonal polynomials associated with these Jacobi operators satisfy an Appell condition, with respect to the q-difference operator Dq . Lax type theorems for the point spectrum of the Jacobi operators associated with these equations are obtained. Examples related with the big q-Legendre, discrete q-Hermite I, and little q-Laguerre orthogonal polynomials and q-Toda and q-Volterra equations are given.

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Between Shi and Ish

Duarte, Rui, Guedes de Oliveira, António

Elsevier

We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a given length is equal, and conjecture that the same happens with all of the members of the family.

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Homogeneous (α, k) -polynomial solutions of the fractional riesz system in hyperbolic space

Orelma, Heikki, Vieira, Nelson Felipe Loureiro

Springer

In this paper we study the fractional analogous of the Laplace-Beltrami equation and the Riesz system studied previously by H. Leutwiler , in $BR^3$. In both cases we replace the integer derivatives by Caputo fractional derivatives of order $0 ria.ua.pt


Weyl Type Bound on Positive Interior Transmission Eigenvalues

Lakshtanov, Evgeny, Vainberg, Boris

Taylor & Francis

This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission eigenvalues. We consider the classical transmission problem as well as the case where the inhomogeneous medium contains an obstacle. One of the essential components of the proof is an estimate for the D-t-N operator for the Helmholtz equation for positive λ that replaces the standard parameter-elliptic estimate valid outside of the positive semi-axis.

ria.ua.pt

Guarding orthogonal galleries with rectangular rooms

Bajuelos, Antonio L, Bereg, Sergey, Martins, Mafalda

Oxford University Press

Consider an orthogonal art gallery partitioned into n rectangular rooms. If two rooms are adjacent, there is a door connecting them and a guard positioned at this door will see both rooms. In Czyzowicz et al. [(1994) Guarding rectangular art galleries. Discrete Appl. Math., 50, 149–157], it is shown that any rectangular gallery can be guarded with ⌈n/2⌉ guards. We prove that the same bound holds for L-shape polygons. We extend it to staircases and prove that an orthogonal staircase with n rooms and r reflex vertices can be guarded with ⌈(n+⌊ r/2⌋)/2⌉ guards. Then we prove an upper bound on the number of guards for arbitrary orthogonal polygon with orthogonal holes. This result improves the previous bound by Czyzowicz et al. [(1994) Guarding rectangular art galleries. Discrete Appl. Math., 50, 149–157] (even in the case of polygon without holes).

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Computing a visibility polygon using few variables

Barba, Luis, Korman, Matias, Langerman, Stefan, Silveira, Rodrigo

Elsevier

We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O(nr¯) time, where r¯ denotes the number of reflex vertices of P that are part of the output. Whenever we are allowed to use O(s) variables, the running time decreases to O(nr2s+nlog2r) (or O(nr2s+nlogr) randomized expected time), where s∈O(logr). This is the first algorithm in which an exponential space-time trade-off for a geometric problem is obtained.

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Facets for the single node fixed-charge network set with a node set-up variable

Agra, Agostinho, Doostmohammadi, Mahdi

Springer

We consider a variant of the well-known Single Node Fixed-Charge Network (SNFCN) set where a set-up variable is associated with the node, indicating whether the node is open or not. This set arises as a relaxation of several practical mixed integer problems. We relate the polyhedral structure of this variant with the polyhedral structure of the SNFCN set. We show that in the presence of the node set-up variable new facet-defining inequalities appear and establish the relation between the new family of inequalities with the flow cover inequalities. For the constant capacitated case we provide a full polyhedral description of the convex hull of the given set.

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Hybrid heuristics for a maritime short sea inventory routing problem

Agra, Agostinho, Christiansen, Marielle, Delgado, Alexandrino, Simonetti, Luidi

Elsevier

We consider a short sea fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The inventory management has to be considered at the demand side only, and the consumption rates are given and assumed to be constant within the planning horizon. The objective is to determine distribution policies that minimize the routing and operating costs, while the inventory levels are maintained within their limits. We propose an arc-load flow formulation for the problem which is tightened with valid inequalities. In order to obtain good feasible solutions for planning horizons of several months, we compare different hybridization strategies. Computational results are reported for real small-size instances.

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Strongly nonlinear second order multivalued Dirichlet systems

Aizicovici, Sergiu, Papageorgiou, Nikolaos Socrates, Staicu, V

Biemdas Academic Publishers Inc.

We consider second order nonlinear Dirichlet systems driven by a nonlinear nonhomogeneous differential operator. The reaction term consists of a maximal monotone map A(⋅) plus a multivalued perturbation F depending also on derivative. Using tools from multivalued analysis and from the theory of nonlinear operators of monotone type, we prove existence theorems both for the "convex" (F is convex-valued) and the "nonconvex" (F is nonconvex-valued) problems. We also present an example of a system with unilateral constraint.

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Hypermonogenic functions of two vector variables

Eriksson, S.-L., Orelma, H., Vieira, Nelson Felipe Loureiro

Springer

In this paper we introduce the modified Dirac operators $mathcal{M}_{m{x}}^kappa f:= ,partial_{m{x}}f-frac{kappa}{x_m}e_mcdot f$ and $mathcal{M}_{m{y}}^tau f:= ,partial_{m{y}}f-frac{tau}{y_m}e_m cdot f$, where $f:Omegasubset mathbb{R}_+^{m}times mathbb{R}_+^{m}toCl_{0,m}$ is differentiable function, and $Cl_{0,m}$ is the Clifford algebra generated by the basis vectors of $mathbb{R}^m$. We look for solutions $f(m{x},m{y}) =f(U{x},x_m,U{y},y_m)$ of the system $mathcal{M}_{m{x}}^kappa f(m{x,y})= mathcal{M}_{m{y}}^tau f(m{x,y})=0$, where the first and third variables are invariant under rotations. These functions are called $(kappa,tau)$-hypermonogenic functions. We discuss about axially symmetric functions with respect to the symmetric group $SO(m-1)$. Some examples of axially symmetric $(kappa,tau)$-hypermonogenic functions generated by homogeneous functions and hypergeometric functions are presented.

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Monitoring maximal outerplanar graphs

Martins, Mafalda, Hernández, Gregorio

Elsevier

In this paper we define a new concept of monitoring the elements of triangulation graphs by faces. Furthermore, we analyze this, and other monitoring concepts (by vertices and by edges), from a combinatorial point of view, on maximal outerplanar graphs.

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Remote Monitoring by Edges and Faces of Maximal Outerplanar Graphs

Martins, Ana Mafalda, Hernández, Gregorio

Oxford University Press. The British Computer Society

The concepts of monitoring the elements of triangulation graphs by edges and faces at a distance k were defined by Hernández and Martins (2014, Electr. Notes Discrete Math., 46, 145–152). Furthermore, for any n-vertex maximal outerplanar graph, they provide combinatorial bounds when k=2. In this paper, we continue their study, generalizing its results to any value of k.

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A new class of monohedral pentagonal spherical tilingswith GeoGebra

Breda, Ana, Santos, José M. Santos dos

European Mathematical Society

By a monohedral spherical tiling we mean a decomposition of the sphereby geodesic congruent polygons. Here, making use of GeoGebra, a well known freeinteractive mathematics software, we show how to generate new classes of monohedralnon-convex triangular and new non-convex pentagonal spherical tilings, changing theside gluing rules of the regular spherical tetrahedral tiling, by means of a local actionof particular subgroups of spherical isometries. In both cases each face haspas areameasure.In relation to the new class of pentagonal tilings, we describe some of their propertiesand show the existence, in a special case, of an associated dihedral triangular spherical til-ing, that is, a tiling composed by two sets of congruent triangles.These classes of spherical tilings have emerged as a result of an interative constructionprocess, only possible by the use of newly produced GeoGebra tools and the dynamic inter-action capabilities of this software.

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A formulation of Noether's theorem for fuzzy problems of the calculus of variations

Fard, Omid Solaymani, Soolaki, Javad, Almeida, Ricardo

Springer

ria.ua.pt

A fractional Malthusian growth model with variable order using an optimization approach

Almeida, Ricardo, Bastos, Nuno R. O., Monteiro, M. Teresa T.

International Academic Press

The objective is to study the population’s growth with a fractional differential equation. The order of the fractional derivative is a function depending on time and the goal is to determine the fractional order function that better fits the given data. The model is than tested to describe the world population growth and of some countries. All the numerical experiments were done in MATLAB, using the routines lsqcurvefit, fminunc and spline.

ria.ua.pt

A projeção estereográfica no GeoGebra

Santos, José Manuel dos Santos dos, Breda, Ana Maria d’Azevedo

Instituto GeoGebra de São Paulo

O GeoGebra permite a manipulação de objetos no plano, no espaço e a representação de funções vetoriais reais uni ou bidimensionais de duas variáveis reais. A criação da ferramenta Projeção Estereográfica de um ponto do plano na esfera de Riemman, estendido com as propriedades das cores dinâmicas que permitiram representar os domínios coloridos, possibilitou o desenvolvimento de aplicações que podem ser usadas no ensino e da aprendizagem de tópicos de análise complexas entre outros. Neste artigo apresentamos o essencial da ferramenta e algumas das suas aplicações para o ensino. GeoGebra allows the manipulation of objects in the plane, in space and the representation of real or two-dimensional vector functions of two real variables. The creation of the Stereographic Projection tool of a point of the plane in the Riemann sphere, extended with the properties of the dynamic colours allowing the representation of coloured domains, allowed the development of applications that can be used, among others, in the teaching and learning of complex analysis topics. In this paper we present the essential tools and some of their applications in the teaching process.

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Calculus of variations involving Caputo-Fabrizio fractional differentiation

Bastos, Nuno R. O.

International Academic Press

This paper is devoted to study some variational problems with functionals containing the Caputo-Fabrizio fractional derivative, that is a fractional derivative with a non-singular kernel.

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New lower bounds for the Randić spread

Andrade, Enide, Freitas, Maria Aguieiras A. de, Robbiano, María, Rodríguez, Jonnathan

Elsevier

Let $G=left( mathcal{V}left( Gright) ,mathcal{E}left( Gright) right) $ be an $left( n,mright) $-graph. The Randi'{c} spread of $G$, $s_{R}(G)$, is defined as the maximum distance of its Randi'{c} eigenvalues, disregarding the Randi'{c} spectral radius of $G$. In this work, we use numerical inequalities and bounds for the matricial spread to obtain relations between this spectral parameter and some structural and algebraic parameters of the underlying graph such as, the sequence of vertex degrees, the nullity, Randi'{c} index, generalized Randi'{c} indices and its independence number. In the last section a comparison is presented for regular graphs.

ria.ua.pt

A sharp lower bound on the signless Laplacian index of graphs with (k,t)-regular sets

Andelic, Milica, Cardoso, Domingos M., Pereira, António

De Gruyter

A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one $(kappa,tau)$-regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching. Furthermore, computational experiments revealed that the introduced lower bound is better than the known ones. The paper also gives sufficient condition for a graph to be non Hamiltonian (or without a perfect matching).

ria.ua.pt

Spectra, signless Laplacian and Laplacian spectra of complementary prisms of graphs

Cardoso, Domingos M., Carvalho, Paula, Freitas, Maria Aguieiras A. de, Vinagre, Cybele T.M.

Elsevier

The complementary prism GG‾ of a graph G is obtained from the disjoint union of G and its complement G‾ by adding an edge for each pair of vertices (v,v′), where v is in G and its copy v′ is in G‾. The Petersen graph C5C5‾ and, for n≥2, the corona product of Kn and K1 which is KnKn‾ are examples of complementary prisms. This paper is devoted to the computation of eigenpairs of the adjacency, signless Laplacian and Laplacian matrices of a complementary prism GG‾ in terms of the eigenpairs of the corresponding matrices of G. Particular attention is given to the complementary prisms of regular graphs. Furthermore, Petersen graph is shown to be the unique complementary prism which is a strongly regular graph.

ria.ua.pt

On the higher differentiability of solutions to a class of variational problems of fast growth

Cellina, Arrigo, Staicu, Vasile

Springer International Publishing AG. Part of Springer Nature.

We consider the higher differentiability of a solution $u$ to the problem of minimizing $$int_{om}[Lambda(x ,|nabla v(x)|) +f(x)v(x)]dx$$ where $Lambda$ is of fast growth in the second variable, i.e., we assume that $Lambda(x,t)$ grows in $t$ faster than $t^N$, where $N$ is the dimension of the space. We do not assume conditions limiting above the size of the second derivative of $Lambda$ with respect to $t$.

ria.ua.pt

Dynamical ejections of stars due to an accelerating gas filament

Boekholt, Tjarda, Stutz, Amelia, Fellhauer, Mike, Schleicher, Dominik, Matus Carrillo, Diego

Oxford University Press

Observations of the Orion A integral shaped filament (ISF) have shown indications of an oscillatory motion of the gas filament. This evidence is based on both the wave-like morphology of the filament and the kinematics of the gas and stars, where the characteristic velocities of the stars require a dynamical heating mechanism. As proposed by Stutz & Gould, such a heating mechanism (the `Slingshot') may be the result of an oscillating gas filament in a gas-dominated (as opposed to stellar-mass dominated) system. Here we test this hypothesis with the first stellar-dynamical simulations in which the stars are subjected to the influence of an oscillating cylindrical potential. The accelerating, cylindrical background potential is populated with a narrow distribution of stars. By coupling the potential to N-body dynamics, we are able to measure the influence of the potential on the stellar distribution. The simulations provide evidence that the slingshot mechanism can successfully reproduce several stringent observational constraints. These include the stellar spread (both in projected position and in velocity) around the filament, the symmetry in these distributions, and a bulk motion of the stars with respect to the filament. Using simple considerations, we show that star-star interactions are incapable of reproducing these spreads on their own when properly accounting for the gas potential. Thus, properly accounting for the gas potential is essential for understanding the dynamical evolution of star-forming filamentary systems in the era of Gaia (Gaia Collaboration 2016).

ria.ua.pt

Combined Fractional Variational Problems of Variable Order and Some Computational Aspects

Tavares, Dina, Almeida, Ricardo, Torres, Delfim F.M.

Elsevier

ria.ua.pt

Formation of massive seed black holes via collisions and accretion

Boekholt, Tjarda, Schleicher, D., Fellhauer, M., Klessen, R., Reinoso, B., Stutz, A., Haemmerle, L.

Oxford University Press

Models aiming to explain the formation of massive black hole seeds, and in particular the direct collapse scenario, face substantial difficulties. These are rooted in rather ad hoc and fine-tuned initial conditions, such as the simultaneous requirements of extremely low metallicities and strong radiation backgrounds. Here, we explore a modification of such scenarios where a massive primordial star cluster is initially produced. Subsequent stellar collisions give rise to the formation of massive (104-105 M⊙) objects. Our calculations demonstrate that the interplay among stellar dynamics, gas accretion, and protostellar evolution is particularly relevant. Gas accretion on to the protostars enhances their radii, resulting in an enhanced collisional cross-section. We show that the fraction of collisions can increase from 0.1 to 1 per cent of the initial population to about 10 per cent when compared to gas-free models or models of protostellar clusters in the local Universe. We conclude that very massive objects can form in spite of initial fragmentation, making the first massive protostellar clusters viable candidate birth places for observed supermassive black holes.

ria.ua.pt

Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence

Portegies Zwart, Simon, Boekholt, Tjarda

Elsevier

Numerical solutions to Newtons equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and the numerical round-off in the least significant figure. This secular growth of error is sometimes attributed to the increase in entropy of the system even though Newton’s equations of motion are strictly time reversible. We demonstrate that when numerical errors are reduced to below the physical perturbation and its exponential growth during integration the microscopic reversibility is retrieved. Time reversibility itself is not a guarantee for a definitive solution to the chaotic N-body problem. However, time reversible algorithms may be used to find initial conditions for which perturbed trajectories converge rather than diverge. The ability to calculate such a converging pair of solutions is a striking illustration which shows that it is possible to compute a definitive solution to a highly unstable problem. This works as follows: If you (i) use a code which is capable of producing a definitive solution (and which will therefore handle converging pairs of solutions correctly), (ii) use it to study the statistical result of some other problem, and then (iii) find that some other code produces a solution with statistical properties which are indistinguishable from those of the definitive solution, then solution may be deemed veracious.

ria.ua.pt

Restriction conditions on PL(7, 2) codes (3 ≤ |g_i| ≤ 7)

Cruz, Catarina N., Breda, Ana

De Gruyter

The Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over Z for n ≥ 3 and r ≥ 2. This problem has received great attention due to its importance in applications in several areas beyond mathematics and computer sciences. Many results on this subject have been achieved, however the conjecture is only solved for some particular values of n and r, namely: 3 ≤ n ≤ 5 and r ≥ 2; n = 6 and r = 2. Here we give an important contribution for the case n = 7 and r = 2, establishing cardinality restrictions on codeword sets.

ria.ua.pt

The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives

Almeida, Ricardo, Morgado, Maria Luísa

Elsevier

ria.ua.pt

On the multiplicity of α as an eigenvalue of Aα(G) of graphs with pendant vertices

Cardoso, Domingos M., Pastén, Germain, Rojo, Oscar

Elsevier

Let $G$ be a simple undirected graph. Let $0leq alpha leq 1$. Let $$A_{alpha}(G)= alpha D(G) + (1-alpha) A(G)$$ where $D(G)$ and $A(G)$ are the diagonal matrix of the vertex degrees of $G$ and the adjacency matrix of $G$, respectively. Let $p(G)>0$ and $q(G)$ be the number of pendant vertices and quasi-pendant vertices of $G$, respectively. Let $m_{G}(alpha)$ be the multiplicity of $alpha$ as eigenvalue of $A_{alpha}(G)$. It is proved that begin{equation*} m_{G}(alpha) geq p(G) - q(G) end{equation*} with equality if each internal vertex is a quasi-pendant vertex. If there is at least one internal vertex which is not a quasi-pendant vertex, the equality begin{equation*} m_{G}(alpha)= p(G)-q(G)+m_{N}(alpha) end{equation*} is determined in which $m_{N}(alpha)$ is the multiplicity of $alpha$ as eigenvalue of the matrix $N$. This matrix is obtained from $A_{alpha}(G)$ taking the entries corresponding to the internal vertices which are non quasi-pendant vertices. These results are applied to search for the multiplicity of $alpha$ as eigenvalue of $A_{alpha}(G)$ when $G$ is a path, a caterpillar, a circular caterpillar, a generalized Bethe tree or a Bethe tree. For the Bethe tree case, a simple formula for the nullity is given.

ria.ua.pt

Realizable lists on a class of nonnegative matrices

Andrade, Enide, Manzaneda, Cristina, Robbiano, María

Elsevier

A square matrix of order $n$ with $ngeq 2$ is called textit{permutative matrix} when all its rows are permutations of the first row. In this paper recalling spectral results for partitioned into $2$-by-$2$ symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given. In particular, we study NIEP and PNIEP when some complex elements in the lists under consideration have non-zero imaginary part. Realizability regions for nonnegative permutative matrices are obtained. A Guo's realizability-preserving perturbations result is obtained.

ria.ua.pt

Analysis of a fractional SEIR model with treatment

Almeida, Ricardo

Elsevier

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First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators

Ferreira, Milton, Rodrigues, Manuela, Vieira, Nelson Felipe Loureiro

Springer

In this work, we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin- Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.

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Smallness and cancellation in some elliptic systems with measure data

Leonetti, Francesco, Rocha, Eugenio, Staicu, Vasile

Elsevier

In a bounded open subset $Omegasubsetmathbb{R}^{n}$, we study Dirichlet problems with elliptic systems, involving a finite Radon measure $mu$ on $mathbb{R}^{n}$ with values into $mathbb{R}^{N}$, defined by $$left{begin{array}{ll} -mbox{div}, A(x,u(x),Du(x)) =mu & mbox{ in }Omega,\ u=0 & mbox{ on }partialOmega, end{array}right.$$ where $A_{i}^{alpha}(x,y,xi)=sumlimits_{beta=1}^{N}sumlimits_{j=1}^{n}a_{i,j}^{alpha,beta}left( x,yright) xi_{j}^{beta}$ with $alphain{1,dots,N}$ the equation index. We prove the existence of a (distributional) solution $u:Omegarightarrowmathbb{R}^{N}$, obtained as the limit of approximations, by assuming: (i) that coefficients $a_{i,j}^{alpha,beta}$ are bounded Carath'eodory functions; (ii) ellipticity of the diagonal coefficients $a_{i,j}^{alpha,alpha}$; and (iii) smallness of the quadratic form associated to the off-diagonal coefficients $a^{alpha,beta}_{i,j}$ (i.e. $alphaneqbeta$) verifying a $r$-staircase support condition with $r>0$. Such a smallness condition is satisfied, for instance, in each one of these cases: (a) $a^{alpha,beta}_{i,j}=-a^{beta,alpha}_{j,i}$ (skew-symmetry); (b) $|a^{alpha,beta}_{i,j}|$ is small; (c) $a^{alpha,beta}_{i,j}$ may be decomposed into two parts, the first enjoying skew-symmetry and the second being small in absolute value. We give an example that satisfies our hypotheses but does not satisfy assumptions introduced in previous works. A Brezis's type nonexistence result is also given for general (smooth) elliptic-hyperbolic systems.

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Methoden zur Identifikation von Zugvorbeifahrten aus kontinuierlichen Messdaten

Abrahamczyk, Lars, Jaouadi, Zouhour, Kähler, Uwe, Legatiuk, Dmitrii

Ernst und Sohn

Tragwerke des Konstruktiven Ingenieurbaus sind in der Regel Unikate. Systematische Untersuchungen dienen daher dem Ziel, Umwelteinflüsse und Einwirkungen auf die Tragwerke und deren tatsächliches statisches und dynamisches Verhalten kurzzeitig und auch langfristig zu erfassen und zu verstehen. Im Rahmen des DFG-geförderten Graduiertenkollegs 1462 wurden drei vorgespannte Schleuderbetonmaste entlang der ICE-Neubaustrecke Erfurt–Leipzig mit verschiedenster Sensorik instrumentiert, um unter anderem das Verhalten der Maste während einer Zugvorbeifahrt zu untersuchen. Die Datenaufzeichnungen werden von Lichtschranken ausgelöst und erfolgen für einen definierten Zeitraum. Infolge von Störfaktoren und der Aufzeichnungslänge sind einerseits eine Vielzahl von Fehlmessungen und andererseits mehrere Zugvorbeifahrten in einem Datenfile zu verzeichnen. Somit sind in einem ersten Schritt die einzelnen Aufzeichnungen für die gezielte Auswertung des Einflusses der Zugvorbeifahrt auf das Verhalten der Oberleitungsmaste zu separieren. Dies erfolgt auch vor dem Hintergrund, dass die Bestimmung einer tatsächlichen Zugvorbeifahrt zukünftig nahezu fehlerfrei automatisiert erfolgen soll. Im Beitrag werden Methoden und erhobene Datensätze unterschiedlicher Sensorik zur Identifikation der Zugvorbeifahrten verglichen. Die Auswertung der gemessenen Daten des Erddrucksensors und der Beschleunigungsaufnehmer erfolgt mittels Techniken der Signalanalyse: Fast Fourier (FFT) und Gabor-Transformation. Civil engineering structures are mostly unique. Stochastic properties of acting loads and the corresponding structure reaction can be determined by help of long-term measurements. The identified loads and reactions can further be used in validation and assessment procedures to analyze static and dynamic behavior of the structure. Three reinforced concrete poles located along the new high-speed railway track Erfurt–Leipzig have been equipped with a monitoring system in the framework of the DFG founded Research Training Group 1462. The goal of the monitoring system is to identify influence of passing trains on the structural behavior of the poles. The measurement record is controlled by two photoelectric sensors. However, due to different disturbing factors fault detections of train passing are possible. Therefore, the obtained measurement data at first step must be classified with respect to actual train passing. Additionally, to simplify analysis of a huge amount of upcoming data, a classification algorithm should work automatically. In this paper, we present a comparative study of train identification methods based on tools of signal analysis compared to the identification based on the signals of photoelectric sensors. Especially, Fast Fourier Transform and Gabor Transform are applied to the time-history records from the soil pressure and acceleration sensors. published

ria.ua.pt

C-groups of high rank for the symmetric groups

Fernandes, Maria Elisa, Leemans, Dimitri

Elsevier

We give presentations for the C-groups of rank n – 1 of the symmetric group Sn. We also classify C-groups of rank n – 2 for Sn. We show that all these C-groups correspond to regular hypertopes, that is, thin, residually connected flag-transitive geometries. Therefore we generalise some similar results obtained in the framework of string C-groups that are in one-to-one correspondence with abstract regular polytopes. This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand and by the Portuguese funds through the CIDMA – Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA – Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. The authors also thank an anonymous referee for useful comments on a preliminary version of this paper. published

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Disparate faculty perspectives on system changes in higher education

Silva, Joaquim S., Peixoto, Paulo, Freitas, Adelaide

Taylor & Francis

Higher education (HE) systems around the world have experienced profound structural changes, particularly since the late 1960s to early 1970s, essentially driven by the need to expand access to tertiary education. This has resulted in a diversity of HE institutions (HEI) with different roles, missions and statuses, as well as academic staff with diverse perspectives and motivations. The present study is based on a survey undertaken in Portugal by a trade union, which aimed to collect faculty perspectives on a proposed HE reform sent out for public discussion by the government. Questions addressed the reorganization of the HEI network, the internal restructuring of HEI, the funding system and the binary divide of HEI (universities and polytechnics). The survey results showed a disparity of faculty perspectives about the proposed reform, closely related to the diversity of HEI. Respondents from lower academic categories and from smaller HEI were more opposed to reorganizing the HEI network. This reorganization was more widely accepted by university staff, who were also more in favour of a binary system than were polytechnic respondents. Although there was general agreement about the need to change the funding system, polytechnic respondents were strongly against a funding differentiation between universities and polytechnics. Despite an overall reformist trend, the enthusiasm for reforms declined substantially when the questions had a direct reference to the respondent’s region or institution. It is argued that HE expansion has driven the diversification of HEI, leading to a range of perspectives about the HE system and the way it should be changed. These conclusions may contribute to insights into other HE systems around the world where institutional diversification has been sought by public policies. The authors are grateful to Jennifer Burdon, Tania Stadler and Matthew Larcombe for the English revision of the manuscript. Adelaide Freitas was supported by CIDMA - Center for Research & Development in Mathematics and Applications, and FCT - Portuguese Science Foundation, within project UID/MAT/04106/2013. published

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Stability and optimal control of a delayed HIV model

Rocha, Diana, Silva, Cristiana J., Torres, Delfim F. M.

Wiley

We propose and investigate a delayed model that studies the relationship between HIV and the immune system during the natural course of infection and in the context of antiviral treatment regimes. Sufficient criteria for local asymptotic stability of the infected and viral free equilibria are given. An optimal control problem with time delays both in state variables (incubation delay) and control (pharmacological delay) is then formulated and analyzed, where the objective consists to find the optimal treatment strategy that maximizes the number of uninfected $CD4^{+}$ T cells as well as CTL immune response cells, keeping the drug therapy as low as possible. This research was partially supported by the Portuguese Foundation for Science and Technology (FCT) within projects UID/MAT/04106/2013 (CIDMA) and PTDC/EEI-AUT/2933/2014 (TOCCATTA), co-funded by FEDER funds through COMPETE2020– Programa Operacional Competitividade e Internacionalização (POCI) and by Project 3599-PPCDT, and by national funds (FCT). Rocha is also supported by the FCT PhD fellowship SFRH/BD/107889/2015; Silva by the FCT post-doc fellowship SFRH/BPD/72061/2010. published

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Dificuldades na aprendizagem da Mediana e Quartis por alunos do 8.º ano de escolaridade: estudo comparativo Fórmula versus Gráfico

Adelaide Freitas, Teresa Simões Figueiredo, Nélia Silva, Maria Cristina Miranda

Departamento de Educação e Psicologia Universidade de Aveiro

na aplicação de algoritmos de cálculo da mediana e na sua interpretação, em alunos de diferentes níveis de ensino. Embora possam existir interações entre as causas que originam tais dificuldades, escasseiam estudos se e como as dificuldades (observáveis) no cálculo e na interpretação da mediana e dos quartis estão interligadas. Partindo de quatro situaçõesproblemas, são analisadas as respostas dadas por 81 alunos do 8.º ano de escolaridade de uma escola, identificando e classificando os erros cometidos no cálculo e interpretação da mediana e dos quartis. Usando o coeficiente de associação V de Cramer, investiga-se também, numa perspetiva quantitativa, a interdependência entre a capacidade de obter os valores da mediana, primeiro quartil e terceiro quartil e a de interpretar o efeito sobre a mediana de uma alteração de um dado, tendo por base um conjunto de dados e um diagrama de extremos e quartis. A análise estatística das respostas assinalou situações onde existem associações fracas ou moderadas; mais ainda, não revelou associação entre a dificuldade de obtenção analítica (via fórmula) e gráfica (via diagrama de extremos e quartis) da mediana, perante uma alteração de dados. Esta constatação leva a crer que os alunos veem a interpretação de resultados obtidos segundo aquelas duas abordagens (via fórmula versus via gráfica) como se de dois tópicos diferentes, não interligados, se tratasse. published

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Approximation in generalized Morrey spaces

Almeida, Alexandre, Samko, Stefan

De Gruyter

In this paper we study the approximation of functions from generalized Morrey spaces by nice functions. We introduce a new subspace whose elements can be approximated by infi nitely diff erentiable compactly supported functions. This provides, in particular, an explicit description of the closure of the set of such functions in generalized Morrey spaces. published

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Homogeneous variable exponent Besov and Triebel-Lizorkin spaces

Almeida, Alexandre, Diening, Lars, Hästö, Peter

Wiley

We introduce homogeneous Besov and Triebel--Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings. published

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Block matrices and Guo’s index for block circulant matrices with circulant blocks

Andrade, Enide, Manzaneda, Cristina, Nina, Hans, Robbiano, María

Elsevier

In this paper we deal with circulant and partitioned into n-by-n circulant blocks matrices and introduce spectral results concerning this class of matrices. The problem of fi nding lists of complex numbers corresponding to a set of eigenvalues of a nonnegative block matrix with circulant blocks is treated. Along the paper we call realizable list if its elements are the eigenvalues of a nonnegative matrix. The Guo's index $lambda_0$ of a realizable list is the minimum spectral radius such that the list (up to the initial spectral radius) together with $lambda_0$ is realizable. The Guo's index of block circulant matrices with circulant blocks is obtained, and in consequence, necessary and suffcient conditions concerning the NIEP, Nonnegative Inverse Eigenvalue Problem, for the realizability of some spectra are given. published

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The structure of a recent nova shell as observed by ALMA

Diaz, Marcos, Abraham, Zulema, Ribeiro, Valério A. R. M., Beaklini, Pedro P. B., Takeda, Larissa

Oxford University Press

High resolution ALMA observations of the recent (2.52 yr old) shell of Nova V5668 Sgr (2015) show a highly structured ionized gas distribution with small (10^15 cm) clumps. These are the smallest structures ever observed in the remnant of a stellar thermonuclear explosion. No extended contiguous emission could be found above the 2.5σ level in our data, while the peak hydrogen densities in the clumps reach 10^6 cm^−3. The millimetre continuum image suggests that large scale structures previously distinguished in other recent nova shells may result from the distribution of bright unresolved condensations. published

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The role of fluctuation-dissipation dynamics in setting initial conditions for inflation

Bastero-Gil, Mar, Berera, Arjun, Brandenberger, Robert, Ramos, Rudnei O., Rosa, João G., Moss, Ian G.

IOP Publishing

We study the problem of initial conditions for slow-roll inflation along a plateau-like scalar potential within the framework of fluctuation-dissipation dynamics. We consider, in particular, that inflation was preceded by a radiation-dominated epoch where the inflaton is coupled to light degrees of freedom and may reach a near-equilibrium state. We show that the homogeneous field component can be sufficiently localized at the origin to trigger a period of slow-roll if the interactions between the inflaton and the thermal degrees of freedom are sufficiently strong and argue that this does not necessarily spoil the flatness of the potential at the quantum level. We further conclude that the inflaton can still be held at the origin after its potential begins to dominate the energy balance, leading to a period of thermal inflation. This then suppresses the effects of nonlinear interactions between the homogeneous and inhomogeneous field modes that could prevent the former from entering a slow-roll regime. Finally, we discuss the possibility of an early period of chaotic inflation, at large field values, followed by a first stage of reheating and subsequently by a second inflationary epoch along the plateau about the origin. This scenario could prevent an early overclosure of the Universe, at the same time yielding a low tensor-to-scalar ratio in agreement with observations. published

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Stimulated Axion Decay in Superradiant Clouds around Primordial Black Holes

Rosa, João G, Kephart, Thomas W

American Physical Society

The superradiant instability can lead to the generation of extremely dense axion clouds around rotating black holes. We show that, despite the long lifetime of the QCD axion with respect to spontaneous decay into photon pairs, stimulated decay becomes significant above a minimum axion density and leads to extremely bright lasers. The lasing threshold can be attained for axion masses μ≳10^{-8}  eV, which implies superradiant instabilities around spinning primordial black holes with mass ≲0.01  M_{⊙}. Although the latter are expected to be nonrotating at formation, a population of spinning black holes may result from subsequent mergers. We further show that lasing can be quenched by Schwinger pair production, which produces a critical electron-positron plasma within the axion cloud. Lasing can nevertheless restart once annihilation lowers the plasma density sufficiently, resulting in multiple laser bursts that repeat until the black hole spins down sufficiently to quench the superradiant instability. In particular, axions with a mass ∼10^{-5}  eV and primordial black holes with mass ∼10^{24}  kg, which may account for all the dark matter in the Universe, lead to millisecond bursts in the GHz radio-frequency range, with peak luminosities ∼10^{42}  erg/s, suggesting a possible link to the observed fast radio bursts. published

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Scalar field dark matter with spontaneous symmetry breaking and the $3.5$ keV line

Cosme, Catarina, Rosa, João G., Bertolami, O.

Elsevier

We show that the present dark matter abundance can be accounted for by an oscillating scalar field that acquires both mass and a non-zero expectation value from interactions with the Higgs field. The dark matter scalar field can be sufficiently heavy during inflation, due to a non-minimal coupling to gravity, so as to avoid the generation of large isocurvature modes in the CMB anisotropies spectrum. The field begins oscillating after reheating, behaving as radiation until the electroweak phase transition and afterwards as non-relativistic matter. The scalar field becomes unstable, although sufficiently long-lived to account for dark matter, due to mass mixing with the Higgs boson, decaying mainly into photon pairs for masses below the MeV scale. In particular, for a mass of $sim 7$ keV, which is effectively the only free parameter, the model predicts a dark matter lifetime compatible with the recent galactic and extragalactic observations of a 3.5 keV X-ray line. published

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Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation

Bastero-Gil, Mar, Berera, Arjun, Ramos, Rudnei O., Rosa, João G.

Springer Verlag

We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states. published

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Scale-invariant scalar field dark matter through the Higgs portal

Cosme, Catarina, Rosa, João G., Bertolami, O.

Springer Verlag

We discuss the dynamics and phenomenology of an oscillating scalar field coupled to the Higgs boson that accounts for the dark matter in the Universe. The model assumes an underlying scale invariance such that the scalar field only acquires mass after the electroweak phase transition, behaving as dark radiation before the latter takes place. While for a positive coupling to the Higgs field the dark scalar is stable, for a negative coupling it acquires a vacuum expectation value after the electroweak phase transition and may decay into photon pairs, albeit with a mean lifetime much larger than the age of the Universe. We explore possible astrophysical and laboratory signatures of such a dark matter candidate in both cases, including annihilation and decay into photons, Higgs decay, photon-dark scalar oscillations and induced oscillations of fundamental constants. We find that dark matter within this scenario will be generically difficult to detect in the near future, except for the promising case of a 7 keV dark scalar decaying into photons, which naturally explains the observed galactic and extra-galactic 3.5 keV X-ray line. published

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Inflation with Planck: a survey of some "exotic" inflationary models

Gomes, Cláudio, Bertolami, Orfeu, Rosa, João G.

American Physical Society

We examine some inflationary models based on modifications of gravity in the light of Planck 2015 data, such as the generalised Chaplygin inspired inflation, models based in $N=1$ supergravity and braneworld scenarios. We also show that, conversely, potentials with a very flat plateau yield a primordial spectrum similar to that of the Starobinsky model with no need to modify general relativity. published

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The Portuguese Manufacturing Sector during 2013-2016 after the Troika Austerity Measures

Murillo, Kelly Patricia, Rocha, Eugénio M.

Dr. Hasan Dudu, European Commission - Joint Research Center, Spain

This work studies the effects of the Troika austerity measures on the Portuguese manufacturing firms in terms of efficiency scores. We adopted a non-parametric approach, which combines multidirectional efficiency analysis with other techniques, to examine two empirical hypotheses after the financial crisis and corresponding intervention of the Troika measures: (a) the performance of firms in the manufacturing sector has improved; (b) the manufacturing sector significantly acquired long-term debt but use it in an efficient way. Our results show that validation of the first hypothesis heavily depends on the firm size, and the second hypothesis is correct only with respect to long-term debt acquiring. In fact, some sectors have managed to maintain an acceptable level of efficiency, according to the circumstances, however, most of them have showed some inefficiency in the management of resources and less than 10% have been able to overcome the difficulties emerged after the intervention of the Troika. A common tool to overcome a crisis is the acquisition of long-term debts, which was done by 77% of firms; but with a lower gain, since it was the most efficient input resourced used. On the contrary, our results show that the number of employees and total assets are better leverage to maintain efficiency. published

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Distance matrices on the H-join of graphs: A general result and applications

Cardoso, Domingos M., Díaz, Roberto C., Rojo, Oscar

Elsevier

Given a graph $H$ with vertices $1,ldots ,s$ and a set of pairwise vertex disjoint graphs $G_{1},ldots ,G_{s},$ the vertex $i$ of $H$ is assigned to $G_{i}.$ Let $G$ be the graph obtained from the graphs $G_{1},ldots ,G_{s}$ and the edges connecting each vertex of $G_{i}$ with all the vertices of $G_{j}$ for all edge $ij$ of $H.$ The graph $G$ is called the $H-join$ of $G_1,ldots,G_s$. Let $M(G)$ be a matrix on a graph $G$. A general result on the eigenvalues of $Mleft( Gright) $, when the all ones vector is an eigenvector of $Mleft( G_{i}right) $ for $i=1,2,ldots ,s$, is given. This result is applied to obtain the distance eigenvalues, the distance Laplacian eigenvalues and as well as the distance signless Laplacian eigenvalues of $G$ when $G_{1},ldots ,G_{s}$ are regular graphs. Finally, we introduce the notions of the distance incidence energy and distance Laplacian-energy like of a graph and we derive sharp lower bounds on these two distance energies among all the connected graphs of prescribed order in terms of the vertex connectivity. The graphs for which those bounds are attained are characterized. published

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Visual stimuli in intervention approaches for pre-schoolers diagnosed with phonological delay

Hall, Andreia, Pedro, Cassandra, Lousada, Marisa, Jesus, Luis Miguel

Taylor and Francis

Purpose: There is a need to develop letter knowledge assessment tools to characterise the letter knowledge in Portuguese pre-schoolers and to compare it with pre-schoolers from other countries, but there are no tools for this purpose in Portugal. The aim of this paper is to describe the development and validation procedures of the Prova de Avaliac¸ao de Compet ~ ^encias de Pr e-Literacia (PACPL), which assesses letter knowledge. Method: This study includes data that has been gathered in two phases: pilot and main study. In the pilot study, an expert panel of six speech and language pathologists analysed the instrument. Children (n ¼ 216) aged 5;0–7;11 participated in the main study that reports data related to the psychometric characteristics of the PACPL. Content validity, internal consistency, reliability and contributing factors to performance were examined statistically. Results: A modified Bland–Altman method revealed good agreement amongst evaluators. The main study showed that the PACPL has a very good internal consistency and high inter-rater (96.2% of agreement and a Cohen’s k value of 0.92) and intra-rater (95.6% of agreement and a Cohen’s k value of 0.91) agreement. Construct validity of the PCAPL was also assured (Cronbach’s a of 0.982). Significant differences were found between age groups with children increasing their letter knowledge with age. In addition, they were better at identifying than at producing both letter names and letter sounds. Conclusions: The PACPL is a valid and reliable instrument to assess letter knowledge in Portuguese children. published

ria.ua.pt

The letter knowledge assessment tool

Pedro, Cassandra, Lousada, Marisa, Pereira, Rita, Hall, Andreia, Jesus, Luis

Taylor and Francis

Purpose: There is a need to develop letter knowledge assessment tools to characterise the letter knowledge in Portuguese pre-schoolers and to compare it with pre-schoolers from other countries, but there are no tools for this purpose in Portugal. The aim of this paper is to describe the development and validation procedures of the Prova de Avaliac¸ao de Compet ~ ^encias de Pr e-Literacia (PACPL), which assesses letter knowledge. Method: This study includes data that has been gathered in two phases: pilot and main study. In the pilot study, an expert panel of six speech and language pathologists analysed the instrument. Children (n ¼ 216) aged 5;0–7;11 participated in the main study that reports data related to the psychometric characteristics of the PACPL. Content validity, internal consistency, reliability and contributing factors to performance were examined statistically. Results: A modified Bland–Altman method revealed good agreement amongst evaluators. The main study showed that the PACPL has a very good internal consistency and high inter-rater (96.2% of agreement and a Cohen’s k value of 0.92) and intra-rater (95.6% of agreement and a Cohen’s k value of 0.91) agreement. Construct validity of the PCAPL was also assured (Cronbach’s a of 0.982). Significant differences were found between age groups with children increasing their letter knowledge with age. In addition, they were better at identifying than at producing both letter names and letter sounds. Conclusions: The PACPL is a valid and reliable instrument to assess letter knowledge in Portuguese children. published

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Learning and teaching symmetry by creating ceramic panels with Escher type tessellations

Hall,Andreia, Pais, Sonia

Centro de Investigação Didática e Tecnologia na Formação de Formadores

Elliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning. This is true for any subject, including mathematics. Some topics of the mathematics school curriculum make a perfect setting for a deeper contribution of art to education and allow for a complete symbiosis between the teaching of mathematics and an artistic education. One such topic is the study of symmetry and isometry, present throughout the school mathematics curriculum from elementary to secondary levels. We believe that the learning and teaching of symmetry and isometry can be greatly facilitated by taking the role of an artist and creating works of art, eventually inspired by renowned artists. In this paper, we present some results of a professional development course for mathematics teachers where the participants created ceramic panels using the same techniques as the Dutch artist M.C. Escher did in his tessellation drawings. Elliot Eisner (1933-2014), pioneiro em educação artística, sugeriu que uma abordagem artística para a educação poderia melhorar a sua qualidade e levar a uma nova visão do ensino e a aprendizagem. Esta ideia aplica-se a qualquer área de ensino, incluindo a matemática. Alguns tópicos do programa de matemática adequam-se perfeitamente a interligação mais profunda da arte com a educação e permitem uma simbiose completa entre o ensino da matemática e uma educação artística. Um desses tópicos é o estudo da simetria e da isometria, presentes ao longo do programa de matemática, desde o ensino básico até ao secundário. Acreditamos que o processo de aprendizagem e de ensino da simetria e da isometria pode ser fortemente facilitado ao se assumir o papel de artista e criar obras de arte, eventualmente inspiradas por artistas bem conhecidos. Neste artigo, apresentamos alguns resultados de uma ação de formação contínua para professores de Matemática onde os participantes criaram painéis cerâmicos replicando as mesmas técnicas que o artista holandês M.C. Escher usou nos seus desenhos de pavimentações Elliot Eisner (1933-2014), pionero en educación artística, sugirió que un enfoque artístico para la educación podría mejorar su calidad y llevar a una nueva visión para la enseñanza y el aprendizaje. Esta idea se aplica a cualquier área de enseñanza, incluyendo las matemáticas. Algunos tópicos del programa de matemática se adecuan perfectamente a la interconexión más profunda del arte con la educación y permiten una simbiosis completa entre la enseñanza de las matemáticas y una educación artística. Uno de estos tópicos es el estudio de la simetría y de la isometria, presentes a lo largo del programa de matemáticas, desde la enseñanza básica hasta el secundario. Creemos que el proceso de aprendizaje y de enseñanza de la simetría y la isometría puede ser fuertemente facilitado al asumir el papel de artista y crear obras de arte, eventualmente inspiradas por artistas bien conocidos. En este artículo, presentamos algunos resultados de una acción de formación continua para profesores de Matemática donde los participantes crearon paneles cerámicos usando las mismas técnicas que el artista holandés M.C. Escher hizo en sus diseños de pavimentaciones. published

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Energy production and C02 emisson efficiency of eight European countries in the manufacturing area

Murillo, Kelly P., Rocha, Eugénio M., Pardo Martínez, Clara Inés

CIRWORLD

An energy efficiency comparison of manufacturing sectors of eight European countries, between 2008-2013, is performed in order to understand how the world economical crisis affected theirperformance. The analysis rely in a combination of multidirectional efficiency analysis blended with other techniques, as nc-value, principal component analysismixed with a dimensionality test.The purpose is to analyse three different approaches organized by: (a) a general viewpoint on countries/sectors; (b) sectors and inefficiency input usage; and (c) intensive versus non-intensive energy sectors. We also consider non-normalized and normalized data, by the total number of firms. The results indicate that the great majority of sectors/countries analyzed show a decrease in the CO2 emissions. Since thecalculated inefficiency indexes expose the sectors which used inputs in excess, we found that the most efficient sectors were: basic metals; rubber and plastic products, products of wood and cork; textiles, wearing apparel and of leather products; whereas chemical products and food;beverages and tobacco products were the most inefficient sectors. Our approach also give indicators about the way each sector/country was affected by the crisis and how they were able to react or adapt to it. published

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Exploring the Usage of MOOCs in Higher Education Institutions

Costa, Carolina, Teixeira, Leonor, Alvelos, Helena

IGI Global

This article analyses the current usage of Massive Open Online Courses (MOOCs) in HEIs. First, a literature review is performed to identify and classify the recent developments in the area and to characterize the most used platforms and courses. Following this, an analysis of MOOCs offered by some HEIs is carried out to characterize and compare the courses available in the platforms. Concerning the main findings, the literature reveals that usage of MOOCs has been growing in recent years and that Coursera and EdX are the two main platforms used. The analysis of MOOCs available in those platforms shows that the number of universities using them and the number of courses offered have been increasing. The comparison between the courses available through the above-mentioned platforms shows that EdX is more interdisciplinary. The outcomes of this article are valuable for researchers on ICT use in HEI and may help professors implementing MOOCs in their own environment. published

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Students' acceptance of an educational videos platform: a study in a portuguese university

Costa, Carolina, Alvelos, Helena, Teixeira, Leonor

IGI Global

The Educast is an  educational  videos’ platform that captures simultaneously video and digital support materials. This paper presents a study on the acceptance of Educast, by students, using the Technology Acceptance Model–TAM. The data was collected through a questionnaire applied to 54 students which results were analyzed using descriptive analysis and non-parametric tests. It was concluded that students expressed a positive attitude towards the variables Perceived Ease Of Use, Perceived Usefulness and Attitude Toward Using. The comparison between ratings assigned to the questionnaire items by the students who viewed video recordings and those that did not was performed, and it was found that the former showed higher levels of agreement with the referred items than the latter. It is considered that introducing some training before students have contact with Educast should be taken into account. The result of this work can be valuable not only for researchers on the Education area, but also for teachers that intend to use educational videos in their teaching/learning environment. published

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Online evaluation of a changes detection algorithm for depth of anesthesia signals

Sebastião, Raquel, Silva, Margarida M., Rabiço, Rui, Gama, João, Mendonça, Teresa

The detection of changes in the signals used to evaluate the depth of anesthesia of patients undergoing surgery is of foremost importance. This detection allows to decide how to adapt the doses of hypnotics and analgesics to be administered to patients for minimally invasive diagnostics and therapeutic procedures. This paper presents an algorithm based on the Page-Hinkley test to automatically detect changes in the referred depth of anesthesia signals of patients undergoing general anesthesia. The performance of the proposed method is evaluated online using data from patients subject to surgery. The results show that most of the detected changes are in accordance with the actions of the clinicians in terms of times where a change in the hypnotic or analgesic rates had occurred. This detection was performed under the presence of noise and sensor faults. The results encourage the inclusion of the proposed algorithm in a decision support system based on depth of anesthesia signals. published

ria.ua.pt

Optimizing make-to-stock policies through a robust lot-sizing model

Agra, Agostinho, Poss, Michael, Santos, Micael

Elsevier

In this paper we consider a practical lot-sizing problem faced by an industrial company. The company plans the production for a set of products following a Make-To-Order policy. When the productive capacity is not fully used, the remaining capacity is devoted to the production of those products whose orders are typically quite below the established minimum production level. For these products the company follows a Make-To-Stock (MTS) policy since part of the production is to fulfill future estimated orders. This yields a particular lot-sizing problem aiming to decide which products should be produced and the corresponding batch sizes. These lot-sizing problems typically face uncertain demands, which we address here through the lens of robust optimization. First we provide a mixed integer formulation assuming the future demands are deterministic and we tighten the model with valid inequalities. Then, in order to account for uncertainty of the demands, we propose a robust approach where demands are assumed to belong to given intervals and the number of deviations to the nominal estimated value is limited. As the number of products can be large and some instances may not be solved to optimality, we propose two heuristics. Computational tests are conducted on a set of instances generated from real data provided by our industrial partner. The heuristics proposed are fast and provide good quality solutions for the tested instances. Moreover, since they are based on the mathematical model and use simple strategies to reduce the instances size, these heuristics could be extended to solve other multi-item lot-sizing problems where demands are uncertain. published

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General quantum variational calculus

Brito da Cruz, A.M.C., Martins, Natália

International Academic Press

We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the q- and Hahn-calculus published

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A hybrid heuristic for a stochastic production-inventory-routing problem

Agra, Agostinho, Requejo, Cristina, Rodrigues, Filipe

Elsevier

We consider a stochastic single item production-inventory-routing problem with a single producer and multiple clients. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented where the production and routing decisions are taken before the scenario is known, and the quantities to deliver to the clients and the inventory levels are adjustable to the scenario. Valid inequalities are introduced and a hybrid heuristic that combines ideas from the sample average approximation method and from relax-and-fix approaches is proposed. Preliminary tests based on randomly generated instances are reported showing that the hybrid heuristic performs better than the classical sample approximation algorithm for hard instances. published

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An adjustable sample average approximation algorithm for the stochastic production-inventory-routing problem

Agra, Agostinho, Requejo, Cristina, Rodrigues, Filipe

Wiley

We consider a stochastic single item production-inventory-routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then, the candidate solutions are tested on a larger sample, and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the first-stage decision variables is fixed, and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances. published

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Robust optimization for a maritime inventory routing problem

Agra, Agostinho, Christiansen, Marielle, Hvattum, Lars Magnus, Rodrigues, Filipe Manuel

INFORMS

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances. published

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An extension of the classification of high rank regular polytopes

Leemans, Dimitri, Mixer, Mark, Fernandes, Maria Elisa

American Mathematical Society

Up to isomorphism and duality, there are exactly two nondegenerate abstract regular polytopes of rank greater than n−3 (one of rank n−1 and one of rank n−2) with automorphism groups that are transitive permutation groups of degree n ≥ 7. In this paper we extend this classification of high rank regular polytopes to include the ranks n − 3 and n − 4. The result is, up to isomorphism and duality, there are exactly seven abstract regular polytopes of rank n − 3 for each n ≥ 9, and there are nine abstract regular polytopes of rank n−4 for each n ≥ 11. Moreover, we show that if a transitive permutation group Γ of degree n ≥ 11 is the automorphism group of an abstract regularpolytope of rank at least n − 4, then Γ~=S_n. published

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Health-Related Quality of Life in Pulmonary Hypertension and Its Clinical Correlates: A Cross-Sectional Study

Reis, Abílio, Santos, Mário, Vicente, Margarida, Furtado, Inês, Cruz, Célia, Melo, Alzira, Carvalho, Luísa, Gonçalves, Fabienne, Almeida, Luís, Sa-Couto, Pedro

Hindawi Publishing Corporation

Background: Health-related quality of life (HRQoL) impairment is common in pulmonary hypertension (PH), but its clinical predictors are not well established. This study aims to characterize the HRQoL of patients with pulmonary arterial hypertension (PAH) and other precapillary forms of PH (pcPH) and to explore its clinical correlates. Materials and Methods: A cross-sectional, observational study of patients with documented PAH and other forms of pcPH. Patients completed two patient-reported outcome measures (PROM): Cambridge Pulmonary Hypertension Outcome Review (CAMPHOR) and Nottingham Health Profile (NHP). Clinical characteristics were retrieved from electronic medical records. Results: Mean CAMPHOR and NHP scores for the study population were indicative of a moderate HRQoL impairment. Patients in World Health Organisation Functional Classes (WHO FC) III/IV showed significantly worse HRQoL. The main clinical correlates of HRQoL were WHO FC, 6-minute walking distance (6MWD), and Borg dyspnoea index. Overall quality of life (QoL), assessed through CAMPHOR's QoL domain, showed patterns comparable to HRQoL measured by both instruments. Conclusions: HRQoL, measured by two different PROMs, is impaired in Portuguese patients with PAH and other forms of pcPH, particularly in patients with increased disease severity. WHO FC, 6MWD, and Borg dyspnoea index are highly correlated with HRQoL and QoL. Actelion Pharmaceuticals Portugal published

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The influence of presurgical factors on the rehabilitation outcome of patients following hip arthroplasty

Simões, João Lindo, Soares, Soraia, Sá-Couto, Pedro, Lopes, Carla, Magina, Daniela, Melo, Elsa, Voegeli, David, Bolhão, Isabel

Lippincott, Williams & Wilkins

The aims of this study were to evaluate the relationship between sociodemographic information, anthropometric values, clinical and presurgery factors, and length of stay (LOS) in older adult patients undergoing total hip arthroplasty (THA) and to predict which factors can delay the start of the rehabilitation program and increase the corresponding LOS. published

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Identification of frailty condition of elderly people in the community

Machado, Inês, Sa-Couto, Pedro, Tavares, João

BMC

published

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Musculoskeletal multisite pain and patterns of association after adjusting for sleep, physical activity, and screen time in adolescents

Silva, Anabela G., Couto, Pedro Sá, Queirós, Alexandra, Neto, Maritza, Rocha, Nelson P.

Lippincott, Williams & Wilkins

Study Design. Cross-sectional. Objective. This study aims to describe how pain at multiple body sites is associated after controlling for other predictive factors such as age, sex, sleeping hours, time spent in physical activity, and time spent in screening based activities in adolescents aged 13 to 19 years. Summary of Background Data. The prevalence of multisite pain in adolescents is high, but studies investigating the patterns of association between painful body sites are scarce. Methods. Pain for the last 3 months was assessed using Nordic Musculoskeletal Questionnaire. In addition, data on time spent in moderate and vigorous physical activity, sleeping, and in screen based activities were also assessed. Results. In univariable analysis of associations, there is a significant association between most painful body sites (odds ratio [OR between 1.52 and 3.73, P<0.05). After controlling for age, sex, physical activity, sleep and screen time, most of the previous associations remain significant (OR between 1.50 and 3.07, P<0.05). published

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Breaking the Habit: The Peculiar 2016 Eruption of the Unique Recurrent Nova M31N 2008-12a

Henze, M., Darnley, M. J., Williams, S. C., Kato, M., Hachisu, I., Anupama, G. C., Arai, A., Boyd, D., Burke, D., Ciardullo, R., Chinetti, K., Cook, L. M., Cook, M. J., Erdman, P., Gao, X., Harris, B., Hartmann, D. H., Hornoch, K., Horst, J. Chuck, Hounsell, R., Husar, D., Itagaki, K., Kabashima, F., Kafka, S., Kaur, A., Kiyota, S., Kojiguchi, N., Kučáková, H., Kuramoto, K., Maehara, H., Mantero, A., Masci, F. J., Matsumoto, K., Naito, H., Ness, J.-U., Nishiyama, K., Oksanen, A., Osborne, J. P., Page, K. L., Paunzen, E., Pavana, M., Pickard, R., Prieto-Arranz, J., Rodríguez-Gil, P., Sala, G., Sano, Y., Shafter, A. W., Sugiura, Y., Tan, H., Tordai, T., Vraštil, J., Wagner, R. M., Watanabe, F., Williams, B. F., Bode, M. F., Bruno, A., Buchheim, B., Crawford, T., Goff, B., Hernanz, M., Igarashi, A. S., José, J., Motta, M., O’Brien, T. J., Oswalt, T., Poyner, G., Ribeiro, V. A. R. M., Sabo, R., Shara, M. M., Shears, J., Starkey, D., Starrfield, S., Woodward, C. E.

Since its discovery in 2008, the Andromeda galaxy nova M31N 2008-12a has been observed in eruption every single year. This unprecedented frequency indicates an extreme object, with a massive white dwarf and a high accretion rate, which is the most promising candidate for the single-degenerate progenitor of a type-Ia supernova known to date. The previous three eruptions of M31N 2008-12a have displayed remarkably homogeneous multi-wavelength properties: (i) From a faint peak, the optical light curve declined rapidly by two magnitudes in less than two days; (ii) Early spectra showed initial high velocities that slowed down significantly within days and displayed clear He/N lines throughout; (iii) The supersoft X-ray source (SSS) phase of the nova began extremely early, six days after eruption, and only lasted for about two weeks. In contrast, the peculiar 2016 eruption was clearly different. Here we report (i) the considerable delay in the 2016 eruption date, (ii) the significantly shorter SSS phase, and (iii) the brighter optical peak magnitude (with a hitherto unobserved cusp shape). Early theoretical models suggest that these three different effects can be consistently understood as caused by a lower quiescence mass-accretion rate. The corresponding higher ignition mass caused a brighter peak in the free-free emission model. The less-massive accretion disk experienced greater disruption, consequently delaying re-establishment of effective accretion. Without the early refueling, the SSS phase was shortened. Observing the next few eruptions will determine whether the properties of the 2016 outburst make it a genuine outlier in the evolution of M31N 2008-12a. published

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Response to letter to the editor: 'Comments on procalcitonin for the early diagnosis of sepsis in burn patients: a retrospective study'

Cabral, Luís, Afreixo, Vera, Santos, Filipe, Almeida, Luís, Paiva, José Artur

Elsevier

published

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Rapid screening of methicillin-resistant Staphylococcus aureus carrying the mecC gene in a Portuguese hospital

Diaz, Raquel, Afreixo, Vera, Ramalheira, Elmano, Gago, Bruno

Pacific Group of e-Journals

Background: The discovery of mecC gene in MRSA isolates and its report in neighboring Spain and France, advices for monitoring its presence in Portuguese hospitals since changes in local epidemiology can occur quickly. The implementation of rapid procedures based on the automated system VITEK2 allow for simple screening of mecC MRSA isolates with the profile of susceptibility to oxacillin and resistance to cefoxitin signaling positive results for detailed analysis. Methods: This works aims to perform a retrospective study for the presence of suspect mecC MRSA in a Portuguese hospital recurring to the two methodologies included in microbiology laboratories routine. Result: Our results do not suggest the presence of mecC MRSA, but highlight the possibility of introducing a simple method in clinical laboratories with high percentage of S. aureus isolates. Conclusion: The implementation of this simple procedure in the laboratory routine is a rapid and economic way to monitoring the presence of mecC MRSA. published

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Evaluation of vancomycin MIC creep in methicillin-resistant Staphylococcus aureus infections-a systematic review and meta-analysis

Diaz, R, Afreixo, V, Ramalheira, E, Rodrigues, C., Gago, B

Elsevier

Vancomycin is currently the primary option treatment for methicillin-resistant Staphylococcus aureus (MRSA). However, an increasing number of MRSA isolates with high MICs, within the susceptible range (vancomycin MIC creep), are being reported worldwide. Resorting to a meta-analysis approach, this study aims to assess the evidence of vancomycin MIC creep. published

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Checking procalcitonin suitability for prognosis and antimicrobial therapy monitoring in burn patients

Cabral, Luís, Afreixo, Vera, Meireles, Rita, Vaz, Miguel, Chaves, Catarina, Caetano, Marisa, Almeida, Luís, Paiva, José Artur

BMC

Due to greater infection susceptibility, sepsis is the main cause of death in burn patients. Quick diagnosis and patient stratification, early and appropriated antimicrobial therapy, and focus control are crucial for patients' survival. On the other hand, superfluous extension of therapy is associated with adverse events and arousal of microbial resistance. The use of biomarkers, necessarily coupled with close clinical examination, may predict outcomes, stratifying patients who need more intensive care, and monitor the efficacy of antimicrobial therapy, allowing faster de-escalation or stop, reducing the development of resistance and possibly the financial burden, without increasing mortality. The aim of this work is to check the suitability of procalcitonin (PCT) to fulfill these goals in a large sample of septic burn patients. published

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Comparing reverse complementary genomic words based on their distance distributions and frequencies

Tavares, Ana Helena, Raymaekers, Jakob, Rousseeuw, Peter J, Silva, Raquel M, Bastos, Carlos A C, Pinho, Armando, Brito, Paula, Afreixo, Vera

Springer Verlag

In this work, we study reverse complementary genomic word pairs in the human DNA, by comparing both the distance distribution and the frequency of a word to those of its reverse complement. Several measures of dissimilarity between distance distributions are considered, and it is found that the peak dissimilarity works best in this setting. We report the existence of reverse complementary word pairs with very dissimilar distance distributions, as well as word pairs with very similar distance distributions even when both distributions are irregular and contain strong peaks. The association between distribution dissimilarity and frequency discrepancy is also explored, and it is speculated that symmetric pairs combining low and high values of each measure may uncover features of interest. Taken together, our results suggest that some asymmetries in the human genome go far beyond Chargaff's rules. This study uses both the complete human genome and its repeat-masked version. published

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Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids

Abrunheiro, Lígia, Colombo, Leonardo

Springer Verlag

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles, Lie algebras, principal bundles, reduced systems, and constrained are included in such description. In this paper, we investigate how to derive the dynamics associated with a Lagrangian system defined on the set of admissible elements of a given Lie algebroid using Tulczyjew’s triple on Lie algebroids and constructing a Lagrangian Lie subalgebroid of a symplectic Lie algebroid, by building on the geometric formalism for mechanics on Lie algebroids developed by M. de León, J.C. Marrero and E. Martínez on “Lagrangian submanifolds and dynamics on Lie algebroids” published

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Composition codes

Fornasini, Ettore, Pinho, Telma, Pinto, Raquel, Rocha, Paula

American Institute of Mathematical Sciences

In this paper we introduce a special class of 2D convolutional codes, called composition codes, which admit encoders G(d1,d2) that can be decomposed as the product of two 1D encoders, i.e., G(d1,d2)=G2(d2)G1(d1). Taking into account this decomposition, we obtain syndrome formers of the code directly from G1(d1) andG2(d2), in case G1(d1) andG2(d2) are right prime. Moreover we consider 2D state-space realizations by means of a separable Roesser model of the encoders and syndrome formers of a composition code and we investigate the minimality of such realizations. In particular, we obtain minimal realizations for composition codes which admit an encoder G(d1,d2)=G2(d2)G1(d1) withG2(d2) a systematic 1D encoder. Finally, we investigate the minimality of 2D separable Roesser state-space realizations for syndrome formers of these codes. published

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Combinatorial identities in the context of hypercomplex function theory

Cação, Isabel, Falcão, M. I., Malonek, Helmuth R.

AIP Publishing

Recently, the authors have shown that a certain combinatorial identity in terms of generators of quaternions is related to a particular sequence of rational numbers (Vietoris’ number sequence). This sequence appeared for the first time in a theorem by Vietoris (1958) and plays an important role in harmonic analysis and in the theory of stable holomorphic functions in the unit disc. We present a generalization of that combinatorial identity involving an arbitrary number of generators of a Cli ord algebra. The result reveals new insights in combinatorial phenomena in the context of hypercomplex function theory. published

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Comparing reverse complementary genomic words based on their distance distributions and frequencies

Tavares, Ana Helena, Raymaekers, Jakob, Rousseeuw, Peter J, Silva, Raquel M, Bastos, Carlos A C, Pinho, Armando, Brito, Paula, Afreixo, Vera

Springer

In this work, we study reverse complementary genomic word pairs in the human DNA, by comparing both the distance distribution and the frequency of a word to those of its reverse complement. Several measures of dissimilarity between distance distributions are considered, and it is found that the peak dissimilarity works best in this setting. We report the existence of reverse complementary word pairs with very dissimilar distance distributions, as well as word pairs with very similar distance distributions even when both distributions are irregular and contain strong peaks. The association between distribution dissimilarity and frequency discrepancy is also explored, and it is speculated that symmetric pairs combining low and high values of each measure may uncover features of interest. Taken together, our results suggest that some asymmetries in the human genome go far beyond Chargaff's rules. This study uses both the complete human genome and its repeat-masked version. published

ria.ua.pt

Methicillin-resistant staphylococcus aureus in poultry and poultry meat: a meta-analysis

Ribeiro, Claudia M, Stefani, Lenita M, Lucheis, Simone B, Okano, Werner, Cruz, Juliano Cezar M, Souza, Guilherme V, Casagrande, Thais A C, Bastos, Paula Andrea S, Pinheiro, Rafael R, Arruda, Mauro M, Afreixo, Vera

International Association for Food Protection

Methicillin-resistant Staphylococcus aureus (MRSA) is a bacterium that colonizes and infects various host species and has been found in the poultry production chain, raising concerns about possible transmission from farm to fork. The objective of this study was to use meta-analytical methods to estimate the pooled prevalence of MRSA in chickens, turkeys, chicken meat, and turkey meat. Three electronic databases (PubMed, LILACS, and SciELO) were searched to establish MRSA prevalence from 51 studies published from 2003 through May 2017. The heterogeneity was assessed, and the pooled MRSA prevalence was calculated by using the random effects model according to the method of DerSimonian and Laird. Pooled MRSA prevalence (95% confidence interval [CI]) in turkeys, turkey meat, broilers, and chicken meat was 36% (1 to 78%), 13% (1 to 28%), 5% (2 to 9%), and 5% (3 to 8%), respectively. South America had the highest MRSA prevalence (27%; 95% CI, 17 to 37%), and North America had the lowest (1%; 95% CI, 0 to 2%). Livestock-associated MRSA has been isolated from poultry and poultry meat, indicating that this variant can spread from farm to fork. The presence of MRSA in poultry and poultry meat poses risks to public health, and steps should be taken to mitigate the contamination and spread of this bacterium along the poultry production chain. published

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Jogos de futebol impróprios para cardíacos (HeartAtaque trial) – Estudo piloto prospetivo

Martins, José Luís, Adrega, Tiago, Santos, Luís, Afreixo, Vera, Viana, Jesus, Santos, José

Elsevier España

Introduction: Behavioral and emotional factors are triggers of cardiovascular events (CVEs). It is uncertain whether soccer fans, particularly individuals with coronary artery disease (CAD), are at increased risk for CVEs. Objectives: To assess the effect of watching soccer matches in patients with known CAD on the incidence of CVEs according to the match result. Methods: We prospectively assessed 82 male soccer fans with a history of acute coronary syndrome during 23 matches of the 2015/2016 season. Each individual was assessed by Holter monitoring on the day of their team's match and on the control day. The primary endpoint was the composite of death, stroke, reinfarction, angina or sustained arrhythmia. Secondary endpoints assessed were episodes of non‐sustained supraventricular or ventricular arrhythmia and mean heart rate (HR). Results: Participants’ mean age was 61 ± 10 years. Compared with the control day, despite a significant increase in HR (p < 0.001) that was independent of the result (p > 0.97), the number of CVEs did not differ according to the result (p > 0.05). Moreover, the number of non‐sustained episodes of supraventricular and ventricular arrhythmia did not differ when stratified according to the match result (p > 0.05). Conclusions: The match result was not associated with a difference in incidence of CVEs in patients with a past history of CAD, with ischemic and arrhythmic substrate, who watched soccer matches on television. Introdução: Fatores comportamentais e emocionais são desencadeantes de eventos cardiovasculares (ECV). Permanece incerto se espetadores de jogos de futebol, em particular indivíduos com doença arterial coronária (DAC), estão expostos a maior risco de ECV. Objetivos: Avaliar o efeito da assistência a jogos de futebol em doentes com DAC na incidência de ECV de acordo com o resultado obtido pela equipa de apoio. Métodos: Avaliados prospetivamente 82 adeptos de futebol do sexo masculino com antecedentes de síndrome coronária aguda, durante 23 jogos de futebol da época 2015/2016. Cada indivíduo foi monitorado com Holter no dia do jogo da sua equipa e em dia controlo em período homólogo à hora do jogo. Avaliado como endpoint primário o composto de morte, acidente vascular cerebral, re‐enfarte, angor ou arritmias mantidas. Avaliados ainda como endpoints secundários, episódios de disritmia supraventricular ou ventricular não mantida e frequência cardíaca média. Resultados: A idade média foi 61 ± 10 anos. Comparado com o dia controlo, apesar do aumento significativo da frequência cardíaca na hora de jogo (p < 0,001) que foi independente do resultado (p > 0,97), o número de eventos cardiovasculares não foi diferente tendo em conta o resultado (p > 0,05). Também o número de episódios de disritmia supraventricular e ventricular não mantida não foi diferente estratificando de acordo com o resultado (p > 0,05). Conclusão: O resultado do jogo não se associou a diferente incidência de eventos cardiovasculares em doentes com substrato isquémico e arrítmico por antecedentes de DAC que assistiram a jogos de futebol na televisão. published

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Procalcitonin kinetics after burn injury and burn surgery in septic and non-septic patients - a retrospective observational study

Cabral, Luís, Afreixo, Vera, Meireles, Rita, Vaz, Miguel, Marques, Margarida, Tourais, Isabel, Chaves, Catarina, Almeida, Luís, Paiva, José Artur

BMC

Early sepsis diagnosis is crucial for the correct management of burn patients, and it clearly influences outcomes. The systemic inflammatory response triggered by burns mimics sepsis presentation and complicates early sepsis diagnosis. Biomarkers were advocated to aid the diagnosis of early sepsis. Serum procalcitonin (PCT) exhibits fair accuracy and good correlation with sepsis severity, being used in diverse clinical settings. However, few studies have evaluated perioperative changes in PCT levels in burn patients. The present study evaluated PCT kinetics during the first days after burn injury and subsequent surgical interventions to assess PCT utility in distinguishing septic from non-septic inflammatory responses. published

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Fractional flow reserve-guided strategy in acute coronary syndrome. a systematic review and meta-analysis

Martins, José Luís, Afreixo, Vera, Santos, José, Gonçalves, Lino

Sociedade Brasileira de Cardiologia

Background: There are limited data on the prognosis of deferral of lesion treatment in patients with acute coronary syndrome (ACS) based on fractional flow reserve (FFR). Objectives: To provide a systematic review of the current evidence on the prognosis of deferred lesions in ACS patients compared with deferred lesions in non-ACS patients, on the basis of FFR. Methods: We searched Medline, EMBASE, and the Cochrane Library for studies published between January 2000 and September 2017 that compared prognosis of deferred revascularization of lesions on the basis of FFR in ACS patients compared with non-ACS patients. We conducted a pooled relative risk meta-analysis of four primary outcomes: mortality, cardiovascular (CV) mortality, myocardial infarction (MI) and target-vessel revascularization (TVR). Results: We identified 7 studies that included a total of 5,107 patients. A pooled meta-analysis showed no significant difference in mortality (relative risk [RR] = 1.44; 95% CI, 0.9–2.4), CV mortality (RR = 1.29; 95% CI = 0.4–4.3) and TVR (RR = 1.46; 95% CI = 0.9–2.3) after deferral of revascularization based on FFR between ACS and non-ACS patients. Such deferral was associated with significant additional risk of MI (RR = 1.83; 95% CI = 1.4–2.4) in ACS patients. Conclusion: The prognostic value of FFR in ACS setting is not as good as in stable patients. The results demonstrate an increased risk of MI but not of mortality, CV mortality, and TVR in ACS patients. published

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Medical treatment or revascularisation as the best approach for spontaneous coronary artery dissection: A systematic review and meta-analysis

Martins, José Luís, Afreixo, Vera, Santos, Luís, Costa, Marco, Santos, José, Gonçalves, Lino

SAGE Publications

INTRODUCTION: Patients presenting with spontaneous coronary artery dissection (SCAD) may receive either conservative medical management or a revascularisation strategy. There is still a lack of consensus with respect to the best treatment approach for SCAD. OBJECTIVES: We sought to determine whether outcomes differ between the first-line treatment approaches (conservative versus revascularisation) in patients with SCAD. METHODS: We searched Medline, EMBASE and the Cochrane Library for studies published from January 1990 to November 2016 that compared first-line treatments for patients with SCAD. We conducted a pooled risk ratio meta-analysis for four main outcomes: mortality, myocardial infarction (MI), SCAD recurrence and target vessel revascularisation (TVR). RESULTS: We identified 11 non-randomised studies that included a total of 631 patients. A pooled meta-analysis showed no significant difference between conservative management and revascularisation approaches in mortality (risk difference [RD] = 0.01; 95% confidence interval [CI] = -0.01 to 0.04; I2 = 0%; p = 1), MI (RD = -0.01; 95% CI = -0.04 to 0.03; I2 = 0%; p = 0.5) or SCAD recurrence (RD = -0.01; 95% CI = -0.06 to 0.05; I2 = 0%; p = 0.74). Revascularisation as an initial first-line approach was associated with an estimated additional risk of TVR of 6.3% (RD = 0.06; 95% CI = 0.01-0.11; I2 = 0%; p = 0.96). CONCLUSION: The results demonstrate an increased risk of TVR when revascularisation was used as the initial first-line treatment approach. The treatment decision must be individualised and be based on both clinical and angiographic factors, but conservative therapy should prevail in most cases. published

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Injectability of calcium phosphate pastes: effects of particle size and state of aggregation of beta-tricalcium phosphate powders

Torres, P. M. C., Gouveia, Sónia, Olhero, S., Kaushal, A., Ferreira, J. M. F.

Elsevier

The present study discloses a systematic study about the influence of some relevant experimental variables on injectability of calcium phosphate cements. Non-reactive and reactive pastes were prepared, based on tricalcium phosphate doped with 5 mol% (Sr-TCP) that was synthesised by co-precipitation. The varied experimental parameters included: (i) the heat treatment temperature within the range of 800–1100 C; (ii) different milling extents of calcined powders; (iii) the liquid-to-powder ratio (LPR); (iv) the use of powder blends with different particle sizes (PS) and particle size distributions (PSD); (v) the partial replacement of fine powders by large spherical dense granules prepared via freeze granulation method to simulate coarse individual particles. The aim was contributing to better understanding of the effects of PS, PSD, morphology and state of aggregation of the starting powders on injectability of pastes produced thereof. Powders heat treated at 800 and 1000 º C with different morphologies but with similar apparent PSD curves obtained by milling/blending originated completely injectable reactive cement pastes at low LPR. This contrasted with non-reactive systems prepared thereof under the same conditions. Hypotheses were put forward to explain why the injectability results collected upon extruding non-reactive pastes cannot be directly transposed to reactive systems. The results obtained underline the interdependent roles of the different powder features and ionic strength in the liquid media on determining the flow and injectability behaviours.

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Convex SIP problems with finitely representable compact index sets: immobile indices and the properties of the auxiliary NLP problem

Kostyukova, O. I., Tchemisova, T. V.

Springer Verlag

In the paper, we consider a problem of convex Semi-Infinite Programming with a compact index set defined by a finite number of nonlinear inequalities. While studying this problem, we apply the approach developed in our previous works and based on the notions of immobile indices, the corresponding immobility orders and the properties of a specially constructed auxiliary nonlinear problem. The main results of the paper consist in the formulation of sufficient optimality conditions for a feasible solution of the original SIP problem in terms of the optimality conditions for this solution in a specially constructed auxiliary nonlinear programming problem and in study of certain useful properties of this finite problem.

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Bethe graphs attached to the vertices of a connected graph: a spectral approach

Andrade, Enide, Cardoso, Domingos M., Medina, Luis, Rojo, Oscar

Taylor & Francis

A weighted Bethe graph $B$ is obtained from a weighted generalized Bethe tree by identifying each set of children with the vertices of a graph belonging to a family $F$ of graphs. The operation of identifying the root vertex of each of $r$ weighted Bethe graphs to the vertices of a connected graph $mathcal{R}$ of order $r$ is introduced as the $mathcal{R}$-concatenation of a family of $r$ weighted Bethe graphs. It is shown that the Laplacian eigenvalues (when $F$ has arbitrary graphs) as well as the signless Laplacian and adjacency eigenvalues (when the graphs in $F$ are all regular) of the $mathcal{R}$-concatenation of a family of weighted Bethe graphs can be computed (in a unified way) using the stable and low computational cost methods available for the determination of the eigenvalues of symmetric tridiagonal matrices. Unlike the previous results already obtained on this topic, the more general context of families of distinct weighted Bethe graphs is herein considered.

ria.ua.pt

Can information be spread as a virus? Viral Marketing as epidemiological model

Rodrigues, Helena Sofia, Fonseca, Manuel José

Wiley

In epidemiology, an epidemic is defined as the spread of an infectious disease to a large number of people in a given population within a short period of time. In the marketing context, a message is viral when it is broadly sent and received by the target market through person-to-person transmission. This specific marketing communication strategy is commonly referred as viral marketing. Because of this similarity between an epidemic and the viral marketing process and because the understanding of the critical factors to this communications strategy effectiveness remain largely unknown, the mathematical models in epidemiology are presented in this marketing specific field. In this paper, an epidemiological model susceptible-infected-recovered to study the effects of a viral marketing strategy is presented. It is made a comparison between the disease parameters and the marketing application, and MATLAB simulations are performed. Finally, some conclusions are carried out and their marketing implications are exposed: interactions across the parameters suggest some recommendations to marketers, as the profitability of the investment or the need to improve the targeting criteria of the communications campaigns.

ria.ua.pt

Combinatorial and spectral properties of König–Egerváry graphs

Cardoso, Domingos M., Robbiano, Maria, Rojo, Oscar

Elsevier

Some combinatorial and spectral properties of König–Egerváry (K–E) graphs are presented. In particular, some new combinatorial characterizations of K–E graphs are introduced, the Laplacian spectrum of particular families of K–E graphs is deduced, and a lower and upper bound on the largest and smallest adjacency eigenvalue, respectively, of a K–E graph are determined.

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A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy

Lakshtanov, Evgeny L., Novikov, Roman G., Vainberg, Boris R.

Università di Trieste

We develop the Riemann-Hilbert problem approach to in- verse scattering for the two-dimensional Schr odinger equation at xed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported poten- tials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.

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Diffraction by a half-plane with different face impedances on an obstacle perpendicular to the boundary

Castro, L.P., Kapanadze, D.

Mathematical Research Publishers

The paper is devoted to study classes of plane wave diffraction problems by a region which involves a crack with impedance boundary conditions. Conditions on the wave number and impedance parameters are found to ensure the well-posedness of the problems in a scale of Bessel potential spaces. Under such conditions, representations of the solutions are also obtained upon the consideration of some associated operators which, in a sense, combine operators of Wiener-Hopf and Hankel type.

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A reproducing kernel Hilbert space constructive approximation for integral equations with Toeplitz and Hankel kernels

Castro, L.P., Silva, A.S., Saitoh, S.

American Romanian Academy of Arts and Sciences

A reproducing kernel Hilbert space approach is proposed to study a class of integral equations with Toeplitz and Hankel kernel functions. The existence property and approximate representations of the solutions are given by constructing appropriate auxiliary operators and positive definite matrices within a reproducing kernel Hilbert space framework. Moreover, conditions for the boundedness and uniqueness of the solution are also obtained.

ria.ua.pt

Krause's model of opinion dynamics on isolated time scales

Girejko, Ewa, Machado, Luís, Malinowska, Agnieszka B., Martins, Natália

Wiley

We analyze a bounded confidence model, introduced by Krause, on isolated time scales. In this model, each agent takes into account only the assessments of the agents whose opinions are not too far away from its own opinion. We show that the behavior of the model depends strongly on the graininess function μ: If μ takes values in the interval ]0,1], then our discrete time scale model behaves similarly to the classical one, but if μ takes values in ]1,+∞[, then the model has different properties. Simulations are performed to validate the theoretical results.

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Higher-order variational problems of Herglotz type with time delay

Santos, Simão P. S., Martins, Natália, Torres, Delfim F.M.

Yokohama Publishers

We study, using an optimal control point of view, higherorder variational problems of Herglotz type with time delay. Main results are higher-order Euler–Lagrange and DuBois–Reymond necessary optimality conditions as well as a higher-order Noether type theorem for delayed variational problems of Herglotz type.

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Quadratic Fourier transforms

Castro, L.P., Haque, M.R., Murshed, M.M., Saitoh, S., Tuan, N.M.

Duke University Press

In this paper we shall examine the quadratic Fourier transform which is introduced by the generalized quadratic function for one order parameter in the ordinary Fourier transform. This will be done by analyzing corresponding six subcases of the quadratic Fourier transform within a reproducing kernel Hilbert spaces framework.

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Mixed boundary value problems of diffraction by a half-plane with an obstacle perpendicular to the boundary

Castro, L.P., Kapanadze, D.

Wiley

The paper is devoted to the analysis of wave diffraction problems modelled by classes of mixed boundary conditions and the Helmholtz equation, within a half-plane with a crack. Potential theory together with Fredholm theory, and explicit operator relations, are conveniently implemented to perform the analysis of the problems. In particular, an interplay between Wiener-Hopf plus/minus Hankel operators and Wiener-Hopf operators assumes a relevant preponderance in the final results. As main conclusions, this study reveals conditions for the well-posedness of the corresponding boundary value problems in certain Sobolev spaces and equivalent reduction to systems of Wiener-Hopf equations.

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A Bessel differential heat initial value problem in a reproducing kernel Hilbert space framework

Castro, L.P., Rodrigues, M.M., Saitoh, S.

American Institute of Physics

For modified Bessel heat equations subjected to an initial condition, we investigate integral transforms with kernels related to the solutions of those equations by using the theory of reproducing kernels. In particular, a new framework within reproducing kernel Hilbert spaces is proposed where we construct the unique solutions of the corresponding initial value problems.

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Deformation of a class of Dihedral Spherical f-Tilings

Breda, A. M. d’Azevedo, Ribeiro, Patrícia S.

Springer Verlag

Deformations of isometric foldings of the euclidian plane into the standard foldingwere described in 1989. Given the intrinsic relation between isometric foldings and folding tilings ( f -tilings for short) an analogous question may be formulated: is any f -tiling deformable into the standard one? In this paper, we show how to deform a class of dihedral spherical f -tilings into the standard one.

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Spherical f-Tilings by Two Noncongruent Classess of Isosceles Triangles

Breda, A. M. d'Azevedo, Dawson, Robert, Ribeiro, Patrícia S.

Cir World

The study of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles was started in two previous papers. Here, we complete the classification, characterizing the f-tilings that satisfy the remaining case of adjacency. As it will be shown, this class is composed by two three-parameter families and a related four-parameter family; two isolated tilings and six distinct discrete families.

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Preface by the Editors from Selected Papers of III Amazonian Symposium on Physics; Guest Editors: Carlos A. R. Herdeiro, Emanuele Berti, Vitor Cardoso, Luis C. B. Crispino, Leonardo Gualtieri and Ulrich Sperhake

Herdeiro, C. A. R., Berti, E., Cardoso, V., Crispino, L. C. B., Gualtieri, L., Sperhake, U.

World Scientific Publishing

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Harmonic analysis on the proper velocity gyrogroup

Ferreira, Milton

Duke University Press

Revista sem período de embargo. In this paper we study harmonic analysis on the Proper Velocity (PV) gyrogroup using the gyrolanguage of analytic hyperbolic geometry. PV addition is the relativistic addition of proper velocities in special relativity and it is related with the hyperboloid model of hyperbolic geometry. The generalized harmonic analysis depends on a complex parameter $z$ and on the radius $t$ of the hyperboloid and comprises the study of the generalized translation operator, the associated convolution operator, the generalized Laplace-Beltrami operator and its eigenfunctions, the generalized Poisson transform and its inverse, the generalized Helgason-Fourier transform, its inverse and Plancherel's Theorem. In the limit of large $t,$ $t rightarrow +infty,$ the generalized harmonic analysis on the hyperboloid tends to the standard Euclidean harmonic analysis on ${mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.

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Approximation in Morrey spaces

Almeida, Alexandre, Samko, Stefan

Elsevier

A new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions is introduced. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalization of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained.

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Spectra and Randic spectra of caterpillar graphs and applications to the energy

Andrade, Enide, Gomes, Helena, Robbiano, María

Let $H$ be an undirected simple graph with vertices $v_{1},ldots ,v_{k}$ and $G_{1},ldots ,G_{k}$ be a sequence formed with $k$ disjoint graphs $G_{i}$, $i=1,ldots ,k$. The $H$-generalized composition (or $H$% -join) of this sequence is denoted by $Hleft[ G_{1},ldots ,G_{k}right] .$ In this work, we characterize the caterpillar graphs as a $H$-generalized composition and we study their spectra and Randi'{c} spectra, respectively. As an application, we obtain an improved and tight upper bound for the Energy and the Randi'{c} energy of these interesting trees.

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A generalized Lyapunov's inequality for a fractional boundary value problem

Chidouh, Amar, Torres, Delfim F.M.

Elsevier

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated through examples. © 2016 Elsevier B.V.

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Existence of solution to a local fractional nonlinear differential equation

Bayour, Benaoumeur, Torres, Delfim F.M.

Elsevier

We prove existence of solution to a local fractional nonlinear differential equation with initial condition. For that we introduce the notion of tube solution. © 2016 Elsevier B.V.

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Optimal control of a tuberculosis model with state and control delays

Silva, Cristiana J., Maurer, Helmut, Torres, Delfim F.M.

American Institute of Mathematical Sciences

We introduce delays in a tuberculosis (TB) model, representing the time delay on the diagnosis and commencement of treatment of individuals with active TB infection. The stability of the disease free and endemic equilibriums is investigated for any time delay. Corresponding optimal control problems, with time delays in both state and control variables, are formulated and studied. Although it is well-known that there is a delay between two to eight weeks between TB infection and reaction of body's immune system to tuberculin, delays for the active infected to be detected and treated, and delays on the treatment of persistent latent individuals due to clinical and patient reasons, which clearly justifies the introduction of time delays on state and control measures, our work seems to be the first to consider such time-delays for TB and apply time-delay optimal control to carry out the optimality analysis. © 2017, Arizona State University. All rights reserved.

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Linear and nonlinear fractional voigt models

Chidouh, Amar, Guezane-Lakoud, Assia, Bebbouchi, Rachid, Bouaricha, Amor, Torres, Delfim F.M.

Springer Verlag

We consider fractional generalizations of the ordinary differential equation that governs the creep phenomenon. Precisely, two Caputo fractional Voigt models are considered: a rheological linear model and a nonlinear one. In the linear case, an explicit Volterra representation of the solution is found, involving the generalized Mittag-Leffler function in the kernel. For the nonlinear fractional Voigt model, an existence result is obtained through a fixed point theorem. A nonlinear example, illustrating the obtained existence result, is given. © Springer International Publishing AG 2017.

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Exponentials and Laplace transforms on nonuniform time scales

Ortigueira, Manuel D., Torres, Delfim F.M., Trujillo, Juan J.

Elsevier

We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla and delta exponentials, computed. With these exponentials, two generalised discrete-time Laplace transforms are deduced and their properties studied. These transforms are compatible with the standard Laplace and Z transforms. They are used to study discrete-time linear systems defined by difference equations. These equations mimic the usual continuous-time equations that are uniformly approximated when the sampling interval becomes small. Impulse response and transfer function notions are introduced. This implies a unified mathematical framework that allows us to approximate the classic continuous-time case when the sampling rate is high or to obtain the standard discrete-time case, based on difference equations, when the time grid becomes uniform. © 2016 Elsevier B.V.

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Dynamics and optimal control of Ebola transmission

Rachah, Amira, Torres, Delfim F.M.

Springer Verlag

A major Ebola outbreak occurs in West Africa since March 2014, being the deadliest epidemic in history. As an infectious disease epidemiology, Ebola is the most lethal and is moving faster than in previous outbreaks. On 8 August 2014, the World Health Organization (WHO) declared the outbreak a public health emergency of international concern. Last update on 7 July 2015 by WHO reports 27,609 cases of Ebola with a total of 11,261 deaths. In this work, we present a mathematical description of the spread of Ebola virus based on the SEIR (Susceptible–Exposed–Infective–Recovered) model and optimal strategies for Ebola control. In order to control the propagation of the virus and to predict the impact of vaccine programmes, we investigate several strategies of optimal control of the spread of Ebola: control infection by vaccination of susceptible; minimize exposed and infected; reduce Ebola infection by vaccination and education. © 2016, Springer International Publishing.

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A hukuhara approach to the study of hybrid fuzzy systems on time scales

Fard, Omid S., Torres, Delfim F.M., Zadeh, Mohadeseh R.

Akademska misao

We introduce a new approach to study the practical stability of hybrid fuzzy systems on time scales in the Lyapunov sense. Our method is based on the delta-Hukuhara derivative for fuzzy valued functions and allow us to obtain new interesting stability criteria. We also show the validity of the results of M. Sambandham: Hybrid fuzzy systems on time scales, Dynam. Systems Appl., 12 (1-2) (2003), 217-227, by embedding the space of all fuzzy subsets into a suitable Banach space.

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Helmholtz Theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus

Pierret, Frédéric, Torres, Delfim F.M.

Hindawi Publishing Corporation

We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associated Hamiltonian. © 2016 Frédéric Pierret and Delfim F. M. Torres.

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Existence and uniqueness of solution for a fractional Riemann-Liouville initial value problem on time scales

Benkhettou, Nadia, Hammoudi, Ahmed, Torres, Delfim F.M.

Elsevier

We introduce the concept of fractional derivative of Riemann-Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value problem on an arbitrary time scale. © 2015 The Authors.

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Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets

Benkhettou, Nadia, Brito da Cruz, Artur M.C., Torres, Delfim F.M.

Wiley

We introduce a nabla, a delta, and a symmetric fractional calculus on arbitrary nonempty closed subsets of the real numbers. These fractional calculi provide a study of differentiation and integration of non-integer order on discrete, continuous, and hybrid settings. Main properties of the new fractional operators are investigated and some fundamental results presented, illustrating the interplay between discrete and continuous behaviors. © 2015 John Wiley & Sons, Ltd.

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A conformable fractional calculus on arbitrary time scales

Benkhettou, Nadia, Hassani, Salima, Torres, Delfim F.M.

Elsevier

A conformable time-scale fractional calculus of order α. ∈]0, 1] is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular case, by choosing α. =. 1. © 2015 The Authors.

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A remark on local fractional calculus and ordinary derivatives

Almeida, Ricardo, Guzowska, Małgorzata, Odzijewicz, Tatiana

De Gruyter Open

In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

ria.ua.pt

Development of synchronized logistics scenarios

Torres, Diamantino, Xambre, Ana Raquel, Teixeira, Leonor

University of Novi Sad, Faculty of Technical Sciences

Internal Logistics is the industrial department responsible, within an organization, for overseeing the information flow and for controlling the physical movements of materials in the warehouse, factory and between workstations. Currently the improvement of Internal Logistics processes is a key factor for delivering products to customers on time and at a competitive price. There is an increasing need for eliminating non-value added tasks and reducing operating costs. In this context, the synchronization of supply routes is very important in order to create standards and improve the use of resources. The purpose of this study is to describe the way Logistics Scenarios were developed in an industrial environment and also to show the importance of Internal Logistics. Interna logistika je industrijski departman koji je odgovoran, unutar organizacije, za nadzor protoka informacija i za kontrolu fizičkog pomeranja materijala u skladištu, fabrici i među radnim stanicama. Trenutno, poboljšanje procesa interne logistike predstavlja ključni faktor isporuke proizvoda potrošačima na vreme i po konkurentskoj ceni. Postoji sve veća potreba za eliminisanje zadataka koji ne donose vrednost i smanjenje operativnih troškova. U ovom kontekstu, sinhronizacija maršuta nabavke je veoma važna kako bi se stvorili standardi i poboljšalo korišćenje resursa. Svrha ove studije je da se opiše način na koji se logistički scenariji razvijaju u industrijskom okruženju, kao i da se pokaže značaj interne logistike.

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Applying value stream mapping to eliminate waste: a case study of an original equipment manufacturer for the automotive industry

Lacerda, António Pedro, Xambre, Ana Raquel, Alvelos, Helena Maria

Taylor & Francis

Since its beginning, lean manufacturing has built a worldwide reputation based on results related to production improvement and cost reduction in several companies. This management philosophy focuses on customer value creation through the elimination of production wastes. Lean methods and techniques have spread their scope from the automotive industry to a wide range of industries and services. This article presents a case study that describes the use of the lean tool value stream mapping in the production process of automotive parts for a major automotive company. At the beginning of the project, relevant data from the process were collected and analysed. Subsequently, the initial process was mapped, the related wastes were identified, and then future processes were mapped and financial results were estimated. The proposals were presented on kaizen meetings, the action plan was discussed and the decision regarding which option to choose was taken. Consequently, the Cycle Time and the level of the workforce were reduced, the process was improved and savings were obtained.

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Analysis and design of a project management information system: practical case in a consulting company

Teixeira, Leonor, Xambre, Ana Raquel, Figueiredo, João, Alvelos, Helena

Elsevier

Nowadays, due to globalization, business diversification and a growing number of different business projects, the need to support people involved in tasks related to project management is becoming increasingly important. Timely and accurate data about projects’ plans, their progress and related costs, are extremely important for project managers and consequently for assuring the success of the project. In this context, Project Management Information Systems (PMIS) are commonly viewed as an important tool for project management. However, this kind of Information Systems (IS) is relatively expensive and therefore out of reach for many small and medium enterprises (SME) that often choose not to use them. As a way to overcome this situation many consulting companies decide to invest in the development of their own PMIS. This paper presents the design process of an Information System for Project Management, whose main purpose is to manage investment projects throughout their life cycle. The system supports all the application process for incentive programs, as well as the documentation and procedures required, and helps to manage the project itself, when it is approved. This solution will thus contribute to the improvement of the performance of the Projects & Incentives’ division of the consulting company, but can also be replicated by other companies that have similar needs.

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A decision support system for the design of cellular manufacturing systems: database conceptualization

Xambre, Ana Raquel, Teixeira, Leonor, Vilarinho, Pedro

Elsevier

In Cellular Manufacturing Systems (CMS) resources are grouped to create independent cells capable of completely processing a set of similar parts. The design of such a system is complex and entails several interconnected problems. The decision process regarding the design of CMS must, therefore, be sustained by solid data and supported by adequate models capable of helping the decision maker in the development of an adequate solution. In this context, a Decision Support System (DSS) for the design of CMS is being developed, and the purpose of this work is to present the conceptualization of the database required for such DSS.

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The minimum cost design of transparent optical networks combining grooming, routing, and wavelength assignment

Agra, Agostinho, Sousa, Amaro de, Doostmohammadi, Mahdi

IEEE

As client demands grow, optical network operators are required to introduce lightpaths of higher line rates in order to groom more demand into their network capacity. For a given fiber network and a given set of client demands, the minimum cost network design is the task of assigning routing paths and wavelengths for a minimum cost set of lightpaths able to groom all client demands. The variant of the optical network design problem addressed in this paper considers a transparent optical network, single hop grooming, client demands of a single interface type, and lightpaths of two line rates. We discuss two slightly different mixed integer linear programming models that define the network design problem combining grooming, routing, and wavelength assignment. Then, we propose a parameters increase rule and three types of additional constraints that, when applied to the previous models, make their linear relaxation solutions closer to the integer solutions. Finally, we use the resulting models to derive a hybrid heuristic method, which combines a relax-and-fix approach with an integer linear programming-based local search approach. We present the computational results showing that the proposed heuristic method is able to find solutions with cost values very close to the optimal ones for a real nation-wide network and considering a realistic fiber link capacity of 80 wavelengths. Moreover, when compared with other approaches used in the problem variants close to the one addressed here, our heuristic is shown to compute solutions, on average, with better cost values and/or in shorter runtimes.

ria.ua.pt

Newton’s problem of minimal resistance under the single-impact assumption

Plakhov, Alexander

IOP Publishing

A parallel flow of non-interacting point particles is incident on a body at rest. When hitting the body’s surface, the particles are reflected elastically. Assuming that each particle hits the body at most once (the single impact condition (SIC)), the force of resistance of the body along the flow direction can be written down in a simple analytical form. The problem of minimal resistance within this model was first considered by Newton (Newton 1687 Philosophiae Naturalis Principia Mathematica) in the class of bodies with a fixed length M along the flow direction and with a fixed maximum orthogonal cross section Ω, under the additional conditions that the body is convex and rotationally symmetric. Here we solve the problem (first stated in Buttazzo et al 1995 Minimum problems over sets of concave functions and related questions Math. Nachr. 173 71–89) for the wider class of bodies satisfying the SIC and with the additional conditions removed. The scheme of solution is inspired by Besicovitch’s method of solving the Kakeya problem (Besicovitch 1963 The Kakeya problem Am. Math. Mon. 70 697– 706). If Ω is a disc, the decrease of resistance as compared with the original Newton problem is more than twofold; the ratio tends to 2 as → M 0 and to 20.25 as →∞ M . We also prove that the infimum of resistance is 0 for a wider class of bodies with both single and double reflections allowed.

ria.ua.pt

Warm little inflaton

Bastero-Gil, Mar, Berera, Arjun, Ramos, Rudnei O., Rosa, João G.

American Physical Society

We show that inflation can naturally occur at a finite temperature T>H that is sustained by dissipative effects, when the inflaton field corresponds to a pseudo Nambu-Goldstone boson of a broken gauge symmetry. Similar to the Little Higgs scenarios for electroweak symmetry breaking, the flatness of the inflaton potential is protected against both quadratic divergences and the leading thermal corrections. We show that, nevertheless, nonlocal dissipative effects are naturally present and are able to sustain a nearly thermal bath of light particles despite the accelerated expansion of the Universe. As an example, we discuss the dynamics of chaotic warm inflation with a quartic potential and show that the associated observational predictions are in very good agreement with the latest Planck results. This model constitutes the first realization of warm inflation requiring only a small number of fields; in particular, the inflaton is directly coupled to just two light fields.

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The use of Web 2.0 tools by students in learning and leisure contexts: a study in a Portuguese institution of higher education

Costa, Carolina, Alvelos, Helena, Teixeira, Leonor

Taylor & Francis

This study analyses and compares the use of Web 2.0 tools by students in both learning and leisure contexts. Data were collected based on a questionnaire applied to 234 students from the University of Aveiro (Portugal) and the results were analysed by using descriptive analysis, paired samples t-tests, cluster analyses and Kruskal–Wallis tests. The results show that the tools most used by students in a learning context are video sharing, social network sites and wikis, and that in a leisure context students use social network sites and video sharing more. The profiles of the groups resulting from the cluster analyses reveal that 42% of the students do not use Web 2.0 tools intensively in either one of the contexts. However, findings from comparing the clusters of both contexts show that students who more frequently use the tools in the leisure context are occasional users in the learning context and vice versa. This study contributes to a better knowledge of the student profiles concerning the use of Web 2.0 tools in learning and leisure contexts which can help teachers direct their strategies to the use of the most appropriate tools, thus improving the success of the teaching/learning process.

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Selecting an open-source framework: a practical case based on software development for sensory analysis

Teixeira, Leonor, Xambre, Ana Raquel, Alvelos, Helena, Filipe, Nelson, Ramos, Ana Luísa

Elsevier

The use of frameworks based on Free Open-Source Software (FOSS) has become a viable alternative in the software development process, when compared with Proprietary Software or Closed Source Software. Given that the quality of Open-Source Software (OSS) products varies widely, the careful evaluation of such frameworks, according to a set of requirements, is an important step in the software development process. This work presents the evaluation of some open-source frameworks in order to find the most suitable one for developing a Decision Support System (DSS) to use in Sensory Analysis. This DSS is being designed to support the evaluation of Tasting Panels in sectors where Sensory Analysis is used to assess products’ quality. The methodology used, based on content analysis in Online Collaborative Spaces, proved to be appropriate to achieve the objectives of this study and therefore, can be extended to select OSS in other areas. Thus, the result of this work is valuable not only for researchers on trends in the OSS area, but also for software developers that intend to implement DSS using FOSS.

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Nível de conhecimento em probabilidade condicionada e independência: um caso de estudo no ensino secundário português

Carvalho, Maria José, Freitas, Adelaide

Comité Latinoamericano de Matemática Educativa

Partindo de duas situações-problema envolvendo probabilidades condicionadas, independência e incompatibilidade, sugere-se quantificar, em paralelo, o grau de desempenho e o grau de rigor de uma resposta usando duas medidas ordinais, ambasem escala de Likert. Uma análise descritiva dessas medidas, numgrupo de 43 alunos do 12.º ano, permitiu estabelecer o nívelde conhecimento desses alunos naqueles conceitos e constatar quenem sempre uma resposta correta é acompanhada de rigor nasua elaboração. Uma análise interpretativa das mesmas respostas permitiu ainda constatar que, no ensino português, persistem conflitos na interpretação e cálculo da probabilidade condicionada e conflitos nas noções de independência e incompatibilidade. O estudo recomenda mais prática na formulação matemáticade enunciados envolvendo probabilidade condicionada e mais ênfase no caracter probabilístico da noção de independência. Partiendo de dos situaciones problemas que refieren a la probabilidad condicional, la independencia y eventos mutuamente excluyentes, se cuantifica, en paralelo, el grado de desempeño y el grado de rigor científico de una respuesta usando dos medidas ordinales en la escala de Likert. Un análisis descriptivo de las medidas, en 43 estudiantes del año terminal del liceo, determinó el grado de conocimiento de los alumnos en los referidos conceptos y apuntó que no siempre una respuesta correcta está descrita con rigor. Del análisis interpretativo de las respuestas se concluye que persisten, enla enseñanza en Portugal, conflictos en la interpretación yen el cálculo de la probabilidad condicionada y en los conceptos de independencia y de eventos mutuamente excluyentes. El estudio recomienda más prácticas involucrando la formulación matemática de problemas de probabilidad condicional y más énfasis en el carácter probabilístico que está asociado al concepto de independencia. Taking two problem-situations involving conditional probability,independence and incompatibility, we suggest the measurements of the performance and the scientific rigor of a response using, in parallel, two ordinal Likert scale measures. Based on the responses given by 43 students in 12th grade (age 17), a descriptive analysis of these measurements was executed in order to evaluate the levels of knowledge of the students in those concepts. The results showed that not always a correct written response comes with rigor. Besides, an interpretative analysis of the same responses confirmed the existence of conflicts inthe teaching of those concepts in Portugal. The conflicts are concerning with the interpretation and the calculation of conditional probabilities and the notions of independence and incompatibility. The present study recommends more practice on the mathematical formulation of statements involving conditional probability and more emphasis on the probabilistic feature of the notion of independence. Partant de deux situations-problème impliquant des probabilités conditionnelles, indépendance et incompatibilité, on suggère dequantifier, en parallèle, le degré de performance et le degréde rigueur d’une réponse utilisant deux mesures ordinales, toutes deux sur l’échelle de Likert. Une analyse descriptive de ces mesures dans un groupe de 43 élèves de Terminal a permis d’établir le niveau de connaissance des élèves, en relation à ces concepts, et de constater qu’une réponse correcte n’est pas toujours accompagnée de rigueur dans son élaboration. Une analyse interprétative de ces réponses a encore permis de voirque, dans l’enseignement portugais, les conflits persistentdans l’interprétation et le calcul des probabilités conditionnelles ainsi que dans les notions d’indépendance et d’incompatibilité. L’étude recommande plus de pratique dans la formulation mathématique des énoncés de probabilités conditionnelles etde mettre davantage l’accent sur le caractère probabiliste associé à la notion d’indépendance.

ria.ua.pt

Wavelet-based clustering of sea level records

Barbosa, S. M., Gouveia, S., Scotto, M. G., Alonso, A. M.

Springer Verlag

The classification of multivariate time series in terms of their corresponding temporal dependence patterns is a common problem in geosciences, particularly for large datasets resulting from environmental monitoring networks. Here a wavelet-based clustering approach is applied to sea level and atmospheric pressure time series at tide gauge locations in the Baltic Sea. The resulting dendrogram discriminates three spatially-coherent groups of stations separating the southernmost tide gauges, reflecting mainly high-frequency variability driven by zonal wind, from the middle-basin stations and the northernmost stations dominated by lower-frequency variability and the response to atmospheric pressure.

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Investigating ozone episodes in Portugal: a wavelet-based approach

Monteiro, A., Gouveia, S., Scotto, M.G., Lopes, J., Gama, C., Feliciano, M., Miranda, A.I.

Springer Verlag

During the summer season, ozone concentrations regularly exceed the legislation limits in the North of Portugal, namely at Douro Norte monitoring station. The origin of such ozone episodes has been widely reported in several studies although uncertainties regarding its origin still remain. This work intends to investigate how the ozone concentrations measured at the Douro Norte nearest stations, located at west and east directions, are related to those measured at Douro Norte by means of coherence and phase transformations methods. The episodes were selected according to the magnitude of the hourly ozone peaks and the occurrence of exceedances of the threshold value at least in two sites. The results point out that 60 % of the selected episodes highlight significant dependence between Douro Norte station and the other two monitoring sites, with different phase signal and a delay range from 2 to 4 h.

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A wavelet-based approach applied to suspended particulate matter time series in Portugal

Cruz, Ana M. J., Alves, Célia, Gouveia, Sónia, Scotto, Manuel G., Freitas, Maria do Carmo, Wolterbeek, Hubert Th

Springer Verlag

This study intends to analyse the particulate matter (PM) levels in Portugal (mainland and islands) throughout a 3-year period. Although a decreasing trend has been observed, the WHO guidelines for the PM10 and PM2.5 annual mean concentrations have been exceeded in all monitoring stations. Most inland urban, rural and suburban sites follow a pronounced seasonal variation with much higher values in winter than in summer. Lower levels and a weak seasonal variability were registered in the two urban background stations of Madeira Island, which are permanently under the influence of clean air masses over the Atlantic. Receiving long-range transported pollution, rural stations located in mountain sites presented an opposite seasonal pattern, with higher levels in summer. Diurnal profiles were also analysed and compared between stations. A mining process was also carried out, consisting in the application of multi-scale wavelet transforms, data pattern identification using cluster analysis and examination of the contribution to the total variance/covariance of the time series per wavelet scale for all stations. Groups of stations exhibiting similar variance/covariance profiles were identified. One group contains urban and rural stations with diurnal and daily time scales. Urban background stations located in the island of Madeira constitute another cluster, corresponding to higher wavelet scales (lower periodicity phenomena). One traffic station in the Oporto metropolitan area was grouped with a suburban/industrial station of central Portugal, suggesting the need for reclassification in what concerns the type of environmental influence.

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A new approach to sex estimation using the mandibular canine index

Silva, Ana Margarida, Pereira, Maria Lurdes, Gouveia, Sónia, Tavares, João Nuno, Azevedo, Álvaro, Caldas, Inês Morais

SAGE Publications

Rao et al.’s mandibular canine index (MCI) is a simple odontometric method which uses the mandibular canine as the key to sex estimation. This index is defined as the ratio between the right canine mesiodistal dimension and the mandibular canine arch width. The aim of this study was to contribute to sex estimation using dental techniques by analysing the MCI efficiency, and to propose a new approach for its use. Measurements were taken from 120 plaster casts (70 females) in the 16–30 year age group. Although statistically significant sexual dimorphism was observed in both the mesiodistal dimension and the mandibular canine arch width, the MCI showed a low accuracy in sex classification (54.2% correct identifications). This accuracy was improved to 64.2% using receiver operating characteristics curve analysis. Yet, despite the better accuracy, these results reinforce the idea that the MCI may not be particularly useful in sex prediction, since it may not reflect the same degree of sexual dimorphism as its absolute measures.

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Binary auto-regressive geometric modelling in a DNA context

Gouveia, Sónia, Scotto, Manuel G., Weiss, Christian H., Ferreira, Paulo Jorge S. G.

Wiley

Symbolic or categorical sequences occur in any contexts and can be characterized, for example, by integer-valued intersymbol distances or binary-valued indicator sequences. The analysis of these numerical sequences often sheds light on the properties of the original symbolic sequences. This work introduces new statistical tools for exploring auto-correlation structure in the indicator sequences, for the specific case of deoxyribonucleic acid (DNA) sequences. It is known that the probability distribution of internucleotide distances of DNA sequences deviates significantly from the distribution obtained by assuming independent random placement (i.e. the geometric distribution) and that the deviations can be used either to discriminate between species or to build phylogenetic trees. To investigate the extent to which auto-correlation structure explains these deviations, the 0–1 indicator sequence of each nucleotide (A, C, G and T) is endowed with a binary auto-regressive (AR) model of optimum order. The corresponding binary AR geometric distribution is derived analytically and compared with the observed internucleotide distance distribution by appropriate goodness-of-fit testing. Results in 34 mitochondrial DNA sequences show that the hypothesis of equal observed/expected frequencies is seldom rejected when a binary AR model is considered instead of independence (76/136 versus 125/136 rejections at the 1% level), in spite of chi-square testing tending to reject for large samples, regardless of how close observed/expected values are. Furthermore, binary AR structure also leads to a median discrepancy reduction of 90% for G, 80% for C, 60% for T and 30% for nucleotide A. Therefore, these models are useful to describe the dependences within a given nucleotide and encourage the development of a model-based framework to compact internucleotide distance information and to understand DNA differences among species further.

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Combinatorial Perron values of trees and bottleneck matrices

Andrade, Enide, Dahl, Geir

Taylor & Francis

The algebraic connectivity $a(G)$ of a graph $G$ is an important parameter, defined as the second smallest eigenvalue of the Laplacian matrix of $G$. If $T$ is a tree, $a(T)$ is closely related to the Perron values (spectral radius) of so-called bottleneck matrices of subtrees of $T$. In this setting we introduce a new parameter called the {em combinatorial Perron value} $rho_c$. This value is a lower bound on the Perron value of such subtrees; typically $rho_c$ is a good approximation to $rho$. We compute exact values of $rho_c$ for certain special subtrees. Moreover, some results concerning $rho_c$ when the tree is modified are established, and it is shown that, among trees with given distance vector (from the root), $rho_c$ is maximized for caterpillars.

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Classification of the regular oriented hypermaps with a prime number of hyperfaces

Breda d’Azevedo, Antonio, Fernandes, Maria Elisa

DMFA Slovenije

Regular oriented hypermaps are triples (G; a; b) consisting of a nite 2-generated group G and a pair a, b of generators of G, where the left cosets of ⟨a⟩, ⟨b⟩ and ⟨ab⟩ describe respectively the hyperfaces, hypervertices and hyperedges. They generalise regular oriented maps (triples with ab of order 2) and describe cellular embeddings of regular hypergraphs on orientable surfaces. In [5] we have classi ed the regular oriented hypermaps with prime number hyperfaces and with no non-trivial regular proper quotients with the same number of hyperfaces (i.e. primer hypermaps with prime number of hyperfaces), which generalises the classi cation of regular oriented maps with prime number of faces and underlying simple graph [13]. Now we classify the regular oriented hypermaps with a prime number of hyperfaces. As a result of this classi cation, we conclude that the regular oriented hypermaps with prime p hyperfaces have metacyclic automorphism groups and the chiral ones have cyclic chirality groups; of these the canonical metacyclic" (i.e. those for which ⟨a⟩ is normal in G) have chirality index a divisor of n (the hyperface valency) and the non canonical metacyclic" have chirality index p. We end the paper by counting, for each positive integer n and each prime p, the number of regular oriented hypermaps with p hyperfaces of valency n.

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Continuity as a computational effect

Neves, Renato, Barbosa, Luis S., Hofmann, Dirk, Martins, Manuel A.

Elsevier

The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes prevalently intertwined with (continuous) physical processes. A possible way to accommodate the latter in component calculi relies on a suitable encoding of continuous behaviour as (yet another) computational effect. This paper introduces such an encoding through a monad which, in the compositional development of hybrid systems, may play a role similar to the one played by 1 + , powerset, and distribution monads in the characterisation of partial, nondeterministic and probabilistic components, respectively. This monad and its Kleisli category provide a universe in which the effects of continuity over (different forms of) composition can be suitably studied.

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Constrained fractional variational problems of variable order

Tavares, Dina, Almeida, Ricardo, Torres, Delfim F. M.

IEEE

Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint. In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational problem subject to a holonomic constraint. We establish necessary optimality conditions in order to determine the minimizers of the fractional problems. The terminal point in the cost integral, as well the terminal state, are considered to be free, and we obtain corresponding natural boundary conditions.

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Compressed sensing for quaternionic signals

Kähler, Uwe, Hartmann, Stefan, Gomes, Narciso

Springer

We study the problem of compressed sensing for quaternionic Fourier matrices as arising in color representation of images. We will show that such matrices are allowing a sparse reconstruction by means of an l1-minimization with high probability. Examples of sparse sampling of color images are provided.

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Numerical null-solutions to iterated Dirac operator on bounded domains

Ku, Min, Kähler, Uwe

Springer

The main purpose of this paper is to study numerical null-solutions to the iterated Dirac operator on bounded domains by using methods of discrete Clifford analysis. First, we study the properties of discrete Euler operators, introduce its inverse operators, and construct a discrete version of the Almansi-type decomposition theorem for the iterated discrete Dirac operator. Then, we give representations of numerical null-solutions to the iterated Dirac operator on a bounded domain in terms of its Taylor series. Finally, in order to illustrate our numerical approach, we present a simple numerical example in form of a discrete approximation of the Stokes’ equation, and show its convergence to the corresponding continuous problem when the lattice constant goes to zero.

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Hospitalização de pessoas idosas: espiritualidade, risco de dependência, quedas e readmissão

Santos, Gorete, Sousa, Liliana, Sá Couto, Pedro

SPPS

Este estudo adota a perspetiva da pessoa idosa (≥65 anos) analisando a influência da hospitalização, em três momentos (admissão, alta e 6 a 12 meses depois), nas variáveis: in/dependência funcional; risco de quebra de cuidados; risco de quedas; espiritualidade. Com base nessas variáveis, organizou-se um modelo preditivo de óbitos. A amostra compreende 250 participantes, 50,4% do sexo feminino. Administrou-se o EASYcare e a Escala da Espiritualidade. Os principais resultados indicam que: i) na admissão, os participantes são mais independentes, ii) na alta e follow-up, são mais dependentes; iii) na admissão, o risco de rutura de cuidados é menor, por comparação com a alta; iv) no follow-u, o risco de queda é menor, enquanto na alta é superior. Os dados sugerem a alta é o momento mais crítico, emergindo alguma recuperação no follow-up. O modelo preditivo de óbitos sugere que os factores protectores de falecimento entre admissão e alta são rendimentos suficientes e ausência de apoio social; os factores de risco de falecimento entre alta e follow-up são idade e risco de queda elevado; os factores protectores de falecimento entre admissão e follow-up são antecedentes clínicos do foro cardíaco. This study adopts the perspective of the elderly people (≥ 65 years old) to examine the influence of hospitalization at three moments (admission, hospital discharge, and follow-up 6 to 12 months later) in the variables: in/dependence; risk of breakdown in care; risk of falls; spirituality. Based on these variables was organized a model predictive of death. The sample comprised 250 participants, 50.4% were female. The EASYcare and Spirituality Scale were administered. The main results are: i) in admission the participants are more independent; ii) in discharge and follow-up are more dependent; iii) in admission the risk of rupture care is lower compared with the discharge; iv) at follow-up the risk of falling is lower, while on discharge is higher. Data suggest that discharge is the most critical moment, emerging some recovery at follow-up. The predictive model of death suggests: protective factors of death between admission and discharge are medium income and lack of social support; risk factors of death between discharge and follow-up are age and high risk of falling; protective factor of death between admission and follow-up is clinical history of cardiac problems.

ria.ua.pt

Ensino personalizado: o MOODLE como ferramenta na busca da aprendizagem significativa

Hannel, Kelly, Lima, José Valdeni de, Descalço, Luís

CINTED - UFRGS

A educação personalizada só é possível após a identificação das dificuldades dos alunos que os impedem de terem os subsunçores necessários para captarem e aprenderem os conteúdos que lhes são ministrados. Com o uso das Tecnologias de Informação e Comunicação (TICs) e dos Ambientes Virtuais de Aprendizagem (AVAs), nesse artigo o MOODLE, são identificados os pontos fortes e fracos de cada aluno, relacionados nesse caso à disciplina de Língua Portuguesa do 6º ano do Ensino Fundamental. Após essa identificação, são indicados conteúdos personalizados visando sanar as possíveis dificuldades de cada indivíduo. Constatou-se que através da indicação de Objetos de Aprendizagem (OAs) que levem em consideração o ritmo e a base de conhecimento individual, pode-se obter melhores resultados para a aprendizagem. Isso ocorre pois o aluno consegue ancorar os novos conteúdos a partir dos seus próprios subsunçores atingindo-se assim a almejada Aprendizagem Significativa.

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Some new properties and applications of a fractional Fourier transform

Rodrigues, M. Manuela, Luchko, Yuri

Ilirias Publications

In this paper, we deal with the fractional Fourier transform in the form introduced a little while ago by the first named author and his coauthors. This transform is closely connected with the Fractional Calculus operators and has been already employed for solving of both the fractional diffusion equation and the fractional Schrödinger equation. In this paper, we continue the investigation of the fractional Fourier transform, and in particular prove some new operational relations for a linear combination of the left- and righthand sided fractional derivatives. As an application of the obtained results, we provide a schema for solving the fractional differential equations with both leftand right-hand sided fractional derivatives without and with delays and give some examples of realization of our method for several fractional differential equations.

ria.ua.pt

Hilbert boundary value problems with Fermionic weight in R^3

Cerejeira, P., Kähler, U., Ku, M.

Springer Verlag

We study the Hilbert boundary value problem with Fermionic weight for the Dirac operator on smooth surfaces of R^3. We give the solution to the Hilbert boundary value problem on the half space and the unit ball of R^3, respectively. Then, we present sufficient and necessary conditions for the solvability of the Hilbert boundary value problem in more general domains with smooth boundary in R^3.

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On the φ-hyperderivative of the ψ-Cauchy-type integral in Clifford analysis

Blaya, Ricardo Abreu, Reyes, Juan Bory, Adán, Alí Guzmán, Kähler, Uwe

Springer

The aim of this paper is to introduce, in the framework of Clifford analysis, the notions of φ-hyperdifferentiability and φ-hyperderivability for ψ- hyperholomorphic functions where (φ,ψ) are two arbitrary orthogonal bases (called structural sets) of a Euclidean space. In this study we will also show how to exchange the integral sign and the φ-hyperderivative of the ψ-Cliffordian Cauchy-type integral. Thereby, we generalize, in a natural way, the corresponding quaternionic antecedent as well as the standard Clifford predecessor.

ria.ua.pt

A short note on cops and robbers playing on total graphs

Dominic, Charles, Cardoso, Domingos M., Witkowski, Lukasz, Witkowski, Marcin

International Knoweledge Press

Cop Robber game is a two player game played on an undirected graph. In this game, the cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be captured. The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G. In this paper, we play the game on the total graph T(G), showing in particular that c(T(G)) ≤ 3 for every planar graph G.

ria.ua.pt

The k-regular induced subgraph problem

Agra, Agostinho, Dahl, Geir, Haufmann, Torkel A., Pinheiro, Sofia J.

Elsevier

We consider the problem of finding a maximum k-regular induced subgraph of a graph G. Theoretical results are established to compare upper bounds obtained from different techniques, including bounds from quadratic programming, Lagrangian relaxation and integer programming. This general problem includes well-known subproblems as particular cases of k. In this paper we focus on two particular cases. The case k=1 which is the maximal cardinality strong-matching and the case of finding the maximal cardinality family of induced cycles (k=2). For each one of the two cases, combinatorial algorithms are presented to solve the problem when graphs have particular structures and polyhedral descriptions of the convex hull of the corresponding feasible set are given. Computational tests are reported to compare the different upper bounds with the optimal values for different values of k, and to test the effectiveness of the inequalities introduced.

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Nonlinear Dirichlet problems with double resonance

Aizicovici, Sergiu, Papageorgiou, Nikolaos S., Staicu, Vasile

American Institute of Mathematical Sciences (AIMS)

We study a nonlinear Dirichlet problem driven by the sum of a $p-$Laplacian ($p>2$) and a Laplacian and which at $pminfty$ is resonant with respect to the spectrum of $left( -triangle_{p},W_{0}^{1,p}left( Omegaright) right) $ and at zero is resonant with respect to the spectrum of $left( -triangle,H_{0}^{1}left( Omegaright) right) $ (double resonance). We prove two multiplicity theorems providing three and four nontrivial solutions respectivelly, all with sign information. Our approach uses critical point theory together with truncation and comparison techniques and Morse theory.

ria.ua.pt

Generalized Fuzzy Euler-Lagrange equations and transversality conditions

Fard, Omid Solaymani, Almeida, Ricardo, Soolaki, Javad, Borzabadi, Akbar Hashemi

De Gruyter

The study of fuzzy fractional variational problems in terms of a fractional Liouville-Caputo derivative is introduced. Necessary optimality conditions for problems of the fuzzy fractional calculus of variations with free end-points are proved, as well as transversality conditions.

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Schwarz Problems for Poly-Hardy Space on the Unit Ball

Kähler, Uwe, Ku, Min, Qian, Tao

Springer Verlag

In this paper we study the Schwarz boundary value problem for the poly-Hardy space defined on the unit ball of higher dimensional Euclidean space R^n. We first discuss the boundary behavior of functions belonging to the poly-Hardy class. Then we construct the Schwarz kernel function, and describe the boundary properties of the Schwarz-type integrable operator. Finally, we study the Schwarz BVP for the Hardy class and the poly-Hardy class on the unit ball of higher dimensional Euclidean space R^n, and obtain explicit expressions of solutions. As an application, the monogenic signals considered for the Hardy spaces defined on the unit sphere are reconstructed when the scalar- and sub-algebra-valued data are given, which is the extension of the analytic signals for the Hardy spaces on the unit circle of the complex plane.

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Spherical Pi-type operators in Clifford analysis and applications

Cheng, Wanqing, Ryan, John, Kähler, Uwe

Springer Verlag

The Pi-operator (Ahlfors–Beurling transform) plays an important role in solving the Beltrami equation. In this paper we define two Pi-operators on the n-sphere. The first spherical Pi-operator is shown to be an L_2 isometry up to isomorphism. To improve this, with the help of the spectrum of the spherical Dirac operator, the second spherical Pi-operator is constructed as an isometric L_2-operator over the sphere. Some analogous properties for both Pi-operators are also developed. We also study the applications of both spherical Pi-operators to the solution of the spherical Beltrami equations.

ria.ua.pt

Inflation in non-minimal matter-curvature coupling theories

Rosa, João Pedro Trancoso Gomes, Gomes, Cláudio, Bertolami, Orfeu

IOP Publishing

We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions for some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.

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Superradiance in the sky

Rosa, João G.

American Physical Society

We discuss the conditions under which plane electromagnetic and gravitational waves can be amplified by a rotating black hole due to superradiant scattering. We show, in particular, that amplification can occur for low-frequency waves with an incidence angle parametrically close to 0 (or π) with respect to the black hole spin axis and with a parametrically small left (or right) polarization. This is the case of the radiation emitted by a spinning electric/magnetic dipole or gravitational quadrupole orbiting a black hole companion at large radius and co-rotating with the latter. This can yield observable effects of superradiance, for example, in neutron star-stellar mass black hole binaries, as well as in triple systems composed by a compact binary orbiting a central supermassive black hole. Due to superradiance, the total source luminosity in these systems exhibits a characteristic orbital modulation that may lead to significant observational signatures, thus paving the way for testing, in the near future, one of the most peculiar predictions of general relativity.

ria.ua.pt

Static Einstein-Maxwell Magnetic Solitons and Black Holes in an Odd Dimensional AdS Spacetime

Blazquez-Salcedo, J. L., Kunz, J., Navarro-Lerida, F., Radu, E.

MDPI (Multidisciplinary Digital Publishing Institute)

We construct a new class of Einstein-Maxwell static solutions with a magnetic field in D-dimensions (with D >= 5 an odd number), approaching at infinity a globally Anti-de Sitter (AdS) spacetime. In addition to the mass, the new solutions possess an extra-parameter associated with a non-zero magnitude of the magnetic potential at infinity. Some of the black holes possess a non-trivial zero-horizon size limit, which corresponds to a solitonic deformation of the AdS background.

ria.ua.pt

Iron K alpha line of Kerr black holes with Proca hair

Zhou, M. L., Bambi, C., Herdeiro, C. A. R., Radu, E

American Physical Society

We continue our study on the capabilities of present and future x-ray missions to test the nature of astrophysical black hole candidates via x-ray reflection spectroscopy and distinguish Kerr black holes from other solutions of 4-dimensional Einstein's gravity in the presence of a matter field. Here we investigate the case of Kerr black holes with Proca hair [1]. The analysis of a sample of these configurations suggests that even extremely hairy black holes can mimic the iron line profile of the standard Kerr black holes, and, at least for the configurations of our study, we find that current x-ray missions cannot distinguish these objects from Kerr black holes. This contrasts with our previous findings for the case of Kerr black holes with scalar (rather than Proca) hair [2], even though such comparison may be biased by the limited sample. Future x-ray missions can detect the presence of Proca hair, but a theoretical knowledge of the expected intensity profile (currently missing) can be crucial to obtain strong constraints.

ria.ua.pt

Shadows of Einstein-dilaton-Gauss-Bonnet black holes

Cunha, P. V. P., Herdeiro, C. A. R., Kleihaus, B., Kunz, J., Radu, E.

Elsevier

We study the shadows of the fully non-linear, asymptotically flat Einstein-dilaton-Gauss-Bonnet (EdGB) black holes (BHs), for both static and rotating solutions. We find that, in all cases, these shadows are smaller than for comparable Kerr BHs, i.e. with the same total mass and angular momentum under similar observation conditions. In order to compare both cases we provide quantitative shadow parameters, observing in particular that the differences in the shadows mean radii are never larger than the percent level. Therefore, generically, EdGB BHs cannot be excluded by (near future) shadow observations alone. On the theoretical side, we find no clear signature of some exotic features of EdGB BHs on the corresponding shadows, such as the regions of negative (Komar, say) energy density outside the horizon. We speculate that this is due to the fact that the Komar energy interior to the light rings (or more precisely, the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane) is always smaller than the ADM mass, and consequently the corresponding shadows are smaller than those of comparable Kerr BHs. The analysis herein provides a clear example that it is the light ring impact parameter, rather than its "size", that determines a BH shadow. (C) 2017 The Authors. Published by Elsevier B.V.

ria.ua.pt

Charged rotating black holes in Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant

Blazquez-Salcedo, J. L., Kunz, J., Navarro-Lerida, F., Radu, E.

American Physical Society

We consider rotating black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and a generic value of the Chern-Simons coupling constant.. Using both analytical and numerical techniques, we focus on cohomogeneity-1 configurations, with two equal-magnitude angular momenta, which approach at infinity a globally anti-de Sitter background. We find that the generic solutions share a number of basic properties with the known Cvetic, Lu, and Pope black holes which have lambda = 1. New features occur as well; for example, when the Chern-Simons coupling constant exceeds a critical value, the solutions are no longer uniquely determined by their global charges. Moreover, the black holes possess radial excitations which can be labelled by the node number of the magnetic gauge potential function. Solutions with small values of. possess other distinct features. For instance, the extremal black holes there form two disconnected branches, while not all near-horizon solutions are associated with global solutions.

ria.ua.pt

Remarks on the Taub-NUT solution in Chern-Simons modified gravity

Brihaye, Y., Radu, E.

Elsevier

We discuss the generalization of the NUT spacetime in General Relativity (GR) within the framework of the (dynamical) Einstein-Chern-Simons (ECS) theory with a massless scalar field. These configurations approach asymptotically the NUT spacetime and are characterized by the 'electric' and 'magnetic' mass parameters and a scalar 'charge'. The solutions are found both analytically and numerically. The analytical approach is perturbative around the Einstein gravity background. Our results indicate that the ECS configurations share all basic properties of the NUT spacetime in GR. However, when considering the solutions inside the event horizon, we find that in contrast to the GR case, the spacetime curvature grows (apparently) without bound. (C) 2016 The Authors. Published by Elsevier B.V.

ria.ua.pt

The rise and fall of V-functors

Clementino, Maria Manuel, Hofmann, Dirk

Elsevier

In this article we study function spaces (rise) and descent (fall) in quantale-enriched categories, paying particular attention to enrichment in the non-negative reals, the quantale of distribution functions and the unit interval equipped with a continuous t-norm.

ria.ua.pt

Applying differential dynamic logic to reconfigurable biological networks

Figueiredo, Daniel, Martins, Manuel A., Chaves, Madalena

Elsevier

Qualitative and quantitative modeling frameworks are widely used for analysis of biological regulatory networks, the former giving a preliminary overview of the system’s global dynamics and the latter pro- viding more detailed solutions. Another approach is to model biological regulatory networks as hybrid systems, i.e., systems which can display both continuous and discrete dynamic behaviors. Actually, the development of synthetic biology has shown that this is a suitable way to think about biological systems, which can often be constructed as networks with discrete controllers, and present hybrid behaviors. In this paper we discuss this approach as a special case of the reconfigurability paradigm, well studied in Computer Science (CS). In CS there are well developed computational tools to reason about hybrid systems. We argue that it is worth applying such tools in a biological context. One interesting tool is differential dynamic logic ( d L ), which has recently been developed by Platzer and applied to many case-studies. In this paper we discuss some simple examples of biological regulatory networks to illustrate how d L can be used as an alternative, or also as a complement to methods already used.

ria.ua.pt

An epidemic model for cholera with optimal control treatment

Lemos-Paião, A. P., Silva, C. J., Torres, D. F. M.

This research was supported by the Portuguese Foundation for Science and Technology (FCT) within projects UID/MAT/04106/2013 (CIDMA) and PTDC/EEI-AUT/2933/2014 (TOCCATA), funded by Project 3599 - Promover a Produção Científica e Desenvolvimento Tecnológico e a Constituição de Redes Temáticas and FEDER funds through COMPETE 2020, Programa Operacional Competitividade e Internacionalização (POCI). Lemos-Paião is also supported by the Ph.D. fellowship PD/BD/114184/2016; Silva by the post-doc fellowship SFRH/BPD/72061/2010. We propose a mathematical model for cholera with treatment through quarantine. The model is shown to be both epidemiologically and mathematically well posed. In particular, we prove that all solutions of the model are positive and bounded; and that every solution with initial conditions in a certain meaningful set remains in that set for all time. The existence of unique disease-free and endemic equilibrium points is proved and the basic reproduction number is computed. Then, we study the local asymptotic stability of these equilibrium points. An optimal control problem is proposed and analyzed, whose goal is to obtain a successful treatment through quarantine. We provide the optimal quarantine strategy for the minimization of the number of infectious individuals and bacteria concentration, as well as the costs associated with the quarantine. Finally, a numerical simulation of the cholera outbreak in the Department of Artibonite (Haiti), in 2010, is carried out, illustrating the usefulness of the model and its analysis. © 2016 Elsevier B.V.

ria.ua.pt

A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde

Silva, Cristiana J., Torres, Delfim F.M.

Elsevier

We propose a new mathematical model for the transmission dynamics of the human immunodeficiency virus (HIV). Global stability of the unique endemic equilibrium is proved. Then, based on data provided by the “Progress Report on the AIDS response in Cape Verde 2015”, we calibrate our model to the cumulative cases of infection by HIV and AIDS from 1987 to 2014 and we show that our model predicts well such reality. Finally, a sensitivity analysis is done for the case study in Cape Verde. We conclude that the goal of the United Nations to end the AIDS epidemic by 2030 is a nontrivial task.

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Variational calculus with conformable fractional derivatives

Lazo, Matheus J., Torres, Delfim F. M.

IEEE

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether U+02BC s symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

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Galerkin spectral method for the fractional nonlocal thermistor problem

Sidi Ammi, M. R., Torres, D. F. M.

Elsevier

We develop and analyse a numerical method for the time-fractional nonlocal thermistor problem. By rigorous proofs, some error estimates in different contexts are derived, showing that the combination of the backward differentiation in time and the Galerkin spectral method in space leads, for an enough smooth solution, to an approximation of exponential convergence in space. © 2016 Elsevier Ltd

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Non-differentiable solutions for local fractional nonlinear riccati differential equations

Yang, Xiao-Jun, Srivastava, H. M., Torres, Delfim F. M., Zhangy, Yudong

IOS Press

We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFNRDE with constant coefficients is considered and non-differentiable solutions for special cases obtained.

ria.ua.pt

Optimal spraying in biological control of pests

Silva, C. J., Torres, D. F. M., Venturino, E.

EDP Sciences

We use optimal control theory with the purpose of finding the best spraying policy with the aim of at least to minimize and possibly to eradicate the number of parasites, i.e., the prey for the spiders living in an agroecosystems. Two different optimal control problems are posed and solved, and their implications discussed. © EDP Sciences, 2017.

ria.ua.pt

Variational Problems Involving a Caputo-Type Fractional Derivative

Almeida, Ricardo

Springer

We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real parameter ρ. We present sufficient and necessary conditions of first and second order to determine the extremizers of a functional. The cases of integral and holomonic constraints are also considered.

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On Optimal Properties of Special Nonlinear and Semi-infinite Problems Arising in Parametric Optimization

Kostyukova, Olga, Tchemisova, Tatiana, Kurdina, Maryia

International Academic Press

We consider a special Nonlinear Programming problem depending on integer parameters. For some values of these parameters (the ``right'' ones), this problem satisfies certain properties used in study of differential properties of optimal solutions in parametric Semi-Infinite Programming. We deduce the conditions guaranteing the existence of the ``right'' parameters values, and propose an algorithm for their determination. The conditions and the algorithm are essentially based on properties of a related linear-quadratic semi-infinite problem.

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A study of one class of NLP problems arising in parametric Semi-Infinite Programming

Kostyukova, O. I., Tchemisova, Tatiana, Kurdina, Maryia

Taylor & Francis

The paper deals with a nonlinear programming (NLP) problem that depends on a finite number of integers (parameters). This problem has a special form, and arises as an auxiliary problem in study of solutions' properties of parametric semi-infinite programming (SIP) problems with finitely representable compact index sets. Therefore, it is important to provide a deep study of this NLP problem and its properties w.r.t. the values of the parameters. We are especially interested in the case when optimal solutions of the NLP problem satisfy certain properties due to some specific requirements arising in parametric SIP. We establish the values of the parameters for which optimal solutions of the corresponding NLP problem fulfil the needed properties, and suggest an algorithm that determines the right values of the parameters. An example is proposed to illustrate the application of the algorithm.

ria.ua.pt

Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

Kostyukova, O., Tchemisova, Tatiana

Springer

In the present paper, we analyze a class of convex Semi-Infinite Programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems

ria.ua.pt

A Generator of Nonregular Semidefinite Programming Problems

Macedo, Eloísa, Tchemisova, Tatiana

Springer

Regularity is an important property of optimization problems. Various notions of regularity are known from the literature, being defined for different classes of problems. Usually, optimization methods are based on the optimality conditions, that in turn, often suppose that the problem is regular. Absence of regularity leads to theoretical and numerical difficulties, and solvers may fail to provide a trustworthy result. Therefore, it is very important to verify if a given problem is regular in terms of certain regularity conditions and in the case of nonregularity, to apply specific methods. On the other hand, in order to test new stopping criteria and the computational behaviour of new methods, it is important to have an access to sets of reasonably-sized nonregular test problems. The paper presents a generator that constructs nonregular Semidefinite Programming (SDP) instances with prescribed irregularity degrees and a database of nonregular test problems created using this generator. Numerical experiments using popular SDP solvers on the problems of the database are carried out and permit to conclude that the most popular SDP solvers are not efficient when applied to nonregular problems.

ria.ua.pt

Special issue: optimization in the natural sciences

Tchemisova, Tatiana, Freitas, Adelaide, Plakhov, Alexander, Weber, Gerhard-Wilhelm

Taylor & Francis

Editorial of the Special Issue dedicated to EURO mini-conference "Optimization in the Natural Sciences".

ria.ua.pt

Applications of Estrada Indices and Energy to a family of compound graphs

Andrade, Enide, Pizarro, Pamela, Robbiano, Maria, San Martin, B., Tapia, Katherine

Elsevier

To track the gradual change of the adjacency matrix of a simple graph $mathcal{G}$ into the signless Laplacian matrix, V. Nikiforov in cite{NKF} suggested the study of the convex linear combination $A_{alpha }$ (textit{$alpha$-adjacency matrix}), [A_{alpha }left( mathcal{G}right)=alpha Dleft( mathcal{G}right) +left( 1-alpha right) Aleft( mathcal{G}right),] for $alpha in left[ 0,1right]$, where $Aleft( mathcal{G}right)$ and $Dleft( mathcal{G}right)$ are the adjacency and the diagonal vertex degrees matrices of $mathcal{G}$, respectively. Taking this definition as an idea the next matrix was considered for $a,b in mathbb{R}$. The matrix $A_{a,b}$ defined by $$ A_{a,b}left( mathcal{G}right) =a Dleft( mathcal{G}right) + b Aleft(mathcal{G}right),$$ extends the previous $alpha$-adjacency matrix. This matrix is designated the textit{$(a,b)$-adjacency matrix of $mathcal{G}$}. Both adjacency matrices are examples of universal matrices already studied by W. Haemers. In this paper, we study the $(a,b)$-adjacency spectra for a family of compound graphs formed by disjoint balanced trees whose roots are identified to the vertices of a given graph. In consequence, new families of cospectral (adjacency, Laplacian and signless Laplacian) graphs, new hypoenergetic graphs (graphs whose energy is less than its vertex number) and new explicit formulae for Estrada, signless Laplacian Estrada and Laplacian Estrada indices of graphs were obtained. Moreover, sharp upper bounds of the above indices for caterpillars, in terms of length of the path and of the maximum number of its pendant vertices, are given.

ria.ua.pt

Realizable lists via the spectra of structured matrices

Manzaneda, Cristina, Andrade, Enide, Robbiano, Maria

Elsevier

A square matrix of order $n$ with $ngeq 2$ is called a textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative matrices are studied. In particular, spectral results for matrices partitioned into $2$-by-$2$ symmetric blocks are presented and, using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed. Guo perturbations on given lists are exhibited.

ria.ua.pt

Uniqueness in potential scattering with reduced data

Lakshtanov, Evgeny, Vainberg, Boris

Taylor & Francis

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value of the energy. We show that these data determine the bounded potential uniquely.

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A test for the existence of exceptional points in the Faddeev scattering problem

Lakshtanov, Evgeny, Vainberg, Boris

Springer

Exceptional points are values of the spectral parameter for which the homogeneous Faddeev scattering problem has a nontrivial solution. We formulate a criterion for existence of exceptional points that belong to a given path. For this, we use measurements at the endpoints of the path. We also study the existence or absence of exceptional points for small perturbations of conductive potentials of arbitrary shape and show that problems with absorbing potentials do not have exceptional points in a neighborhood of the origin.

ria.ua.pt

Intelligent tutorial system based on personalized system of instruction to teach or remind mathematical concepts

Paiva, Rui C., Ferreira, Milton, Frade, M. M.

John Wiley & Sons Ltd

The growth of the higher education population and different school paths to access an academic degree has increased the heterogeneity of students inside the classroom. Consequently, the effectiveness of traditional teaching methods has reduced. This paper describes the design, development, implementation and evaluation of a tutorial system (TS) to improve student's engagement in higher mathematics. The TS design was based on the Personalized System of Instruction of the Mastery Learning pedagogical approach and can be implemented in any higher education course with mathematics needs. The TS consists on small self-paced modularized units of educational contents, including tutorial videos, notes and formative e-assessment with personalized feedback. The TS ensures that the student is only allowed to proceed to the next unit after he or she achieves the required mastery criterion of the current unit. The TS was implemented in the Quantitative Methods course of an undergraduate degree and received good acceptance from students. It was also recognized that TS contributed to learning and engagement with the discipline. Through an experimental research experience it has been shown that the imposition of restrictions on the advance to the next level by a mastery criterion leads to a significant improvement in student’s engagement and performance.

ria.ua.pt

Combined ship routing and inventory management in the salmon farming industry

Agra, Agostinho, Christiansen, Marielle, Ivarsoy, Kristine S., Solhaug, Ida Elise, Tomasgard, Asgeir

Springer

We consider a maritime inventory routing problem for Norway's largest salmon farmer both producing the feed at a production factory and being responsible for fish farms located along the Norwegian coast. The company has bought two new ships to transport the feed from the factory to the fish farms and is responsible for the routing and scheduling of the ships. In addition, the company has to ensure that the feed at the production factory as well as at the fish farms is within the inventory limits. A mathematical model of the problem is presented, and this model is reformulated to improve the efficiency of the branch-and-bound algorithm and tightened with valid inequalities. To derive good solutions quickly, several practical aspects of the problem are utilized and two matheuristics developed. Computational results are reported for instances based on the real problem of the salmon farmer.

ria.ua.pt

A decomposition approach for the p-median problem on disconnected graphs

Agra, Agostinho, Cerdeira, Jorge Orestes, Requejo, Cristina

Elsevier

The p-median problem seeks for the location of p facilities on the vertices (customers) of a graph to minimize the sum of transportation costs for satisfying the demands of the customers from the facilities. In many real applications of the p-median problem the underlying graph is disconnected. That is the case of p-median problem defined over split administrative regions or regions geographically apart (e.g. archipelagos), and the case of problems coming from industry such as the optimal diversity management problem. In such cases the problem can be decomposed into smaller p-median problems which are solved in each component k for different feasible values of pk, and the global solution is obtained by finding the best combination of pk medians. This approach has the advantage that it permits to solve larger instances since only the sizes of the connected components are important and not the size of the whole graph. However, since the optimal number of facilities to select from each component is not known, it is necessary to solve p-median problems for every feasible number of facilities on each component. In this paper we give a decomposition algorithm that uses a procedure to reduce the number of subproblems to solve. Computational tests on real instances of the optimal diversity management problem and on simulated instances are reported showing that the reduction of subproblems is significant, and that optimal solutions were found within reasonable time.

ria.ua.pt

Feasibility check for the distance geometry problem: an application to molecular conformations

Agra, Agostinho, Figueiredo, Rosa, Lavor, Carlile, Maculan, Nelson, Pereira, António, Requejo, Cristina

Wiley

The distance geometry problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, including two integer programming (IP) models and a constraint programming (CP) approach, are presented to test the feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities, and the CP approach is improved using an algorithm to perform a domain reduction. The main motivation for this work is to derive new pruning devices within branch-and-prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP. A computational study based on a set of small-sized instances from molecular conformations is reported. This study compares the running times of the different approaches to check feasibility.

ria.ua.pt

MIP approaches for the integrated berth allocation and quay crane assignment and scheduling problem

Agostinho Agra, Oliveira, Maryse

Elsevier

In this paper we consider an integrated berth allocation and quay crane assignment and scheduling problem motivated by a real case where a heterogeneous set of cranes is considered. A first mathematical model based on the {it relative position formulation} (RPF) for the berth allocation aspects is presented. Then, a new model is introduced to avoid the big-M constraints included in the RPF. This model results from a discretization of the time and space variables. For the new discretized model several enhancements, such as valid inequalities, are introduced. In order to derive good feasible solutions, a rolling horizon heuristic (RHH) is presented. A branch and cut approach that uses the enhanced discretized model and incorporates the upper bounds provided by the RHH solution is proposed. Computational tests are reported to show (i) the quality of the linear relaxation of the enhanced models; (ii) the effectiveness of the exact approach to solve to optimality a set of real instances; and (iii) the scalability of the RHH based on the enhanced mathematical model which is able to provide good feasible solutions for large size instances.

ria.ua.pt

Fundamental solution of the multi-dimensional time fractional telegraph equation

Ferreira, Milton dos Santos, Rodrigues, Maria Manuela Fernandes, Vieira, Nelson Felipe Loureiro

de Gruyter

In this paper we study the fundamental solution (FS) of the multidimensional time-fractional telegraph equation with time-fractional derivatives of orders $alpha in ]0,1]$ and $beta in ]1,2]$ in the Caputo sense. Using the Fourier transform we obtain an integral representation of the FS expressed in terms of a multivariate Mittag-Leffler function in the Fourier domain. The Fourier inversion leads to a double Mellin-Barnes type integral representation and consequently to a H-function of two variables. An explicit series representation of the FS, depending on the parity of the dimension, is also obtained. As an application, we study a telegraph process with Brownian time. Finally, we present some moments of integer order of the FS, and some plots of the FS for some particular values of the dimension $n$ and of the fractional parameters $alpha$ and $beta$.

ria.ua.pt

The modified Schultz index of graph operations

Carvalho, Paula, Rama, Paula

Given a simple and connected graph G with vertex set V , denoting by dG(u) the degree of a vertex u and dG(u, v) the distance of two vertices, the modified Schultz index of G is given by S ∗ P (G) = {u,v}⊆V dG(u) dG(v) dG(u, v), where the summation goes over all non ordered pairs of vertices of G. In this paper we consider some graph operations, namely cartesian product, complete product, composition and subdivision, and we obtain explicit formulae for the modified Schultz index of a graph in terms of the number of vertices and edges as well as some other topological invariants such as the Wiener index, the Schultz index and the first and second Zagreb indices.

ria.ua.pt

Uniqueness in the Inverse Conductivity Problem for Complex-Valued Lipschitz Conductivities in the Plane

Lakshtanov, Evgeny, Vainberg, Boris, Tejero, Jorge

Society for Industrial and Applied Mathematics

We consider the inverse impedance tomography problem in the plane. Using Bukhgeim's scattering data for the Dirac problem, we prove that the conductivity is uniquely determined by the Dirichlet-to-Neuman map. Read More: http://epubs.siam.org/doi/abs/10.1137/17M1120981

ria.ua.pt

Recovery of L p-potential in the plane

Lakshtanov, Evgeny, Vainberg, Boris

De Gruyter

An inverse problem for the two-dimensional Schrödinger equation with Lp-potential, p>1, is considered. Using the dbar-method, the potential is recovered from the Dirichlet-to-Neumann map on the boundary of a domain containing the support of the potential. We do not assume that the potential is small or that the Faddeev scattering problem does not have exceptional points. The paper contains a new estimate on the Faddeev Green function that immediately implies the absence of exceptional points near the origin and infinity when the potential v belongs to Lp.

ria.ua.pt

Recovery of interior eigenvalues from reduced near field data

Lakshtanov, Evgeny, Vainberg, Boris

Taylor & Francis

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The domain can be arbitrarily small but fixed.The scattered waves are measured on the same surface. An effective procedure is suggested for recovery of interior eigenvalues by these data.

ria.ua.pt

MDS 2D convolutional codes with optimal 1D horizontal projections

Almeida, Paulo J., Napp, Diego, Pinto, Raquel

Springer Link

Two dimensional (2D) convolutional codes is a class of codes that generalizes standard one-dimensional (1D) convolutional codes in order to treat two dimensional data. In this paper we present a novel and concrete construction of 2D convolutional codes with the particular property that their projection onto the horizontal lines yield optimal [in the sense of Almeida et al. (Linear Algebra Appl 499:1–25, 2016)] 1D convolutional codes with a certain rate and certain Forney indices. Moreover, using this property we show that the proposed constructions are indeed maximum distance separable, i.e., are 2D convolutional codes having the maximum possible distance among all 2D convolutional codes with the same parameters. The key idea is to use a particular type of superregular matrices to build the generator matrix.

ria.ua.pt

A Gronwall inequality for a general Caputo fractional operator

Almeida, Ricardo

Ele-Math

In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo–Hadamard fractional derivative operators. We study some properties of the operator, namely we prove that it is the inverse operation of a generalized fractional integral. A relation between this operator and a Riemann–Liouville type is established. We end with a fractional Gronwall inequality type, which is useful to compare solutions of fractional differential equations.

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Optimality conditions for fractional variational problems with free terminal time

Almeida, Ricardo

American Institute of Mathematical Sciences

This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler–Lagrange equations are established for the fundamental problem and when in presence of an integral constraint. A Legendre condition, which is a second-order necessary condition, is also obtained. Other cases, such as the infinite horizon problem, the problem with delays in the Lagrangian, and the problem with high-order derivatives, are considered. Finally, a necessary condition for the optimal fractional order to satisfy is proved.

ria.ua.pt

Fractional Herglotz variational problem of variable order

Tavares, Dina, Almeida, Ricardo, Torres, Delfim F.M.

American Institute of Mathematical Sciences (AIMS)

We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved. Two different cases are considered: the fundamental problem, with one independent variable, and the general case, with several independent variables. We end with some illustrative examples of the results of the paper.

ria.ua.pt

Strong controlled-invariance of behavioural nD systems

Pereira, Ricardo, Rocha, Paula

Taylor & Francis

In this paper we give a stronger version of the notion of behavioral controlled invariance introduced in (Pereira & Rocha, 2017) in the context of regular partial interconnections. In such interconnections, the variables are divided into two sets: the variables to-be-controlled and the variables on which it is allowed to enforce restrictions (control variables); moreover, regularity means that the restrictions of the controller do not overlap with the ones already implied by the laws of the original behavior. A complete characterization of strong controlled invariance for nD behaviors is derived making use of a special controller behavior known as the canonical controller.

ria.ua.pt

An operational method to solve fractional differential equations

Rodrigues, M. M., Vieira, N.

Seenith Sivasundaram

In this paper, we present an operational method for solving two fractional equations, namely, the Legendre and the Laguerre equations. Based on operational approach for the Laplace and Mellin, we obtain a particular solution as a generalized power series for both equations, where the fractional derivatives are defined in the Riemann-Liouville sense. We prove the existence and uniqueness of solutions via Banach fix point theorem.

ria.ua.pt

A Riemannn surface approach for diffraction from rational wedges

Ehrhardt, Torsten, Nolasco, Ana Paula, Speck, Frank-Olme

Element

This paper aims at the explicit analytical representation of acoustic, electromagnetic or elastic, time-harmonic waves diffracted from wedges in R-3 in a correct setting of Sobolev spaces. Various problems are modelled by Dirichlet or Neumann boundary value problems for the 2D Helmholtz equation with complex wave number. They have been analyzed before by several methods such as the Malinzhinets method using Sommerfeld integrals, the method of boundary integral equations from potential theory or Mellin transformation techniques. These approaches lead to results which are particularly useful for asymptotic and numerical treatment. Here we develop new representation formulas of the solutions which are based upon the solutions to Sommerfeld diffraction problems. We make use of symmetry properties, which require a generalization of these formulas to Riemann surfaces in order to cover arbitrary rational angles of the wedge. The approach allows us to prove well-posedness in suitable Sobolev spaces and to obtain explicit solutions in a new, perhaps surprising, form provided the angle is rational, i.e., alpha = pi m/n where m, n is an element of N.

ria.ua.pt

A matrix approach to Sheffer polynomials

Aceto, Lídia, Cação, Isabel

Elsevier

This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a special subdiagonal matrix having as nonzero entries positive integer numbers, whose exponential coincides with the well-known Pascal matrix. In fact, Sheffer polynomials may be expressed in terms of two matrices both connected to it. As we will show, one of them is strictly related to Appell polynomials, while the other is linked to a binomial type sequence. Consequently, different types of Sheffer polynomials correspond to different choices of these two matrices.

ria.ua.pt

Mixture models of geometric distributions in genomic analysis of inter-nucleotide distances

Freitas, A., Afreixo, V., Escudeiro, S.

International Academic Press

The mapping defined by inter-nucleotide distances (InD) provides a reversible numerical representation of the primary structure of DNA. If nucleotides were independently placed along the genome, a finite mixture model of four geometric distributions could be fitted to the InD where the four marginal distributions would be the expected distributions of the four nucleotide types. We analyze a finite mixture model of geometric distributions (f2), with marginals not explicitly addressed to the nucleotide types, as an approximation to the InD. We use BIC in the composite likelihood framework for choosing the number of components of the mixture and the EM algorithm for estimating the model parameters. Based on divergence profiles, an experimental study was carried out on the complete genomes of 45 species to evaluate f2. Although the proposed model is not suited to the InD, our analysis shows that divergence profiles involving the empirical distribution of the InD are also exhibited by profiles involving f2. It suggests that statistical regularities of the InD can be described by the model f2. Some characteristics of the DNA sequences captured by the model f2 are illustrated. In particular, clusterings of subgroups of eukaryotes (primates, mammalians, animals and plants) are detected.

ria.ua.pt

What is the best fractional derivative to fit data?

Almeida, Ricardo

University of Belgrade

The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the order of the fractional differential equation that better describes the experimental data, for different types of fractional derivatives.

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Lexicographic polynomials of graphs and their spectra

Cardoso, Domingos M., Carvalho, Paula, Rama, Paula, Simic, Slobodan K., Stanic, Zoran

University of Belgrade

For a (simple) graph $H$ and non-negative integers $c_0,c_1,ldots,c_d$ ($c_d neq 0$), $p(H)=sum_{k=0}^d{c_k cdot H^k}$ is the lexicographic polynomial in $H$ of degree $d$, where the sum of two graphs is their join and $c_k cdot H^k$ is the join of $c_k$ copies of $H^k$. The graph $H^k$ is the $k$th power of $H$ with respect to the lexicographic product ($H^0 = K_1$). The spectrum (if $H$ is regular) and the Laplacian spectrum (in general case) of $p(H)$ are determined in terms of the spectrum of $H$ and~$c_k$'s. Constructions of infinite families of cospectral or integral graphs are also announced.

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Sensitivity of directional technical inefficiency measures to the choice of the direction vector: a simulation study

Macedo, Pedro, Silva, Elvira

Economics Bulletin

The purpose of this note is to provide new insights on the sensitivity of technical inefficiency scores, estimated using a directional distance function with small samples and the presence of outliers, to the choice of the direction vector. A simulation study with a geometric illustration is conducted considering several direction vectors. To the best of authors' knowledge, this is the first simulation work comparing 16 direction vectors, some of which are often employed in empirical studies. The four directional vectors that consistently provide the best results are identified and used in the empirical application discussed in this study.

ria.ua.pt

Pain, pain intensity and pain disability in high school students are differently associated with physical activity, screening hours and sleep

Silva, A. G., Sa-Couto, P., Queirós, A., Neto, M., Rocha, N. P.

Springer

Background: Studies exploring the association between physical activity, screen time and sleep and pain usually focus on a limited number of painful body sites. Nevertheless, pain at different body sites is likely to be of different nature. Therefore, this study aims to explore and compare the association between time spent in self-reported physical activity, in screen based activities and sleeping and i) pain presence in the last 7-days for 9 different body sites; ii) pain intensity at 9 different body sites and iii) global disability. Methods: Nine hundred sixty nine students completed a questionnaire on pain, time spent in moderate and vigorous physical activity, screen based time watching TV/DVD, playing, using mobile phones and computers and sleeping hours. Univariate and multivariate associations between pain presence, pain intensity and disability and physical activity, screen based time and sleeping hours were investigated. Results: Pain presence: sleeping remained in the multivariable model for the neck, mid back, wrists, knees and ankles/feet (OR 1.17 to 2.11); moderate physical activity remained in the multivariate model for the neck, shoulders, wrists, hips and ankles/feet (OR 1.06 to 1.08); vigorous physical activity remained in the multivariate model for mid back, knees and ankles/feet (OR 1.05 to 1.09) and screen time remained in the multivariate model for the low back (OR = 2.34. Pain intensity: screen time and moderate physical activity remained in the multivariable model for pain intensity at the neck, mid back, low back, shoulder, knees and ankles/feet (Rp2 0.02 to 0.04) and at the wrists (Rp2 = 0.04), respectively. Disability showed no association with sleeping, screen time or physical activity. Conclusions: This study suggests both similarities and differences in the patterns of association between time spent in physical activity, sleeping and in screen based activities and pain presence at 8 different body sites. In addition, they also suggest that the factors associated with the presence of pain, pain intensity and pain associated disability are different.

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Chronic pain in high school students is associated with physical activity and sleeping hours but not with screen time

Silva, A. G., Couto, P. S., Queiros, A., Neto, M., Rocha, N. P.

Degruyter

Existing studies on the association between physical activity (PA), screen based time and sleeping show conflicting results. Objective: This study investigates the association between chronic pain at different body regions and selfreported PA, screen based time and sleeping hours in high school students. Subjects: A total of 969 students aged 13–19 years old. Methods: Participants completed a questionnaire on chronic pain, time spent in moderate and vigorous PA, screen based time watching televivsion (TV)/digital versatile discs (DVD), playing, using mobile phones and computers and sleeping hours. Univariate and multivariate associations between pain and PA, screen based time and sleeping hours were investigated. Results: In the univariate model time spent in moderate and vigorous PA, in screen based activities and sleeping were associated with pain in at least one body site. In the multivariate model, screen based activities were not associated with pain; sleeping 7 h or less and increased time in moderate PA were associated with pain at almost all body sites [odds ratio (OR) between 2.69–3.66 and 1.06–1.10, respectively]. Conclusion: Time spent in PA and sleeping increased the risk of chronic pain in almost all body regions and might confound the association between screen based time and pain.

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Knotty inflation and the dimensionality of spacetime

Berera, Arjun, Buniy, Roman V., Kephart, Thomas W., Pas, Heinrich, Rosa, João G.

Springer

We suggest a structure for the vacuum comprised of a network of tightly knotted/linked flux tubes formed in a QCD-like cosmological phase transition and show that such a network can drive cosmological inflation. As the network can be topologically stable only in three space dimensions, this scenario provides a dynamical explanation for the existence of exactly three large spatial dimensions in our Universe.

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Identification of Seniors at Risk (ISAR) in the emergency room: a prospective study

Tavares, J. P. A., Sá-Couto, P., Boltz, M., Capezuti, E.

Elsevier

Introduction: The Identification of Seniors at Risk (ISAR) is one of the most frequently utilized risk screening tools in emergency departments (ED). The goal of this study was to evaluate the predictive validity of the ISAR screening tool for adverse outcomes in an ED. Methods: This was a prospective single-center observational study in a Portuguese urban university hospital ED, and included 402 older adults (OA). After triage, baseline sociodemographic and clinic data were collected by the researcher and the ISAR was administered. Baseline ISAR, adverse outcomes (ED revisits and hospital admission) at 30 (early) and 180 (late) days were evaluated. Results: ISAR screening showed that 308 (76.62%) OAs were at risk (cutoff 2). High-risk patients were more like to be older, take more medication, have urgent or very urgent ED visits and have longer ED lengths of stay. The high-risk group were more likely to demonstrate both early (OR = 2.43, 95% CI 1.35–4.35, p < 0.01) and late returns to the ED (AO = 1.70, 95% CI 1.04–2.79, p < 0.05). The ISAR did not predict any significant variable for hospital admission in 30 or 180 days. Discussion: The ISAR predicted returns to EDs at 30 and 180 days for OAs at risk, but was unable to predict early or late hospital readmission.

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Portuguese older adults presenting at the emergency department: Predictive validity of the identification of seniors at risk (ISAR) tool

de Almeida Tavares, J., Sá-Couto, P., Boltz, M., Capezuti, E.

Healio

Following an emergency department (ED) visit, older adults are more likely to experience poorer outcomes than younger adults. It is crucial to identify older patients using a validated tool.One of the most studied tools is the Identification of Seniors at Risk (ISAR), which is used to identify older adults at risk of adverse outcomes after ED admission. The purpose of the current study was to examine the sensitivity, specificity, and interrater reliability of the Portuguese version of the ISAR when considering early (30 days) and late (180 days) outcomes. Four hundred two older adults presenting in EDs from January 2013 to August 2014 were prospectively enrolled and surveyed. The ISAR threshold (cutoff ≥2) presented a better compromise between sensitivity (81.8% to 88.7%) and specificity (14.7% to 28.1%) when compared to cutoffs ≥1 or ≥3, respectively. Interrater reliability results were very good (0.81 to 0.94). Overall, the Portuguese ISAR appears worthwhile for screening older adults at risk in EDs

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Biological dose-escalated definitive radiation therapy in head and neck cancer

Costa Ferreira, B., Sá-Couto, P., Khouri, L., Lopes, M. C.

British Institute of Radiology

To compare treatment outcome of patients with head and neck (HN) tumours treated with definitive radiation therapy that, mainly owing to differences in the fractionation scheme used with simultaneous integrated boost techniques, resulted in a different biological dose. Methods: 181 patients with HN cancer, prescribed to about 70.2Gy in the primary tumour, were included in this study. Population cohort was divided into Group ,70 and Group $70 when the mean dose converted to a 2 Gy fractionation in the primary tumour was less or higher than 70.2Gy, respectively. The probability of local control (LC), locoregional control (LRC), disease-free survival (DFS) and overall survival (OS) was determined for both groups. The incidence of acute and late complications was compared between the two groups. Results: At 24 months for Groups ,70 and $70, LC was 83.2% and 87.5%, LRC was 79.5% and 81.6%, DFS was 56.3% and 66.8% and OS was 63.9% and 71.5% p5ns, respectively. The incidence of acute dysphagia, odynophagia and pain, and late mucositis was significantly higher in Group $70 than in Group ,70. The rate of xerostomia, dysphonia, radiodermatitis, alopecia, dental complications, hypoacusia and weight loss was comparable between the two groups. Conclusion: The biological dose escalation was safe, but an increase in the incidence of the acute side effects: dysphagia, odynophagia and pain and late mucositis, was obtained. Advances in knowledge: Despite the significant biological dose escalation, within the range of doses delivered to this cohort, no clear dose–response effect was observed

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Design approach of mathematics learning activities in a digital environment for children with autism spectrum disorders

Santos, Maria Isabel Gomes dos, Breda, Ana, Almeida, Ana Margarida Pisco

Springer

Learning environment on mathematics for autistic children is a prototype of a digital environment with dynamic adaptation features designed to offer activities towards the development of mathematical reasoning in children aged 6–12 years, diagnosed with autism spectrum disorders (ASD), a neurodevelopmental disorder characterized by deficits in social communication and social interaction as well as restricted and repetitive patterns of behaviour, interests or activities. This paper, with a primarily conceptual and analytical scope, discusses the mathematical difficulties that some children with ASD have, and presents strategies that can be used to overcome them. Based on a literature review and on the results of a preliminary study already conducted, we present results concerning the proposal of a set of learning activities for the prototype under development, specifically targeted to promote mathematical reasoning in students with ASD. Guidelines for future research are also discussed.

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Smart context-aware QoS-based admission control for biomedical wireless sensor networks

Abreu, Carlos, Miranda, Francisco, Mendes, P. M.

Elsevier

Wireless sensor networks are being used as the enabling technology that helps to support the development of new applications and services targeting the domain of healthcare, in particular, regarding data collection for continuous health monitoring of patients or to help physicians in their diagnosis and further treatment assessment. Therefore, due to the critical nature of both medical data and medical applications, such networks have to satisfy demanding quality of service requirements. (...)

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Aspects of algebraic algebras

Hofmann, Dirk, Sousa, Lurdes

International Federation of Computational Logic

In this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg--Moore category, for a Kock-Z"oberlein monad on an order-enriched category. Firstly, we give a characterisation of free algebras in the spirit of domain theory. Secondly, we study the existence of weighted (co)limits, both on the abstract level and for specific categories of domain theory like the category of algebraic lattices. Finally, we apply these results to give a description of the idempotent split completion of the Kleisli category of the filter monad on the category of topological spaces.

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No Neon, but Jets in the Remarkable Recurrent Nova M31N 2008-12a?—Hubble Space Telescope Spectroscopy of the 2015 Eruption

Darnley, M. J., Hounsell, R., Godon, P., Perley, D. A., Henze, M., Kuin, N. P. M., Williams, B. F., Williams, S. C., Bode, M. F., Harman, D. J., Hornoch, K., Link, M., Ness, J.-U., Ribeiro, V. A. R. M., Sion, E. M., Shafter, A. W., Shara, M. M.

IOP Publishing

The 2008 discovery of an eruption of M31N 2008-12a began a journey on which the true nature of this remarkable recurrent nova continues to be revealed. M31N 2008-12a contains a white dwarf (WD) close to the Chandrasekhar limit, accreting at a high rate from its companion, and undergoes thermonuclear eruptions that are observed yearly and may even be twice as frequent. In this paper, we report on Hubble Space Telescope Space Telescope Imaging Spectrograph ultraviolet spectroscopy taken within days of the predicted 2015 eruption, coupled with Keck spectroscopy of the 2013 eruption. Together, this spectroscopy permits the reddening to be constrained to E(B-V)=0.10+/- 0.03. The UV spectroscopy reveals evidence for highly ionized, structured, and high-velocity ejecta at early times. No evidence for neon is seen in these spectra, however, but it may be that little insight can be gained regarding the composition of the WD (CO versus ONe).

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Convolutional neural networks for transient candidate vetting in large-scale surveys

Gieseke, Fabian, Bloemen, Steven, van den Bogaard, Cas, Heskes, Tom, Kindler, Jonas, Scalzo, Richard A., Ribeiro, Valério A. R. M., van Roestel, Jan, Groot, Paul J., Yuan, Fang, Möller, Anais, Tucker, Brad E.

Oxford University Press

Current synoptic sky surveys monitor large areas of the sky to find variable and transient astronomical sources. As the number of detections per night at a single telescope easily exceeds several thousand, current detection pipelines make intensive use of machine learning algorithms to classify the detected objects and to filter out the most interesting candidates. A number of upcoming surveys will produce up to three orders of magnitude more data, which renders high-precision classification systems essential to reduce the manual and, hence, expensive vetting by human experts. We present an approach based on convolutional neural networks to discriminate between true astrophysical sources and artefacts in reference-subtracted optical images. We show that relatively simple networks are already competitive with state-of-the-art systems and that their quality can further be improved via slightly deeper networks and additional pre-processing steps – eventually yielding models outperforming state-of-the-art systems. In particular, our best model correctly classifies about 97.3 per cent of all ‘real’ and 99.7 per cent of all ‘bogus’ instances on a test set containing 1942 ‘bogus’ and 227 ‘real’ instances in total. Furthermore, the networks considered in this work can also successfully classify these objects at hand without relying on difference images, which might pave the way for future detection pipelines not containing image subtraction steps at all.

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Inflows, Outflows, and a Giant Donor in the Remarkable Recurrent Nova M31N 2008-12a? - Hubble Space Telescope Photometry of the 2015 Eruption

Darnley, M. J., Hounsell, R., Godon, P., Perley, D. A., Henze, M., Kuin, N. P. M., Williams, B. F., Williams, S. C., Bode, M. F., Harman, D. J., Hornoch, K., Link, M., Ness, J.-U., Ribeiro, V. A. R. M., Sion, E. M., Shafter, A. W., Shara, M. M.

American Astronomical Society

The recurrent nova M31N 2008-12a experiences annual eruptions, contains a near-Chandrasekhar-mass white dwarf, and has the largest mass accretion rate in any nova system. In this paper, we present Hubble Space Telescope (HST) WFC3/UVIS photometry of the late decline of the 2015 eruption. We couple these new data with archival HST observations of the quiescent system and Keck spectroscopy of the 2014 eruption. The late-time photometry reveals a rapid decline to a minimum luminosity state, before a possible recovery/rebrightening in the run up to the next eruption. Comparison with accretion disk models supports the survival of the accretion disk during the eruptions, and uncovers a quiescent disk mass accretion rate of the order of ${10}^{-6},{M}_{odot },{mathrm{yr}}^{-1}$, which may rise beyond ${10}^{-5},{M}_{odot },{mathrm{yr}}^{-1}$ during the super-soft source phase—both of which could be problematic for a number of well-established nova eruption models. Such large accretion rates, close to the Eddington limit, might be expected to be accompanied by additional mass loss from the disk through a wind and even through collimated outflows. The archival HST observations, combined with the disk modeling, provide the first constraints on the mass donor: ${L}_{mathrm{donor}}={103}_{-11}^{+12},{L}_{odot },{R}_{mathrm{donor}}={14.14}_{-0.47}^{+0.46},{R}_{odot }$, and ${T}_{mathrm{eff},mathrm{donor}}=4890pm 110$ K, which may be consistent with an irradiated M31 red-clump star. Such a donor would require a system orbital period $gtrsim 5$ days. Our updated analysis predicts that the M31N 2008-12a WD could reach the Chandrasekhar mass in $lt 20$ kyr.

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Mediana de dados não agrupados: a questão de ser pelo menos 50%

Freitas, Adelaide, Cruz, João Pedro, Silva, Nélia

Associação de Professores de Matemática

Com o presente trabalho temos como objetivo ilustrar exemplos que abrangem as diferentes situações que podem ocorrer no cálculo da mediana de uma coleção de dados. Pretendemos mostrar, com exemplos, as possíveis interpretações válidas de mediana que, de forma similar, podem ser extensíveis aos outros quartis. Com esses exemplos pretendemos discutir o eventual confronto entre a noção intuitiva de mediana e sua interpretação. Deste modo, esperamos contribuir para uma melhor compreensão de possíveis deduções, consequentes da interpretação de mediana, que por vezes causam alguma estranheza entre os estudantes, nomeadamente quando, por exemplo, existem observações repetidas e iguais à mediana numa coleção de dados.

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Stability of Simultaneously Block Triangularizable Switched Systems with Partial State Reset

Brás, Isabel, Rocha, Paula, Carapito, Ana Catarina

Taylor and Francis

We study the stability of a certain class of switched systems where discontinuous jumps (resets) on some of the state components are allowed, at the switching instants. It is known that, if all components of the state are available for reset, the system can be stabilizable by an adequate choice of resets. However, this question may have negative answer if there are forbidden state components for reset. We give a sufficient condition for the stabilizability of a switched system, under arbitrary switching, by partial state reset in terms of a block simultaneous triangularizability condition. Based on this sufficient condition, we show that the particular class of systems with partially commuting stable system matrices is stabilizable by partial state reset. We also provide an algorithm that allows testing whether a switched system belongs to this particular class of systems.

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Nonlinear nonconvex second order multivalued systems with maximal monotone terms

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

Yokohama Publishers

We consider a multivalued system in RN driven by the vector p-Laplacian, with maximal monotone terms and multivalued perturbations. The boundary condition is nonlinear and general and incorporate as special cases the Dirichlet, Neumann and periodic problems. We first prove the existence of extremal trajectories. Then, for the semilinear systems (that is, p = 2) and for particular boundary conditions, we prove a strong relaxation theorem, showing that the extremal trajectories are dense in the solution set of the convexified system.

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On p-superlinear equations with a nonhomogeneous differential operator

Aizicovici, Sergiu, Papageorgiou, Nikolaos S., Staicu, Vasile

Springer Basel AG

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator and with a (p−1)-superlinear Carath´eodory reaction. Our formulation incorporates as a special case equations monitored by the p-Laplacian. Using variational methods coupled with truncation techniques and comparison principles,

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Francesco S. De Blasi remembered by close friends and colleagues

Staicu, V.

American Romanian Academy

remembered by close friends and colleagues

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In memory of Professor Francesco Saverio De Blasi

Staicu, Vasile

American Romanian Academy

Editorial introduction to the issue dedicated to Francesco S. De Blasi

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Nonlinear periodic problems superlinear at $+infty$ and sublinear at. $-infty$

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

American Romanian Academy

We consider a nonlinear periodic problem driven by a nonlinear, nonhomogeneous differential operator with a reaction which exhibits an asymmetric growth at $+infty$ and at $-infty$. It is $left( p-1right) -$superlinear near $+infty$ and $left( p-1right) -$ sublinear near $-infty$. A particular case of our problem is that of periodic equations with the scalar $p-$ Laplacian and an asymmetric nonlinearity. Using variational methods and Morse theory, we prove the existence of at least three nontrivial solutions.

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Nodal and multiple solutions for nonlinear periodic problems with competing nonlinearities

Aizicovicim, S., Papageorgiou, N. S., Staicu, Vasile

World Scientific

We consider a nonlinear periodic problem drive driven by a nonhomogeneous differential operator which incorporates as a special case the scalar p-Laplacian, and a reaction which exhibits the competition of concave and convex terms. Using variational methods based on critical point theory, together with suitable truncation techniques and Morse theory (critical groups), we establish the existence of five nontrivial solutions, two positive, two negative and the fifth nodal (sign-changing). In the process, we also prove some auxiliary results of independent interest.

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Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations

Aizicovici, S., Papageorgiou, N. S., Staicu, Vasile

Yokohama Publishers

We consider nonlinear, nonhomogeneous Dirichlet problems driven by the sum of a p−Laplacian (p > 2) and a Laplacian, with a reaction term which has space dependent zeros of constant sign. We prove three muliplicity theorems for such equations providing precise sign information for all solutions. In the first multiplicity theorem, we do not impose any growth condition on the reaction near ±∞: In the other two, we assume that the reaction is (p − 1)− linear and resonant with respect to principal eigenvalue of ( −△p;W1,p 0 (Ω) ) : Our approach uses variational methods based on the critical point theory, together with suitable truncation and comparison techniques and Morse theory (critical groups).

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Sublinear and superlinear Ambrosetti-Prodi problems for the Dirichlet p-Laplacian

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

Elsevier

We deal with an Ambrosetti–Prodi problem driven by the p-Laplace differential operator, with a ‘‘crossing’’ reaction which can be sublinear or superlinear (in the positive direction). Using variational methods based on the critical point theory, together with upper–lower solutions, truncation and comparison techniques and critical groups, we show the existence of a unique critical parameter value λ∗ such that for λ < λ∗ there are at least two nontrivial solutions, for λ = λ∗ there is at least one nontrivial solution, and for λ > λ∗ no solutions exist. We extend several recent results on this problem.

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Nodal solutions for nonlinear nonhomogeneous Neumann equations

Aizicovici, S., Papageorgiou, N. S., Staicu, Vasile

Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies

We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a Caratheodory reaction which is $(p-1)$-sublinear near $pminfty$. Using variational tools we show that the problem has at least three nontrivial smooth solutions (one positive, one negative and a third nodal). Our formulation unifies problems driven by the $p$-Laplacian, the $(p,q) $ Laplacian and the $p$-generalized mean curvature operator.

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Existence Results for Quasilinear Elliptic Equations with Multivalued Nonlinear Terms

Otani, Mitsuharu, Staicu, Vasile

Springer

In this paper we study the existence of solutions u ∈ W1,p0(Ω) with △pu ∈ L2(Ω) for the Dirichlet problem {−△pu(x)∈−∂Φ(u(x))+G(x,u(x)),x∈Ω,u∣∂Ω=0, (1) where Ω ⊆ RN is a bounded open set with boundary ∂Ω, △p stands for the p−Laplace differential operator, ∂Φ denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function Φ and G : Ω × R → 2R is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map u ↦ G(x, u) is upper semicontinuous with closed convex values and the second one deals with the case when u ↦ G(x, u) is lower semicontinuous with closed (not necessarily convex) values.

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Exceptional symmetry by genomic word: A Statistical Analysis

Afreixo, Vera, Rodrigues, João M. O. S., Bastos, Carlos, Tavares, Ana H. M. P., Silva, Raquel M.

Springer

Single-strand DNA symmetry is pointed as a universal law observed in the genomes from all living organisms. It is a somewhat broadly defined concept, which has been refined into some more specific measurable effects. Here we discuss the exceptional symmetry effect. Exceptional symmetry is the symmetry effect beyond that expected in independence contexts, and it can be measured for each word, for each equivalent composition group, or globally, combining the effects of all possible words of a given length. Global exceptional symmetry was found in several species, but there are genomic words with no exceptional symmetry effect, whereas others show a very high exceptional symmetry effect. In this work, we discuss a measure to evaluate the exceptional symmetry effect by symmetric word pair, and compare it with others. We present a detailed study of the exceptional symmetry by symmetric pairs and take the CG content into account. We also introduce and discuss the exceptional symmetry profile for the DNA of each organism, and we perform a multiple comparison for 31 genomes: 7 viruses; 5 archaea; 5 bacteria; 14 eukaryotes.

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Procalcitoninfor the earlydiagnosis of sepsis inburn patients: A retrospective study

Cabral, Luís, Afreixo, Vera, Santos, Filipe, Almeida, Luís, Paiva, José Artur

Elsevier

Background: The gold standard for sepsis diagnosis in burn patient still relies on microbiological cultures, which take 48–72h to provide results, delaying the start of antimicrobial therapy. Thus, biomarkers allowing an earlier sepsis diagnosis in burn patients are needed. Methods: This retrospective observational study included 150 burn patients with total burned surface area >=15%. Clinical diagnosis of sepsis among these patients was done according to the American Burn Association criteria. Biomarker (procalcitonin, white blood cells and platelet countings, prothrombinemia, D-dimers, C-reactive protein, blood lactate and temperature) values were available for 48 patients without sepsis (2767 timepoints) and 102 patients with sepsis (652 timepoints). Quantitative variables were compared with Mann– Whitney tests and qualitative variables were compared with Pearson chi-square test. Effect size was measured by the probability of superiority. Receiver operating characteristic (ROC) curves evaluate capacity for sepsis diagnosis. Sensitivity, specificity, positive and negative predictive values were calculated for some cut-off values, including the best cut-off defined by the maximum of Youden index. Results: Statistically significant differences between the groups of septic and non-septic patients, with medium to large effect size, were detected for all the biomarkers considered, except temperature. PCT was the biomarker with the largest AUC and effect size (AUC=0.71). Analysis of the PCT ROC curve showed that 0.5ng/mL cut-off presented highest sensitivity and lowest specificity, whereas 1.5ng/mL cut-off was associated with lowest sensitivity and highest specificity. Conclusion: Procalcitonin showed to be the best of the biomarkers studied for an early diagnosis of sepsis. Its use should be considered in antimicrobial stewardship programs in Burn Units.

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Modeling and optimal control of HIV/AIDS prevention through PrEP

Silva, C.J., Torres, D.F.M.

American Institute of Mathematical Sciences

Pre-exposure prophylaxis (PrEP) consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals and has recently demonstrated to be highly efficacious for HIV prevention. We propose a new epidemiological model for HIV/AIDS transmission including PrEP. Existence, uniqueness and global stability of the disease free and endemic equilibriums are proved. The model with no PrEP is calibrated with the cumulative cases of infection by HIV and AIDS reported in Cape Verde from 1987 to 2014, showing that it predicts well such reality. An optimal control problem with a mixed state control constraint is then proposed and analyzed, where the control function represents the PrEP strategy and the mixed constraint models the fact that, due to PrEP costs, epidemic context and program coverage, the number of individuals under PrEP is limited at each instant of time. The objective is to determine the PrEP strategy that satisfies the mixed state control constraint and minimizes the number of individuals with pre-AIDS HIV-infection as well as the costs associated with PrEP. The optimal control problem is studied analytically. Through numerical simulations, we demonstrate that PrEP reduces HIV transmission significantly.

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A necessary condition of pontryagin type for fuzzy fractional optimal control problems

Fard, O. S., Soolaki, J., Torres, D. F. M.

We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the extremals of three fuzzy optimal control systems, which improve recent results of Najariyan and Farahi. © 2018, American Institute of Mathematical Sciences. All rights reserved.

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Noether currents for higher-order variational problems of Herglotz type with time delay

Santos, S. P. S., Martins, N., Torres, D. F. M.

American Institute of Mathematical Sciences

We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such generalized variational problems, which are particularly useful in the search of extremals. The proof is based on the idea of rewriting the higher-order delayed generalized variational problem as a first-order optimal control problem without time delays. © 2018, American Institute of Mathematical Sciences. All rights reserved.

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Preface of Special Issue on Optimization and Differential Equations

Choquet, C., Martins, N., Sidi Ammi, M.R., Tilioua, M., Torres, D.F.M.

American Institute of Mathematical Sciences

The present volume is a Special Issue on Optimization and Differential Equations.

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A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives

Jahanshahi, S., Babolian, E., Torres, D. F. M., Vahidi, A. R.

Elsevier

We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving fractional boundary value problems. As an application, we solve a special class of fractional Euler–Lagrange equations. The method is based on Hale and Townsend algorithm for finding the roots and weights of the fractional Gauss–Jacobi quadrature rule and the predictor-corrector method introduced by Diethelm for solving fractional differential equations. Illustrative examples show that the given method is more accurate than the one introduced in [26], which uses the Golub–Welsch algorithm for evaluating fractional directional integrals. © 2017

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Fractional Herglotz variational principles with generalized Caputo derivatives

Garra, R., Taverna, G. S., Torres, D. F. M.

Elsevier

We obtain Euler–Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscillator with time-depending mass and elasticity, and arbitrary memory effects. © 2017 Elsevier Ltd

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Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations

Debbouche, A., Nieto, J. J., Torres, D. F. M.

Springer

We introduce the optimality question to the relaxation in multiple control problems described by Sobolev-type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of systems with respect to the trajectory, multicontrols, and the functional in suitable topologies. © 2015, Springer Science+Business Media New York.

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A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems

Jahanshahi, S., Torres, D. F. M.

Springer

We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann–Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we rewrite the fractional functional dynamical optimization problem as a classical static optimization problem. The method for classical optimal control problems is called Ritz’s method. Examples show that the proposed approach is more accurate than recent methods available in the literature. © 2016, Springer Science+Business Media New York.

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A table of derivatives on arbitrary time scales

Torres, D. F. M.

MUK Publications

This paper presents a collection of useful formulas of dynamic derivatives on time scales, systematically collected for reference purposes. As an application, we define trigonometric and hyperbolic functions on time scales in such a way the most essential qualitative properties of the corresponding continuous functions are generalized in a proper way.

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Direct and inverse variational problems on time scales: A survey

Dryl, M., Torres, D. F. M.

Springer

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler–Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler–Lagrange equation (Helmholtz’s problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field. © 2017, Springer International Publishing AG.

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Shifted Generalized Pascal Matrices in the Context of Cli ord Algebra-Valued Polynomial Sequences

Cação, Isabel, Malonek, Helmuth, Tomaz, Graça

Springer

The paper shows the role of shifted generalized Pascal matrices in a matrix representation of hypercomplex orthogonal Appell systems. It extends results obtained in previous works in the context of Appell sequences whose rst term is a real constant to sequences whose initial term is a suitable chosen polynomial of n variables.

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The influence of inspiratory muscle training on lung function in female basketball players: a randomized controlled trial

Vasconcelos, Tiago, Hall, Andreia, Viana, Rui

PBJ-Associação Porto Biomedical/Porto Biomedical Society

Inspiratory muscle fatigue may inhibit healthy athletes to achieve maximum performance, compromising blood flow and perfusion on locomotor muscles. Recent studies have showed irregular influence of inspiratory muscle training (IMT) on resting lung function. It was hypothesized that a 4-week IMT protocol would improve pulmonary function of basketball players. Twenty-one female basketball players were randomly assigned to an experimental group (EG) (n = 11) or a control group (CG) (n = 10). Pre- and post-forced expiratory volume in first second (FEV1), forced vital capacity (FVC) and peak expiratory flow (PEF) were assessed with spirometry in the beginning of the sport's season, at the first day of protocol and four weeks after. The EG (22.00 ± 5.00 years) was submitted to IMT using a threshold, 5 times a week, for a 4-week protocol (30 maximal repetitions (RM) against a pressure threshold load equivalent to 50% of maximal inspiratory pressure), while the CG (18.50 ± 5.75 years) was not subjected to any intervention during the same period. Baseline sociodemographic and anthropometric characteristics were not significantly different with the exception of age (p = 0.036). No significant differences were found in baseline pulmonary volumes (0.173 ≤ p ≤ 0.848) neither in predicted pulmonary variables (0.223 ≤ p ≤ 0.654). Significant increase on FEV1, FVC and PEF was found in the EG post-protocol (p < 0.001). In the CG, an improvement of PEF was found (p = 0.042). This type of specific inspiratory training appears to improve pulmonary function. Results suggest that the applied IMT protocol is effective. Further research is needed to assess the sustainability of the findings and to conclude the short and long term effects of IMT on basketball players.

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Asymptotically flat scalar, Dirac and Proca stars: Discrete vs. continuous families of solutions

Herdeiro, C. A. R., Pombo, A. M., Radu, E.

Elsevier

The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field - geons - was conjectured more than half a century ago. If one insists on exactstationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar) boson stars. Similar geons have subsequently been found in Einstein-Dirac theory and, more recently, in Einstein-Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin 0, 1/2 and 1, emphasizingthe mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermioniccases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case. (C) 2017 The Authors. Published by Elsevier B.V.

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Reissner-Nordstrom black holes with non-Abelian hair

Herdeiro, C., Paturyan, V., Radu, E., Tchrakian, D. H.

Elsevier

We consider d >= 4 Einstein-(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearisingthe (extended) Yang- Mills equations on the background of the electric Reissner-Nordstrm (RN) black hole, we show the existence of normalisable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realisationof these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically preferred over the RN solution, which, in this model, becomes unstable against the formation of non-Abelian hair, for sufficiently large values of the electric charge. (C) 2017 The Authors. Published by Elsevier B.V.

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Synchronous frequencies of extremal Kerr black holes: Resonances, scattering, and stability

Richartz, M., Herdeiro, C. A. R., Berti, E.

American Physical Society

The characteristic damping times of the natural oscillations of a Kerr black hole become arbitrarily large as the extremal limit is approached. This behavior is associated with the so-called zero damped modes (ZDMs), and suggests that extremal black holes are characterized by quasinormal modes whose frequencies are purely real. Since these frequencies correspond to oscillations whose angular phase velocity matches the horizon angular velocity of the black hole, they are sometimes called "synchronous frequencies." Several authors have studied the ZDMs for near-extremal black holes. Recently, their correspondence to branch points of the Green's function of the wave equation was linked to the Aretakis instability of extremal black holes. Here we investigate the existence of ZDMs for extremal black holes, showing that these real-axis resonances of the field are unphysical as natural black hole oscillations: the corresponding frequency is always associated with a scattering mode. By analyzing the behavior of these modes near the event horizon we obtain new insight into the transition to extremality, including a simple way to understand the Aretakis instability.

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Iron K alpha line of Proca stars

Shen, T. L., Zhou, M. L., Bambi, C., Herdeiro, C. A. R., Radu, E.

IOP Publishing

X-ray reflection spectroscopy can be a powerful tool to test the nature of astrophysical black holes. Extending previous work on Kerr black holes with scalar hair [1] and on boson stars [2], here we study whether astrophysical black hole candidates may be horizonless, self-gravitating, vector Bose-Einstein condensates, known as Proca stars [3]. We find that observations with current X-ray missions can only provide weak constraints and rule out solely Proca stars with low compactness. There are two reasons. First, at the moment we do not know the geometry of the corona, and therefore the uncertainty in the emissivity pro file limits the ability to constrain the background metric. Second, the photon number count is low even in the case of a bright black hole binary, and we cannot have a precise measurement of the spectrum.

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Constraining black holes with light boson hair and boson stars using epicyclic frequencies and quasiperiodic oscillations

Franchini, N., Pani, P., Maselli, A., Gualtieri, L., Herdeiro, C. A. R., Radu, E., Ferrari, V.

American Physical Society

Light bosonic fields are ubiquitous in extensions of the Standard Model. Even when minimally coupled to gravity, these fields might evade the assumptions of the black-hole no-hair theorems and give rise to spinning black holes which can be drastically different from the Kerr metric. Furthermore, they allow for self-gravitating compact solitons, known as (scalar or Proca) boson stars. The quasiperiodic oscillations (QPOs) observed in the x-ray flux emitted by accreting compact objects carry information about the strong-field region, thus providing a powerful tool to constrain deviations from Kerr's geometry and to search for exotic compact objects. By using the relativistic precession model as a proxy to interpret the QPOs in terms of geodesic frequencies, we investigate how the QPO frequencies could be used to test the no-hair theorem and the existence of light bosonic fields near accreting compact objects. We show that a detection of two QPO triplets with current sensitivity can already constrain these models and that the future eXTP mission or a LOFT-like mission can set very stringent constraints on black holes with bosonic hair and on (scalar or Proca) boson stars. The peculiar geodesic structure of compact scalar/Proca boson stars implies that these objects can easily be ruled out as alternative models for x-ray source GRO J1655-40.

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Fundamental solution of the time-fractional telegraph Dirac operator

Ferreira, Milton dos Santos, Rodrigues, Maria Manuela Fernandes, Vieira, Nelson Felipe Loureiro

Wiley

In this work we obtain the fundamental solution (FS) of the multidimensional time-fractional telegraph Dirac operator where the two time-fractional derivatives of orders $alpha in ]0,1]$ and $beta in ]1,2]$ are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters $alpha$ and $beta$. Finally, using the FS we study some Poisson and Cauchy problems.

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Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations

Castro, L. P., Simões, A. M.

Faculty of Sciences and Mathematics, University of Nis, Serbia

We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of {it semi-Hyers-Ulam-Rassias stability}, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.

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Global existence of solutions for a fractional Caputo nonlocal thermistor problem

Sidi Ammi, M. R., Jamiai, I., Torres, D. F. M.

Springer

We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem. Then additional existence and continuation theorems are obtained, ensuring global existence of solutions.

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On Cops and Robbers on $G^{Xi}$ and cop-edge critical graphs

Cardoso, Domingos M., Dominic, Charles, Witkowski, Lukasz, Witkowski, Marcin

University of Calgary

Cop Robber game is a two player game played on an undirected graph. In this game cops try to capture a robber moving on the vertices of the graph. The cop number of a graph is the least number of cops needed to guarantee that the robber will be caught. In this paper we presents results concerning games on $G^{Xi}$, that is the graph obtained by connecting the corresponding vertices in $G$ and its complement $overline{G}$. In particular we show that for planar graphs $c(G^{Xi})leq 3$. Furthermore we investigate the cop-edge critical graphs, i.e. graphs that for any edge $e$ in $G$ we have either $c(G-e)c(G)$. We show couple examples of cop-edge critical graphs having cop number equal to $3$.

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Existence theorem and optimality conditions for a class of convex

Kostyukova, Olga, Tchemisova, Tatiana, Kurdina, Maryia

International Academic Press

The paper is devoted to study of a special class of semi-infinite problems arising in nonlinear parametric optimization. These semi-infinite problems are convex and possess noncompact index sets. In the paper, we present conditions, which guarantee the existence of optimal solutions, and prove new optimality criterion. An example illustrating the obtained results is presented.

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Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable

Kostyukova, Olga, Tchemisova, Tatiana

Springer

In the present paper, we analyze a class of convex Semi-Infinite Programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems.

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A study of one class of NLP problems arising in parametric Semi-Infinite Programming

Kostyukova, Olga, Tchemisova, Tatiana, Kurdina, Maryia

Taylor and Francis

The paper deals with a nonlinear programming (NLP) problem that depends on a finite number of integers(parameters). This problem has a special form, and arises as an auxiliary problem in study of solutions’ properties of parametric semi-infinite programming (SIP) problems with finitely representable compact index sets. Therefore, it is important to provide a deep study of this NLP problem and its properties w.r.t. the values of the parameters. We are especially interested in the case when optimal solutions of the NLP problem satisfy certain properties due to some specific requirements arising in parametric SIP. We establish the values of the parameters for which optimal solutions of the corresponding NLP problem fulfil the needed properties, and suggest an algorithm that determines the right values of the parameters. An example is proposed to illustrate the application of the algorithm.

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Simetrias nas Cercaduras das Fachadas de Azulejos de Aveiro, usando o GeoGebra

Carlos, Lurdes, Breda, Ana

Instituto GeoGebra de São Paulo - PUC/SP

Com este trabalho pretende-se classificar os motivos existentes nas cercaduras3 dos azulejos que revestem fachadas de Aveiro, estabelecendo uma ligação entre este Património e a Matemática. As atividades a desenvolver com os alunos requerem um trabalho prévio de recolha fotográfica, que se pode estender a qualquer parte do país, e que pode envolver uma visita de estudo, saída de campo ou trabalho de casa, sendo solicitado que cada aluno fotografe uma cercadura. Neste trabalho seguimos duas vertentes: criar com o GeoGebra, exemplares dos 7 frisos a partir de um elemento recolhido num motivo dos azulejos ou procurar as simetrias existentes nas cercaduras fotagrafadas utilizando o GeoGebra e proceder à sua classificação.

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Billiard transformations of parallel flows: a periscope theorem

Plakhov, Alexander, Tabachnikov, Sergey, Treschev, Dmitry

Elsevier

We consider the following problem: given two parallel and identically oriented bundles of light rays in R^{n+1} and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We prove that a 2-mirror realization is possible, if and only if the diffeomorphism is the gradient of a function. We further prove that any orientation reversing diffeomorphism of domains in R^2 is locally the composition of two gradient diffeomorphisms, and therefore can be realized by 4 mirror reflections of light rays in R^3, while an orientation preserving diffeomorphism can be realized by 6 reflections. In general, we prove that an (orientation reversing or preserving) diffeomorphism of wave fronts of two normal families of light rays in R^3 can be realized by 6 or 7 reflections.

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The problem of camouflaging via mirror reflections

Plakhov, Alexander

The Royal Society Publishing

This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is therefore natural to search for bodies that are, in a sense, close to invisible. We introduce a visibility index of a body measuring the mean angle of deviation of incident light rays, and derive a lower estimate for this index. This estimate is a function of the body's volume and of the minimal radius of a ball containing the body. This result is far from being final and opens a possibility for further research.

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Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications

Almeida, Ricardo, Malinowska, Agnieszka B., Monteiro, Maria Teresa T.

Wiley

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Paraconsistency in hybrid logic

Costa, Diana, Martins, Manuel A.

Oxford University Press

As in standard knowledge bases, hybrid knowledge bases (i.e. sets of information specified by hybrid formulas) may contain inconsistencies arising from different sources, namely from the many mechanisms used to collect relevant information. Being a fact, rather than a queer anomaly, inconsistency also needs to be addressed in the context of hybrid logic applications. This article introduces a paraconsistent version of hybrid logic which is able to accommodate inconsistencies at local points without implying global failure. A main feature of the resulting logic, crucial to our approach, is the fact that every hybrid formula has an equivalent formula in negation normal form. The article also provides a measure to quantify the inconsistency of a hybrid knowledge base, useful as a possible basis for comparing knowledge bases. Finally, the concepts of extrinsic and intrinsic inconsistency of a theory are discussed.

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Computing the Laplacian spectra of some graphs

Cardoso, Domingos M., Martins, Enide A., Robbiano, Maria, Trevisan, Vilmar

Elsevier

In this paper we give a simple characterization of the Laplacian spectra of a family of graphs as the eigenvalues of symmetric tridiagonal matrices. In addition, we apply our result to obtain upper and lower bounds for the Laplacian-energy-like invariant of these graphs. The class of graphs considered are obtained from copies of modified generalized Bethe trees (obtained by joining the vertices at some level by paths), identifying their roots with the vertices of a regular graph or a path. Center for Research and Development in Mathematics and Applications FCT FEDER/POCI 2010 Fondecyt-IC Project 11090211 CNPq—Grants 309531/2009-8 CNPq—Grants 473815/2010-9

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Implicit optimality criterion for convex SIP problem with box constrained index set

Kostyukova, O. I., Tchemisova, T. V.

Springer Verlag

We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for SIP and show its efficiency in the convex case.

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Convex semi-infinite programming: Implicit optimality criterion based on the concept of immobile indices

Kostyukova, O. I., Tchemisova, T. V., Yermalinskaya, S. A.

Springer Verlag

We state a new implicit optimality criterion for convex semi-infinite programming (SIP) problems. This criterion does not require any constraint qualification and is based on concepts of immobile index and immobility order. Given a convex SIP problem with a continuum of constraints, we use an information about its immobile indices to construct a nonlinear programming (NLP) problem of a special form. We prove that a feasible point of the original infinite SIP problem is optimal if and only if it is optimal in the corresponding finite NLP problem. This fact allows us to obtain new efficient optimality conditions for convex SIP problems using known results of the optimality theory of NLP. To construct the NLP problem, we use the DIO algorithm. A comparison of the optimality conditions obtained in the paper with known results is provided.

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Sufficient optimality conditions for convex semi-infinite programming

Kostyukova, O. I., Tchemisova, T. V.

Taylor & Francis

We consider a convex semi-infinite programming (SIP) problem whose objective and constraint functions are convex w.r.t. a finite-dimensional variable x and whose constraint function also depends on a so-called index variable that ranges over a compact set inR. In our previous paper [O.I.Kostyukova,T.V. Tchemisova, and S.A.Yermalinskaya, On the algorithm of determination of immobile indices for convex SIP problems, IJAMAS Int. J. Math. Stat. 13(J08) (2008), pp. 13–33], we have proved an implicit optimality criterion that is based on concepts of immobile index and immobility order. This criterion permitted us to replace the optimality conditions for a feasible solution x0 in the convex SIP problem by similar conditions for x0 in certain finite nonlinear programming problems under the assumption that the active index set is finite in the original semi-infinite problem. In the present paper, we generalize the implicit optimality criterion for the case of an infinite active index set and obtain newfirst- and second-order sufficient optimality conditions for convex semi-infinite problems. The comparison with some other known optimality conditions is provided.

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Rigidity of abnormal extrema in nonlinear programming problems with equality and inequality constraints

Tchemisova, T. V.

Elsevier

Optimality conditions for nonlinear problems with equality and inequality constraints are considered. In the case when no constraint qualification (or regularity) is assumed, the Lagrange multiplier corresponding to the objective function can vanish in first order necessary optimality conditions given by Fritz John and the corresponding extremum is called abnormal. In the paper we consider second order sufficient optimality conditions that guarantee the rigidity of abnormal extrema (i.e. their isolatedness in the admissible sets).

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Force acting on a rough disk spinning in a flow of noninteracting particles

Plakhov, A. Yu., Tchemisova, T. V.

Pressure force exerted on a rough disk spinning in a flow of noninteracting particles is determined by considering that a flow of point particles impinges on a body spinning around a fixed point. The rough disk is identical with the sequence of sets and thus the sets can be viewed as successive approximations of the rough disk. A proper choice of sequence of sets shows that the characteristic of billiard scattering is independent of n, and the billiard scattering on the rough set is defined. The pressure force exerted on the disk is independent of its angular velocity and that the characteristic of the interaction that is the moment of the pressure force slows down the rotation of the rough disk. The transverse force aligned with the instantaneous velocity of the front point of the body results in Magnus effect.

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Modelling the problem of the food distribution by the Portuguese food banks

Martins, I., Guedes, T., Rama, P., Ramos, J., Tchemisova, T.

Inderscience

A food bank is a non-pro t, social solidarity organization that typically distributes the donated food among a wide variety of local non-pro t, social solidarity institutions which in turn feed the lowincome people. The problem presented by the Portuguese Federation of Food Banks is to determine, for a speci c food bank, the quantities of the donated products that must be assigned to each local social solidarity institution in order to satisfy the needs of the supported people as much as possible, without favouring any institution. We propose a linear programming model followed by a rounding heuristic to obtain a solution to the problem described. Computational results are reported.

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Optimality criteria without constraint qualications for linear semidenite problems

Kostyukova, O. I., Tchemisova, T. V.

Springer Verlag

We consider two closely related optimization problems: a problem of convex Semi- Infinite Programming with multidimensional index set and a linear problem of Semidefinite Programming. In study of these problems we apply the approach suggested in our recent paper [14] and based on the notions of immobile indices and their immobility orders. For the linear semidefinite problem, we define the subspace of immobile indices and formulate the first order optimality conditions in terms of a basic matrix of this subspace. These conditions are explicit, do not use constraint qualifications, and have the form of criterion. An algorithm determining a basis of the subspace of immobile indices in a finite number of steps is suggested. The optimality conditions obtained are compared with other known optimality conditions.

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Fractional and time-scales differential equations

Baleanu, D., Bhrawy, A. H., Torres, D. F. M., Salahshour, S.

Hindawi Publishing Corporation

Resumo indisponível.

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Spectral characterization of families of split graphs

Andelic, M., Cardoso, Domingos M.

Springer

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted.

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Necessary and sufficient conditions for a Hamiltonian graph

Sciriha, I, Cardoso, Domingos M.

Charles Babbage Research Centre

A graph is singular if the zero eigenvalue is in the spectrum of its 0-1 adjacency matrix A. If an eigenvector belonging to the zero eigenspace of A has no zero entries, then the singular graph is said to be a core graph. A ( k,t)-regular set is a subset of the vertices inducing a k -regular subgraph such that every vertex not in the subset has t neighbours in it. We consider the case when k=t which relates to the eigenvalue zero under certain conditions. We show that if a regular graph has a ( k,k )-regular set, then it is a core graph. By considering the walk matrix we develop an algorithm to extract ( k,k )-regular sets and formulate a necessary and sufficient condition for a graph to be Hamiltonian.

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The Jordan canonical form for a class of weighted directed graphs

Nina, H., Soto, R. L., Cardoso, Domingos M.

Elsevier

Recently, Cardon and Tuckfield (2011) [1] have described the Jordan canonical form for a class of zero-one matrices, in terms of its associated directed graph. In this paper, we generalize this result to describe the Jordan canonical form of a weighted adjacency matrix A in terms of its weighted directed graph.

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Spectra of graphs obtained by a generalization of the join graph operation

Cardoso, Domingos M., Freitas, M. A. A. de, Martins, E. A., Robbiano, M.

Elsevier

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.

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Relations between (κ, τ)-regular sets and star complements

Andelic, M., Cardoso, Domingos M., Simic, S. K .

Springer

Let G be a finite graph with an eigenvalue μ of multiplicity m. A set X of m vertices in G is called a star set for μ in G if μ is not an eigenvalue of the star complement GX which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (k ,t)-regular if it induces a k -regular subgraph and every vertex not in the subset has t neighbors in it. We investigate the graphs having a (k,t)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.

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A recursive construction of the regular exceptional graphs with least eigenvalue -2

Barbedo, I., Cardoso, Domingos M., Cvetkovic, D., Rama, P., Simic, S. K.

European Mathematical Society Publishing House

In spectral graph theory a graph with least eigenvalue 2 is exceptional if it is connected, has least eigenvalue greater than or equal to 2, and it is not a generalized line graph. A ðk; tÞ-regular set S of a graph is a vertex subset, inducing a k-regular subgraph such that every vertex not in S has t neighbors in S. We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.

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On the Faria's inequality for the Laplacian and signless Laplacian spectra: a unified approach

Andrade, E., Cardoso, Domingos M., Pastén, G., Rojo, O.

Elsevier

Let p(G)p(G) and q(G)q(G) be the number of pendant vertices and quasi-pendant vertices of a simple undirected graph G, respectively. Let m_L±(G)(1) be the multiplicity of 1 as eigenvalue of a matrix which can be either the Laplacian or the signless Laplacian of a graph G. A result due to I. Faria states that mL±(G)(1) is bounded below by p(G)−q(G). Let r(G) be the number of internal vertices of G. If r(G)=q(G), following a unified approach we prove that mL±(G)(1)=p(G)−q(G). If r(G)>q(G) then we determine the equality mL±(G)(1)=p(G)−q(G)+mN±(1), where mN±(1) denotes the multiplicity of 1 as eigenvalue of a matrix N±. This matrix is obtained from either the Laplacian or signless Laplacian matrix of the subgraph induced by the internal vertices which are non-quasi-pendant vertices. Furthermore, conditions for 1 to be an eigenvalue of a principal submatrix are deduced and applied to some families of graphs.

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Some results on the lattice parameters of quaternionic Gabor frames

Hartmann, Stefan

Springer

Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor frames to the quaternionic case and give new density results. The key tool is the two-sided windowed quaternionic Fourier transform (WQFT). As in the complex case, we want to write the WQFT as an inner product between a quaternion-valued signal and shifts and modulates of a real-valued window function. We demonstrate a Heisenberg uncertainty principle and for the results regarding the density, we employ the quaternionic Zak transform to obtain necessary and sufficient conditions to ensure that a quaternionic Gabor system is a quaternionic Gabor frame. We conclude with a proof that the Gabor conjecture do not hold true in the quaternionic case.

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Representable ((mathbb {T}, V))-categories

Chikhladze, Dimitri, Clementino, Maria Manuel, Hofmann, Dirk

Springer Verlag

Working in the framework of ((mathbb {T},textbf {V}))-categories, for a symmetric monoidal closed category V and a (not necessarily cartesian) monad (mathbb {T}), we present a common account to the study of ordered compact Hausdorff spaces and stably compact spaces on one side and monoidal categories and representable multicategories on the other one. In this setting we introduce the notion of dual for ((mathbb {T},textbf {V}))-categories. Working in the framework of (T, V)-categories, for a symmetric monoidal closed category V and a (not necessarily cartesian) monad T, we present a common account to the study of ordered compact Hausdorff spaces and stably compact spaces on one side and monoidal categories and representable multicategories on the other one. In this setting we introduce the notion of dual for (T, V)-categories.

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Regular pseudo-oriented maps and hypermaps of low genus

Catalano, Domenico, d'Azevedo, António Breda, Duarte, Rui

Elsevier

Pseudo-orientable maps were introduced by Wilson in 1976 to describe non-orientable regular maps for which it is possible to assign an orientation to each vertex in such a way that adjacent vertices have opposite orientations. This property extends naturally to non- orientable and orientable hypermaps. In this paper we classify the regular pseudo-oriented maps and hypermaps of characteristic χ > −3. With the help of GAP (The GAP group, 2014) and its library of small groups, we extend the classification down to characteristic χ = −16 (Tables 7–19 in the Appendix).

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Constant sign and nodal solutions for a class of nonlinear Dirichlet problems

Papageorgiou, N. S., Santos, S. R. Andrade, Staicu, V.

Elsevier

We consider a nonlinear Dirichlet problem with a Carathéodory reaction which has arbitrary growth from below. We show that the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal. In the semilinear case (i.e., p =2), with the reaction f(z, .)being C1and with subcritical growth, we show that there is a second nodal solution, for a total of four nontrivial smooth solutions. Finally,when the reaction has concave terms and is subcritical and for the nonlinear problem (i.e., 1

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Positive solutions for parametric nonlinear periodic problems with competing nonlinearities

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

Texas State University, Department of Mathematics

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator plus an indefinite potential and a reaction having the competing effects of concave and convex terms. For the superlinear (concave) term we do not employ the usual in such cases Ambrosetti-Rabinowitz condition. Using variational methods together with truncation, perturbation and comparison techniques, we prove a bifurcation-type theorem describing the set of positive solutions as the parameter varies.

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Nodal solutions for (p, 2)-equations

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

American Mathematical Society

In this paper, we study a nonlinear elliptic equation driven by the sum of a p-Laplacian and a Laplacian ((p, 2)-equation), with a Carathéodory (p − 1)-(sub-)linear reaction. Using variational methods combined with Morse theory, we prove two multiplicity theorems providing precise sign information for all the solutions (constant sign and nodal solutions). In the process, we prove two auxiliary results of independent interest.

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Dirichlet problems with singular and superlinear terms

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

World Scientific

We consider a parametric nonlinear Dirichlet problem driven by the p-Laplacian, with a singular term and a p-superlinear perturbation, which need not satisfy the usual Ambrosetti–Rabinowitz condition. Using variational methods together with truncation techniques, we prove a bifurcation-type theorem describing the behaviour of the set of positive solutions as the parameter varies.

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Women’s experiences of low back pain during pregnancy

Mota, Maria João, Cardoso, Mirtha, Carvalho, Andreia, Marques, Alda, Sá-Couto, Pedro, Demain, Sara

IOS press

OBJECTIVES: This study investigated the self-reported prevalence and impact of low back pain (LBP) during pregnancy in primiparous and multiparous women, and their treatment-seeking rationales and experiences, including their use of physiotherapy. METHODS: A sample of 105 post-partum women was recruited. All participants answered a questionnaire; women who experienced LBP during pregnancy (n=71) continue in the study and later they were also interviewed. Content analysis, descriptive and inferential statistics were used to analyse the data. RESULTS: Reports of LBP were common (n=71; 67.6%) and slightly more frequent in primiparous (n=40; 56.3%) than multiparous (n=31; 43.7%) women. Multiparous women with LBP were significantly older (p< 0.001) and reported more sleep disturbances (p=0.026) than primiparous women with LBP. LBP prevented women performing their daily activities (n=41; 57.7%) and worsened with the advance of pregnancy (n=55; 77.5%), yet 93.0% (n=66) of these women received no treatment. CONCLUSION: LBP is a prevalent and important clinical condition affecting the daily life of many pregnant women. Nevertheless, few women seek any treatment and physiotherapy is rarely considered. Given the significant impact on quality of life, health professionals need to be proactive in asking women about LBP.

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Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities

Aizicovici, S., Papageorgiou, N. S., Staicu, V.

International Press

We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter > 0, the problem has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign.

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Discrete-time positive periodic systems with state and control constraints

Rami, Mustapha Ait, Napp, Diego

IEEE

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

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Portuguese nurses’ knowledge of and attitudes toward hospitalized older adults

Tavares, João Paulo de Almeida, Silva, Alcione Leite da, Sá-Couto, Pedro, Boltz, Marie, Capezuti, Elizabeth

Wiley

Portugal is impacted by the rapid growth of the aging population, which has significant implications for its health care system. However, nurses have received little education focusing on the unique and complex care needs of older adults. This gap in the nurses′ education has an enormous impact in their knowledge and attitudes and affects the quality of nursing care provided to older adults. A cross-sectional study was conducted among 1068 Portuguese nurses in five hospitals (northern and central region) with the following purposes: (i) explore the knowledge and attitudes of nurses about four common geriatric syndromes (pressure ulcer, incontinence, restraint use and sleep disturbance) in Portuguese hospitals; and (ii) evaluate the influence of demographic, professional and nurses' perception about hospital educational support, geriatric knowledge, and burden of caring for older adults upon geriatric nursing knowledge and attitudes. The mean knowledge and attitudes scores were 0.41 ± 0.15 and 0.40 ± 0.21, respectively (the maximum score was 1). Knowledge of nurses in Portuguese hospitals about the four geriatric syndromes (pressure ulcers, sleep disturbance, urinary incontinence and restraint use) was found inadequate. The nurses' attitudes towards caring for hospitalized older adults were generally negative. Nurses who work in academic hospitals demonstrated significantly more knowledge than nurses in hospital centers. The attitudes of nurses were significantly associated with the hospital and unit type, region, hospital educational support, staff knowledge, and perceived burden of caring for older adults. The study findings support the need for improving nurses' knowledge and attitudes towards hospitalized older adults and implementing evidence-based guidelines in their practice.

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Assessment and topographic characterization of locoregional recurrences in head and neck tumours

Ferreira, Brigida Costa, Marques, Rui Vale, Khouri, Leila, Santos, Tânia, Sá-Couto, Pedro, Lopes, Maria do Carmo

BioMed Central

Purpose: To evaluate the differences between three methods of classification of recurrences in patients with head and neck tumours treated with Radiation Therapy (RT). Materials and methods: 367 patients with head and neck tumours were included in the study. Tumour recurrences were delineated in the CT images taken during patient follow-up and deformable registration was used to transfer this volume into the planning CT. The methods used to classify recurrences were: methodCTV quantified the intersection volume between the recurrence and the Clinical Target Volume (CTV); methodTV quantified the intersection between the Treated Volume and the recurrence (for method CTV and TV, recurrences were classified in-field if more than 95% of their volume were inside the volume of interest, marginal if the intersection was between 20-95% and outfield otherwise); and methodCOM was based on the position of the Centre Of Mass of the recurrence. A dose assessment in the recurrence volume was also made. Results: The 2-year Kaplan-Meier locoregional recurrence incidence was 10%. Tumour recurrences occurred in 22 patients in a mean time of 16.5 ± 9.4 months resulting in 28 recurrence volumes. The percentage of in-field recurrences for methods CTV, TV and COM was 7%, 43% and 50%, respectively. Agreement between the three methods in characterizing individually in-field and marginal recurrences was found only in six cases. Methods CTV and COM agreed in 14. The percentage of outfield recurrences was 29% using all methods. For local recurrences (in-field or marginal to gross disease) the average difference between the prescribed dose and D 98% in the recurrence volume was -5.2 ± 3.5% (range: -10.1%-0.9%). Conclusions: The classification of in-field and marginal recurrences is very dependent on the method used to characterize recurrences. Using methods TV and COM the largest percentage of tumour recurrences occurred in-field in tissues irradiated with high doses. Keywords: Head and neck tumours, Radiation therapy, Characterization of tumour recurrences, Geometric methods, Dosimetric assessment

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Cluster analysis in phenotyping a Portuguese population

Loureiro, Cláudia Chaves, Sá-Couto, Pedro, Todo-Bom, Ana, Bousquet, Jean

Elsevier

Background: Unbiased cluster analysis using clinical parameters has identified asthma pheno- types. Adding inflammatory biomarkers to this analysis provided a better insight into the disease mechanisms. This approach has not yet been applied to asthmatic Portuguese patients. Aim: To identify phenotypes of asthma using cluster analysis in a Portuguese asthmatic popu- lation treated in secondary medical care. Methods: Consecutive patients with asthma were recruited from the outpatient clinic. Patients were optimally treated according to GINA guidelines and enrolled in the study. Procedures were performed according to a standard evaluation of asthma. Phenotypes were identified by cluster analysis using Ward’s clustering method. Results: Of the 72 patients enrolled, 57 had full data and were included for cluster analysis. Distribution was set in 5 clusters described as follows: cluster (C) 1, early onset mild aller- gic asthma; C2, moderate allergic asthma, with long evolution, female prevalence and mixed inflammation; C3, allergic brittle asthma in young females with early disease onset and no evidence of inflammation; C4, severe asthma in obese females with late disease onset, highly symptomatic despite low Th2 inflammation; C5, severe asthma with chronic airflow obstruction, late disease onset and eosinophilic inflammation. Conclusions: In our study population, the identified clusters were mainly coincident with other larger-scale cluster analysis. Variables such as age at disease onset, obesity, lung function, FeNO (Th2 biomarker) and disease severity were important for cluster distinction.

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Goal setting for cerebral palsy children in context therapy: improve reliability when linking to ICF

Alvarelhão, Joaquim, Queirós, Alexandra, Sá-Couto, Pedro, Rocha, Nelson Pacheco

IOS press

The linking process of information to ICF is a common task in different strategies used in rehabilitation practise but is a time consuming process mainly due to reliability issues. This work aims to developed additional rules to those already published in order to improve reliability of the linking process to ICF. The results are encouraging and these work could help to develop in formation technologies tools for facilitate this process.

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Self-reported disability: association with lower extremity performance and other determinants in older adults attending primary care

Silva, Anabela Gonçalves, Queirós, Alexandra, Sá-Couto, Pedro, Rocha, Nelson Pacheco

American Physical Therapy Association

Background. Measurement of function usually involves the use of both performance-based and self-report instruments. However, the relationship between both types of measures is not yet completely understood, in particular for older adults attending primary care. Objective. The main objective of the study was to investigate the association between the World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0) and the Short Physical Performance Battery (SPPB) for older adults at primary care. A secondary objective was to determine the influence of sociodemographic and health-related variables on this relationship. Design. This was a cross-sectional study. Methods. A total of 504 participants aged 60 years and older from 18 different primary care centers underwent a one-session assessment including: sociodemographic variables, comorbidities, performance, self-reported disability, pain, depressive symptoms, and physical activity. Performance was assessed using the SPPB, and self-reported disability was assessed using the WHODAS 2.0. Results. The correlation between WHODAS 2.0 and SPPB scores was strong (r=.65). Regression analysis showed that the SPPB total score explained 41.7% of the variance in WHODAS 2.0 scores (adjusted R2=41.6%). A second model including the SPPB subtests (balance, gait, and sit-to-stand), depressive symptoms, number of pain sites, pain intensity, and level of physical activity explained 61.7% of the variance in WHODAS 2.0 scores (adjusted R2=60.4%). No model improvement was found when considering the 6 WHODAS 2.0 individual domains. Limitations. The cross-sectional nature of the study does not allow inferences on causal relationships. Conclusions. This study's findings confirm that self-report and performance-based measures relate to different aspects of functioning. Further study is needed to determine if primary care interventions targeting lower extremity performance and depressive symptoms improve self-reported disability.

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Refinement in hybridised institutions

Madeira, Alexandre, Martins, Manuel A., Barbosa, Luis S., Hennicker, Rolf

Springer Verlag

Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimuli or internal performance measures. A formal representation of such systems is through transition structures whose states correspond to the different configurations they may adopt. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. This paper characterises equivalence and refinement for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional, equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem is proved for hybridised logics.

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On some structural sets and a quaternionic (φ, ψ)-hyperholomorphic function theory

Abreu Blaya, Ricardo, Bory Reyes, Ricardo, Guzman Adan, Ali, Kähler, Uwe

Wiley-VCH Verlag

Quaternionic analysis is regarded as a broadly accepted branch of classical analysis referring to many different types of extensions of the Cauchy-Riemann equations to the quaternion skew field H. It relies heavily on results on functions defined on domains in R4 or R3 with values in H. This theory is centred around the concept of ψ-hyperholomorphic functions related to a so-called structural set ψ of H4 or H3 respectively. The main goal of this paper is to develop the nucleus of the (φ,ψ)-hyperholomorphic function theory, i.e., simultaneous null solutions of two Cauchy-Riemann operators associated to a pair φ,ψ of structural sets of H4. Following a matrix approach, a generalized Borel-Pompeiu formula and the corresponding Plemelj-Sokhotzki formulae are established.

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Fluctuation-dissipation dynamics of cosmological scalar fields

Bartrum, Sam, Berera, Arjun, Rosa, João G.

American Physical Society

We show that dissipative effects have a significant impact on the evolution of cosmological scalar fields, leading to friction, entropy production and field fluctuations. We explicitly compute the dissipation coefficient for different scalar fields within the standard model and some of its most widely considered extensions, in different parametric regimes. We describe the generic consequences of fluctuation-dissipation dynamics in the postinflationary universe, focusing in particular on friction and particle production, and analyze in detail two important effects. First, we show that dissipative friction delays the process of spontaneous symmetry breaking and may even damp the motion of a Higgs field sufficiently to induce a late period of warm inflation. Along with dissipative entropy production, this may parametrically dilute the abundance of dangerous thermal relics. Second, we show that dissipation can generate the observed baryon asymmetry without symmetry restoration, and we develop in detail a model of dissipative leptogenesis. We further show that this generically leads to characteristic baryon isocurvature perturbations that can be tested with cosmic microwave background observations. This work provides a fundamental framework to go beyond the leading thermal equilibrium semiclassical approximation in addressing fundamental problems in modern cosmology.

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Testing black hole superradiance with pulsar companions

Rosa, João G.

Elsevier

We show that the magnetic dipole and gravitational radiation emitted by a pulsar can undergo superradiant scattering off a spinning black hole companion. We find that the relative amount of superradiant modes in the radiation depends on the pulsar's angular position relative to the black hole's equatorial plane. In particular, when the pulsar and black hole spins are aligned, superradiant modes are dominant at large angles, leading to an amplification of the pulsar's luminosity, whereas for small angles the radiation is dominantly composed of non-superradiant modes and the signal is attenuated. This results in a characteristic orbital modulation of the pulsar's luminosity, up to the percent level within our approximations, which may potentially yield a signature of superradiant scattering in astrophysical black holes and hence an important test of general relativity.

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Quaternion Zernike Spherical Polynomials

Morais, J., Cação, I.

American Mathematical Society

Over the past few years considerable attention has been given to the role played by the Zernike polynomials (ZPs) in many different fields of geometrical optics, optical engineering, and astronomy. The ZPs and their applications to corneal surface modeling played a key role in this development. These polynomials are a complete set of orthogonal functions over the unit circle and are commonly used to describe balanced aberrations. In the present paper we introduce the Zernike spherical polynomials within quaternionic analysis ((R)QZSPs), which refine and extend the Zernike moments (defined through their polynomial counterparts). In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with $ mathbb{R}^3$ and $ mathbb{R}^4$). (R)QZSPs are orthonormal in the unit ball. The representation of these functions in terms of spherical monogenics over the unit sphere are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of their fundamental properties and a further second order homogeneous differential equation are also discussed. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach. (R)QZSPs are new in literature and have some consequences that are now under investigation.

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Integer-valued self-exciting periodic threshold autoregressive processes

Pereira, Isabel, Scotto, Manuel, Nicolette, Raquel

Departamento de Matemática da Universidade de Coimbra

In this paper, the periodic self-exciting threshold integer-valued autoregressive model of order one with period $T$ driven by a periodic sequence of independent Poisson-distributed random variables is introduced and analyzed in detail. Basic probabilistic and statistical properties of the model are discussed as well as parameter estimation and forecasting.

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An approximation formula for the Katugampola integral

Almeida, Ricardo, Bastos, Nuno R.O.

ILIRIAS Research Institute

The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus converts the fractional problem into a standard one. With some examples, we show the accuracy of the method, and then we present the utility of the method by solving a fractional integral equation.

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La Pratica d’arismetica de Ruy Mendes dans le contexte des arithmétiques marchandes ibériques

Clain, Teresa Costa

Société Mathématique de France

Au xvie siècle furent publiés les premiers ouvrages sur l arithmé- tique marchande imprimés au Portugal tels que le Tratado da Pratica Darismetica de Gaspar Nicolas édité pour la première fois en 1519, la Pratica d Arismetica de Ruy Mendes de 1540 et le Tratado da arte de Arismetica de Bento Fernandes en 1555. Dans tous ces traités sont présents des modèles arithmétiques liés aux opérations nancières, sous la forme de règles propres issues du commerce portugais des épices et de sa diffusion dans toute l Europe. Nous donnerons une brève présentation de la Pratica d Arismetica de Ruy Mendes que nous replacerons dans le corpus des uvres d arithmétique marchande au Portugal, en indiquant leurs sources et leurs in uences relativement au contexte ibérique. In the sixteenth century began the publication of mercantile arithmetic treatises printed in Portugal, such as the Tratado da Pratica Darismetica of Gaspar Nicolas, rst published in 1519, the Pratica d Arismetica of Ruy Mendes, with only one edition in 1540 and the Tratado da arte de Arismetica published by Bento Fernandes in 1555. We can nd, in these treatises, arithmetical models linked to nancial transactions with speci c rules of Portuguese trade of spices and its distribution in Europe. We will present a brief introduction of the Pratica d Arismetica of Ruy Mendes and its place with respect to other works in mercantile arithmetic produced in Portugal. We also highlight sources and in uences with respect to the Iberian context. No século XVI inciou-se a publicação de obras de aritmética mercantil impressas em Portugal, tais como o "Tratado da Pratica Darismetica" de Gaspar Nicolas, publicado pela primeira vez em 1519, a "Pratica d'Arismetica" de Ruy Mendes de 1540 e o "Tratado da arte de Arismetica", de Bento Fernandes em 1555. Nos tratados encontramos uma modelação aritmética ligada às operações financeiras, na forma de regras próprias do comércio português das especiarias e da sua distribuição pela Europa. Faremos uma breve apresentação da "Pratica d'Arismetica" de Ruy Mendes e do seu enquadramento nas obras em aritmética mercantil produzidas em Portugal, referenciando ainda fontes e influências presentes tendo em conta o contexto ibérico.

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Four solutions of an inhomogeneous elliptic equation with critical exponent and singular term

Chen, Jianqing, Rocha, Eugénio M.

Elsevier

In this paper, we prove the existence of four nontrivial solutions of a elliptic equation with a Hardy singularity and show that at least one of them is sign changing. Our results extend some previous works on the literature, as Tarantello(1993), Kang-Deng(2005) and Hirano-Shioji(2005).

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Maximum distance separable 2D convolutional codes

Climent, J.-J., Napp, D., Perea, C., Pinto, Raquel

IEEE

Maximum distance separable (MDS) block codes and MDS 1D convolutional codes are the most robust codes for error correction within the class of block codes of a fixed rate and 1D convolutional codes of a certain rate and degree, respectively. In this paper, we generalize this concept to the class of 2D convolutional codes. For that, we introduce a natural bound on the distance of a 2D convolutional code of rate $k/n$ and degree $delta $ , which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then, we prove the existence of 2D convolutional codes of rate $k/n$ and degree $delta $ that reach such bound when $n geq k (({(lfloor ({delta }/{k}) rfloor + 2)(lfloor ({delta }/{k}) rfloor + 3)})/{2})$ if $k {nmid } delta $ , or $n geq k (({(({delta }/{k}) + 1)(({delta }/{k}) + 2)})/{2})$ if $k mid delta $ , by presenting a concrete constructive procedure.

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Periodic problems with a reaction of arbitrary growth

Aizicovici, S., Papageorgiou, N. S., Staicu, Vasile

Yokohama Publishers

We consider nonlinear periodic equations driven by the scalar p-Laplacian and with a Carath eodory reaction which does not satisfy a global growth condition. Using truncation-perurbation techniques, variational methods and Morse theory, we prove a "three solutions theorem", providing sign information for all the solutions. In the semilinear case (p = 2), we produce a second nodal solution, for a total of four nontrivial solutions. We also cover problems which are resonant at zero.

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Minimal resistance of curves under the single impact assumption

Akopyan, Arseniy, Plakhov, Alexander

Society for Industrial and Applied Mathematics

We consider the hollow on the half-plane ${ (x,y) : y le 0 } subset mathbb{R}^2$ defined by a function $u : (-1,, 1) to mathbb{R}$, $u(x) < 0$, and a vertical flow of point particles incident on the hollow. It is assumed that $u$ satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph$(u)$ and goes away without hitting the graph of $u$ anymore. We solve the problem: find the function $u$ minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the $y$-axis. Assuming that the resistance of $u equiv 0$ equals 1, we show that the minimal resistance equals $pi/2 - 2arctan(1/2) approx 0.6435$. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730--2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space ${(x_1,ldots,x_d, y) : y le 0 } subset mathbb{R}^{d+1}$ is defined by a radial function $U$ satisfying the SIC, $U(x) = u(|x|)$, with $x = (x_1,ldots,x_d)$, $u(xi) < 0$ for $0 le xi < 1$, and $u(xi) = 0$ for $xi ge 1$, and the flow is parallel to the $y$-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as $d to infty$.

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Bodies with mirror surface invisible from two points

Plakhov, Alexander, Roshchina, Vera

IOP Publishing

We consider a setting where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with mirror surface, and the billiard in the complement of the set is identified with the dynamics of light rays outside the body in the framework of geometric optics. We show that in this setting it is possible to construct a body invisible from two points.

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The problem of minimal resistance for functions and domains

Plakhov, Alexander

Society for Industrial and Applied Mathematics

Here we solve the problem posed by Comte and Lachand-Robert in [SIAM J. Math. Anal., 34 (2002), pp. 101–120]. Take a bounded domain Ω ⊂ R2 and a piecewise smooth nonpositive function u : ¯Ω → R vanishing on ∂Ω. Consider a flow of point particles falling vertically down and reflected elastically from the graph of u. It is assumed that each particle is reflected no more than once (no multiple reflections are allowed); then the resistance of the graph to the flow is expressed as R(u; Ω) = 1 |Ω| Ω(1 + |∇u(x)|2)−1dx. We need to find infΩ,u R(u;Ω). One can easily see that |∇u(x)| < 1 for all regular x ∈ Ω, and therefore one always has R(u; Ω) > 1/2. We prove that the infimum of R is exactly 1/2. This result is somewhat paradoxical, and the proof is inspired by, and partly similar to, the paradoxical solution given by Besicovitch to the Kakeya problem [Amer. Math. Monthly, 70 (1963), pp. 697–706].

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Fractal bodies invisible in 2 and 3 directions

Plakhov, Alexander, Roshchina, Vera

American Institute of Mathematical Sciences (AIMS)

We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fractal body invisible in these directions. Moreover, there exists a three-dimensional fractal body invisible in three orthogonal directions. The work continues the previous study in [1, 12], where two-dimensional bodies invisible in one direction and three dimensional bodies invisible in one and two orthogonal directions were constructed.

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Optimal roughening of convex bodies

Plakhov, Alexander

University of Toronto Press

A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies C1 and C2 such that C1 ⊂ C2 ⊂ R3 and ∂C1 ∩ ∂C2 = ∅, minimize the resistance in the class of connected bodies B such that C1 ⊂ B ⊂ C2. We prove that the infimum of resistance is zero; that is, there exist ”almost perfectly streamlined” bodies.

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Billiards, scattering by rough obstacles, and optimal mass transportation

Plakhov, Alexander

Springer

This article presents a brief exposition of recent results of the author on billiard scattering by rough obstacles. We define the notion of a rough body and give a characterization of scattering by rough bodies. Then we define the resistance of a rough body; it can be interpreted as the aerodynamic resistance of the somersaulting body moving through a rarefied medium. We solve the problems of maximum and minimum resistance for rough bodies (more precisely, for bodies obtained by roughening a prescribed convex set) in arbitrary dimension. Surprisingly, these problems are reduced to special problems of optimal mass transportation on the sphere.

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An inverse problem of Newtonian aerodynamics

Plakhov, Alexander, Samko, Stefan

We consider a rarefied medium in Rd, d ≥ 2 consisting of non-interacting point masses moving at unit velocity in all directions. Given the density of velocity distribution, one easily calculates the pressure created by the medium in any direction. We then consider the inverse problem: given the pressure distribution f : Sd−1 →R+, determine the density ρ : Sd−1 →R+. Assuming that the reflection of medium particles by obstacles is elastic, we show that the solution for the inverse problem is generally non-unique, derive exact inversion formulas, and state necessary and sufficient conditions for existence of a solution. We also present arguments indicating that the inversion is typically unique in the case of non-elastic reflection, and derive exact inversion formulas in a special case of such reflection.

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Lower bounds for the approximation with variation-diminishing splines

Cerejeiras, Paula, Forster, Brigitte, Nagler, Johannes

Elsevier

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0, 1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.

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Independência funcional de pessoas idosas com perturbações mentais: um estudo num serviço de psicogeriatria em Portugal

Brandão, Maria Piedade, Gonçalves, Joana, Sá-Couto, Pedro, Sousa, Liliana

Elsevier España; Universidade Nova de Lisboa, Escola Nacional de Saúde Pública

A dependência funcional em pessoas idosas aumenta a necessidade de cuidados sociais e de saúde. Contudo, a vasta literatura sobre independência funcional raramente se tem centrado nas pessoas idosas com perturbações mentais. Este estudo avalia a independência funcional de pessoas idosas (≥ 65 anos) com perturbações mentais. Trata‐se de um estudo transversal e retrospetivo em que os dados foram obtidos a partir de processos clínicos no serviço de psicogeriatria do Hospital Magalhães de Lemos, Porto, Portugal. A amostra compreende 157 participantes. A independência funcional foi avaliada através do sistema de avaliação de pessoas idosas EASYCare e as perturbações mentais obtidas a partir do diagnóstico clínico. Os principais resultados indicam 4 grupos considerando a independência funcional: independentes (44,7%), dependentes ligeiros (36,8%), dependentes moderados (13,2%) e dependentes severos (5,3%). A independência funcional em pessoas idosas com perturbação mental é relevante para os serviços sociais e de saúde planificarem programas de promoção da autonomia e bem‐estar. Functional dependency in older persons increases the need of social and health care. However the vast literature on functional independency has rarely focused on older people with mental disorders. This study examines functional independency in older persons (≥65 years old) with mental disorders. This is a cross-sectional and retrospective study; data were obtained from clinical processes at the psychogeriatric unit of the Hospital Magalhães Lemos, Porto, Portugal. The sample comprises 157 participants. Functional independence was assessed with EASYCare (Elderly Assessment System); mental disorders were obtained from the clinical diagnosis. Main findings suggest four groups according to functional in/dependency: independent (44.7%), light dependent, (36.8%), moderate dependent (13.2%)and severe dependent (5.3%). Functional independence in older persons with mental disorders is relevant for social and health services to plan programs that promote autonomy and well-being.

ria.ua.pt

A simplex like approach based on star sets for recognizing convex-QP adverse graphs

Cardoso, Domingos M., Luz, Carlos J.

Springer

A graph G with convex-QP stability number (or simply a convex-QP graph) is a graph for which the stability number is equal to the optimal value of a convex quadratic program, say P(G). There are polynomial-time procedures to recognize convex-QP graphs, except when the graph G is adverse or contains an adverse subgraph (that is, a non complete graph, without isolated vertices, such that the least eigenvalue of its adjacency matrix and the optimal value of P(G) are both integer and none of them changes when the neighborhood of any vertex of G is deleted). In this paper, from a characterization of convex-QP graphs based on star sets associated to the least eigenvalue of its adjacency matrix, a simplex-like algorithm for the recognition of convex-QP adverse graphs is introduced.

ria.ua.pt

Sharp weyl law for signed counting function of positive interior transmission eigenvalues

Lakshtanov, E., Vainberg, B.

Society for Industrial and Applied Mathematics

We consider the interior transmission eigenvalue (ITE) problem that arises when scattering by inhomogeneous media is studied. The ITE problem is not self-adjoint. We show that positive ITEs are observable together with plus or minus signs that are defined by the direction of motion of the corresponding eigenvalues of the scattering matrix (as they approach $z=1$). We obtain a Weyl-type formula for the counting function of positive ITEs, which are taken together with the ascribed signs. The results are applicable to the case when the medium contains an unpenetrable obstacle.

ria.ua.pt

A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials

Cação, I, Falcão, M. I., Malonek, H. R.

Springer Basel

Recently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of Hypercomplex Function Theory (Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory, 12 (2012), no. 2, 371-391). This paper deals with an extension of that approach to a recurrence relation for the construction of a complete system of orthogonal Clifford-algebra valued polynomials of arbitrary degree. At the same time the matrix approach sheds new light on results about systems of Clifford algebra-valued orthogonal polynomials obtained by Gurlebeck, Bock, Lavika, Delanghe et al. during the last five years. In fact, it allows to prove directly some intrinsic properties of the building blocks essential in the construction process, but not studied so far.

ria.ua.pt

Monogenic pseudo-complex power functions and their applications

Cruz, Carla, Falcão, Maria Irene, Malonek, Helmuth R.

John Wiley & Sons

The use of a non-commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. Naturally arises the question of their relationships and the advantages or disadvantages of different types of polynomials. In this sense, the present paper investigates the intrinsic relationship between two different types of monogenic Appell polynomials. Several authors payed attention to the construction of complete sets of monogenic Appell polynomials, orthogonal with respect to a certain inner product, and used them advantageously for the study of problems in 3D-elasticity and other problems. Our goal is to show that, as consequence of the binomial nature of those generalized Appell polynomials, their inner structure is determined by interesting combinatorial relations in which the central binomial coefficients play a special role. As a byproduct of own interest, a Riordan-Sofo type binomial identity is also proved.

ria.ua.pt

Matrix representations of a special polynomial sequence in arbitrary dimension

Cação, Isabel, Falcão, Maria Irene, Malonek, Helmuth Robert

Springer Verlag

This paper provides an insight into different structures of a special polynomial sequence of binomial type in higher dimensions with values in a Clifford algebra. The elements of the special polynomial sequence are homogeneous hypercomplex differentiable (monogenic) functions of different degrees and their matrix representation allows to prove their recursive construction in analogy to the complex power functions. This property can somehow be considered as a compensation for the loss of ultiplicativity caused by the non-commutativity of the underlying algebra.

ria.ua.pt

Laguerre derivative and monogenic Laguerre polynomials: an operational approach

Cação, Isabel, Falcão, Maria Irene, Malonek, Helmuth Robert

Elsevier

Hypercomplex function theory generalizes the theory of holomorphic functions of one complex variable by using Clifford Algebras and provides the fundamentals of Clifford Analysis as a refinement of Harmonic Analysis in higher dimensions. We define the Laguerre derivative operator in hypercomplex context and by using operational techniques we construct generalized hypercomplex monogenic Laguerre polynomials. Moreover, Laguerre-type exponentials of order mm are defined.

ria.ua.pt

A note on a one-parameter family of non-symmetric number triangles

Falcão, Irene, Malonek, Helmuth Robert

AGH University of Science and Technology Press

The recently growing interest in special Clifford Algebra valued polynomial solutions of generalized Cauchy-Riemann systems in (n + 1)-dimensional Euclidean spaces suggested a detailed study of the arithmetical properties of their coefficients, due to their combinatoric relevance. This concerns, in particular, a generalized Appell sequence of homogeneous polynomials whose coe cient's set can be treated as a one-parameter family of non-symmetric triangles of fractions. The discussion of its properties, similar to those of the ordinary Pascal triangle (which itself does not belong to the family), is carried out in this paper.

ria.ua.pt

On paravector valued homogeneous monogenic polynomials with binomial expansion

Malonek, Helmuth Robert, Falcão, Maria Irene

SP Birkhäuser Verlag Basel

The aim of this note is to study a set of paravector valued homogeneous monogenic polynomials that can be used for a construction of sequences of generalized Appell polynomials in the context of Clifford analysis. Therefore, we admit a general form of the vector part of the first degree polynomial in the Appell sequence. This approach is different from the one presented in recent papers on this subject. We show that in the case of paravector valued polynomials of three real variables, there exist essentially two different types of such polynomials together with two other trivial types of polynomials. The proof indicates a way of obtaining analogous results in the case of polynomials of more than three variables.

ria.ua.pt

Valid inequalities for the single arc design problem with set-ups

Agra, Agostinho, Doostmohammadi, Mahdi, Louveaux, Quentin

Elsevier

We consider a mixed integer set which generalizes two well-known sets: the single node fixed-charge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed integer problems such as lot-sizing and network design problems. We derive several families of valid inequalities that, in particular, generalize the arc residual capacity inequalities and the flow cover inequalities. For the constant capacitated case we provide an extended compact formulation and give a partial description of the convex hull in the original space which is exact under a certain condition. By lifting some basic inequalities we provide some insight on the difficulty of obtaining such a full polyhedral description for the constant capacitated case. Preliminary computational results are presented.

ria.ua.pt

A maritime inventory routing problem with stochastic sailing and port times

Agra, Agostinho, Christiansen, Marielle, Delgado, Alexandrino, Hvattum, Lars Magnus

Elsevier

This paper describes a stochastic short sea shipping problem where a company is responsible for both the distribution of oil products between islands and the inventory management of those products at consumption storage tanks located at ports. In general, ship routing and scheduling is associated with uncertainty in weather conditions and unpredictable waiting times at ports. In this work, both sailing times and port times are considered to be stochastic parameters. A two-stage stochastic programming model with recourse is presented where the first stage consists of routing, loading and unloading decisions, and the second stage consists of scheduling and inventory decisions. The model is solved using a decomposition approach similar to an L-shaped algorithm where optimality cuts are added dynamically, and this solution process is embedded within the sample average approximation method. A computational study based on real-world instances is presented.

ria.ua.pt

A characterization of the weighted Lovász number based on convex quadratic programming

Luz, Carlos J.

Springer

Luz and Schrijver (SIAM J Discrete Math 19(2):382–387, 2005) introduced a characterization of the Lovász number based on convex quadratic programming. This characterization is now extended to the weighted version of that number. In consequence, a class of graphs for which the weighted Lovász number coincides with the weighted stability number is characterized. Several examples of graphs of this class are presented.

ria.ua.pt

Distance domination, guarding and covering of maximal outerplanar graphs

Canales, Santiago, Hernández, Gregorio, Martins, Mafalda, Matos, Inês

Elsevier

In this paper we introduce the notion of distance k-guarding applied to triangulation graphs, and associate it with distance k-domination and distance k-covering. We obtain results for maximal outerplanar graphs when k=2. A set S of vertices in a triangulation graph T is a distance 2-guarding set (or 2d-guarding set for short) if every face of T has a vertex adjacent to a vertex of S. We show that ⌊n/5⌋ (respectively, ⌊n/4⌋) vertices are sufficient to 2d-guard and 2d-dominate (respectively, 2d-cover) any n-vertex maximal outerplanar graph. We also show that these bounds are tight.

ria.ua.pt

Random extremal solutions of differential inclusions

Bressan, Alberto, Staicu, Vasile

Springer

Given a Lipschitz continuous multifunction $F$ on ${mathbb{R}}^{n}$, we construct a probability measure on the set of all solutions to the Cauchy problem $dot xin F(x)$ with $x(0)=0$. With probability one, the derivatives of these random solutions take values within the set $ext F(x)$ of extreme points for a.e.~time $t$. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.

ria.ua.pt

The existence of solutions to variational problems of slow growth

Cellina, Arrigo, Staicu, Vasile

Elsevier

We consider the existence of solutions, in the space W^{1,1}(Ω), to the problem minimize ∫_{Ω}L(∇v(x))dx on φ+W₀^{1,1}(Ω) where L is of slow (linear or at most quadratic) growth. We present a necessary and sufficient condition in order that, for any smooth boundary datum φ and for any bounded Ω with smooth boundary, the minimum problem be solvable.

ria.ua.pt

Body with mirror surface and connected interior invisible from one point

Aleksenko, Alena

L.N. Gumilyov Eurasian National University

Here we demonstrate existence of a piecewise smooth obstacle having connected interior and invisible from a point in the framework of geometric optics.

ria.ua.pt

Gyroharmonic analysis on relativistic gyrogroups

Ferreira, M.

University of Kashan

Einstein, Möbius, and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis. Although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. Our study focus on the translation and convolution operators, eigenfunctions of the Laplace-Beltrami operator, Poisson transform, Fourier-Helgason transform, its inverse, and Plancherel's Theorem. We show that in the limit of large $t,$ $t rightarrow +infty,$ the resulting gyroharmonic analysis tends to the standard Euclidean harmonic analysis on ${mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.

ria.ua.pt

On the sequence $alpha n!$

Aleksenko, Alena

Mathematical Institute of the Slovak Academy of Sciences

We prove that there exists α ∈ R such that for any N the dicrepancy DN of the sequence 1αn!l, 1 ⩽ n ⩽ N satisfies DN = O(log N).

ria.ua.pt

A spectrum associated with Minkowski diagonal continued fraction

Aleksenko, Alena

Tula State Pedagogical University

ria.ua.pt

Semilinear neumann equations with indefinite and unbounded potential

Aizicovici, Sergiu, Papageorgiou, Nikolaos S., Staicu, Vasile

University of Houston

We consider a semilinear Neumann problem with an indefinite and unbounded potential, and a Carathéodory reaction term. Under asymptotic conditions on the reaction which make the energy functional coercive, we prove multiplicity theorems producing three or four solutions with sign information on them. Our approach combines variational methods based on the critical point theory with suitable perturbation and truncation techniques, and with Morse theory.

ria.ua.pt

Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction

Aizicovici, Sergiu, Papageorgiou, Nikolaos S., Staicu, Vasile

Juliusz Schauder Centre for Nonlinear Studies, Nicolaus Copernicus University

We consider a parametric semilinear Dirichlet problem driven by the Laplacian plus an indefinite unbounded potential and with a reaction of superdifissive type. Using variational and truncation techniques, we show that there exists a critical parameter value λ_{∗}>0 such that for all λ> λ_{∗} the problem has least two positive solutions, for λ= λ_{∗} the problem has at least one positive solutions, and no positive solutions exist when λ∈(0,λ_{∗}). Also, we show that for λ≥ λ_{∗} the problem has a smallest positive solution.

ria.ua.pt

Riemann-Hilbert problems for monogenic functions in axially symmetric domains

He, Fuli, Ku, Min, Kähler, Uwe, Sommen, Frank, Bernstein, Swanhild

SpringerOpen

We consider Riemann-Hilbert boundary value problems (for short RHBVPs) with variable coefficients for axially symmetric monogenic functions defined in axial symmetric domains. This is done by constructing a method to reduce the RHBVPs for axially symmetric monogenic functions defined in four-dimensional axial symmetric domains into the RHBVPs for analytic functions defined over the complex plane. Then we derive solutions to the corresponding Schwarz problem. Finally, we generalize the results obtained to null-solutions of (D−α)ϕ=0, α∈R, where R denotes the field of real numbers.

ria.ua.pt

Problems of optimal transportation on the circle and their mechanical applications

Plakhov, Alexander, Tchemisova, Tatiana

Elsevier

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

ria.ua.pt

Random extremal solutions of differential inclusions

Bressan, Alberto, Staicu, Vasile

Springer Verlag; Birkhäuser Basel

Given a Lipschitz continuous multifunction F on Rⁿ, we construct a probability measure on the set of all solutions to the Cauchy problem x∈F(x) with x(0)=0. With probability one, the derivatives of these random solutions take values within the set extF(x) of extreme points for a.e. time t. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.

ria.ua.pt

On (p, q) − equations with concave terms

Papageorgiou, Nikolaos S., Santos, Sandrina R. A., Staicu, Vasile

Gakkotosho

We consider a (p, q)− equation (1 < q < p, p ≥ 2) with a parametric concave term and a (p − 1)− linear perturbation. We show that the problem have five nontrivial smooth solutions: four of constant sign and the fifth nodal. When q = 2 (i.e., (p, 2) equation) we show that the problem has six nontrivial smooth solutions, but we do not specify the sign of the sixth solution. Our approach uses variational methods, together with truncation and comparison techniques and Morse theory.

ria.ua.pt

Traces for Besov spaces on fractal h-sets and dichotomy results

Caetano, António, Haroske, Dorothee

Institute of Mathematics of the Polish Academy of Sciences

We study the existence of traces of Besov spaces on fractal h-sets Γ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that—depending on the function space and the set Γ —there occurs an alternative: either the trace on Γ exists, or smooth functions compactly supported outside Γ are dense in the space. This notion was introduced by Triebel (2008) for the special case of d-sets.

ria.ua.pt

Quasilinear elliptic systems with measure data

Leonetti, Francesco, Rocha, Eugénio, Staicu, Vasile

Elsevier

We study the existence of solutions of quasilinear elliptic systems involving $N$ equations and a measure on the right hand side, with the form $$left{begin{array}{ll} -sum_{i=1}^n frac{partial}{partial x_i}left(sumlimits_{beta=1}^{N}sumlimits_{j=1}^{n}% a_{i,j}^{alpha,beta}left( x,uright)frac{partial}{partial x_j}u^betaright)=mu^alpha& mbox{ in }Omega ,\ u=0 & mbox{ on }partialOmega, end{array}right.$$ where $alphain{1,dots,N}$ is the equation index, $Omega$ is an open bounded subset of $mathbb{R}^{n}$, $u:Omegarightarrowmathbb{R}^{N}$ and $mu$ is a finite Randon measure on $mathbb{R}^{n}$ with values into $mathbb{R}^{N}$. Existence of a solution is proved for two different sets of assumptions on $A$. Examples are provided that satisfy our conditions, but do not satisfy conditions required on previous works on this matter.

ria.ua.pt

Optimal control of affine connection control systems from the point of view of Lie algebroids

Abrunheiro, L., Camarinha, M.

World Scientific Publishing Company

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

ria.ua.pt

The Herglotz variational problem on spheres and its optimal control approach

Abrunheiro, Lígia, Machado, Luís, Martins, Natália

Ilirias Publications

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

ria.ua.pt

Geometric Hamiltonian formulation of a variational problem depending on the covariant acceleration

Abrunheiro, Lígia, Camarinha, Margarida, Clemente-Gallardo, Jesús

Hindawi Publishing Corporation

We consider a second-order variational problem depending on the covariant acceleration, which is related to the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of Pontryagin’s maximum principle, allows us to study the dynamics of the control problem.

ria.ua.pt

A Discretization of the Hadamard fractional derivative

Almeida, Ricardo, Bastos, Nuno

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.

ria.ua.pt

Constructing strongly-MDS convolutional codes with maximum distance profile

Napp, Diego, Smarandache, Roxana

American Institute of Mathematical Sciences (AIMS)

This paper revisits strongly-MDS convolutional codes with maximum distance profile (MDP). These are (non-binary) convolutional codes that have an optimum sequence of column distances and attains the generalized Singleton bound at the earliest possible time frame. These properties make these convolutional codes applicable over the erasure channel, since they are able to correct a large number of erasures per time interval. The existence of these codes have been shown only for some specific cases. This paper shows by construction the existence of convolutional codes that are both strongly-MDS and MDP for all choices of parameters.

ria.ua.pt

Superregular matrices and applications to convolutional codes

Almeida, P. J., Napp, D., Pinto, R.

Elsevier

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature.

ria.ua.pt

Behavioral equivalence of hidden k-logics: an abstract algebraic approach

Babenyshev, Sergey, Martins, Manuel A.

Elsevier

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence — the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent.

ria.ua.pt

Riemann-Hilbert problems for poly-Hardy space on the unit ball

He, Fuli, Ku, Min, Dang, Pei, Kähler, Uwe

Taylor and Francis

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

ria.ua.pt

A scale variational principle of Herglotz

Almeida, Ricardo

University of Debrecen, Hungary

The Herglotz problem is a generalization of the fundamental problem of the calculus of variations. In this paper, we consider a class of non-differentiable functions, where the dynamics is described by a scale derivative. Necessary conditions are derived to determine the optimal solution for the problem. Some other problems are considered, like transversality conditions, the multi-dimensional case, higher-order derivatives and for several independent variables.

ria.ua.pt

Inflaton dark matter from incomplete decay

Bastero-Gil, Mar, Cerezo, Rafael, Rosa, João G.

American Physical Society

We show that the decay of the inflaton field may be incomplete, while nevertheless successfully reheating the Universe and leaving a stable remnant that accounts for the present dark matter abundance. We note, in particular, that since the mass of the inflaton decay products is field dependent, one can construct models, endowed with an appropriate discrete symmetry, where inflaton decay is kinematically forbidden at late times and only occurs during the initial stages of field oscillations after inflation. We show that this is sufficient to ensure the transition to a radiation-dominated era and that inflaton particles typically thermalize in the process. They eventually decouple and freeze out, yielding a thermal dark matter relic. We discuss possible implementations of this generic mechanism within consistent cosmological and particle physics scenarios, for both single-field and hybrid inflation.

ria.ua.pt

Scalar field dark matter and the Higgs field

Bertolami, Orfeu, Cosme, Catarina, Rosa, João G.

Elsevier

We discuss the possibility that dark matter corresponds to an oscillating scalar field coupled to the Higgs boson. We argue that the initial field amplitude should generically be of the order of the Hubble parameter during inflation, as a result of its quasi-de Sitter fluctuations. This implies that such a field may account for the present dark matter abundance for masses in the range 10^-6 - 10^-4 eV, if the tensor-to-scalar ratio is within the range of planned CMB experiments. We show that such mass values can naturally be obtained through either Planck-suppressed non-renormalizable interactions with the Higgs boson or, alternatively, through renormalizable interactions within the Randall–Sundrum scenario, where the dark matter scalar resides in the bulk of the warped extra-dimension and the Higgs is confined to the infrared brane.

ria.ua.pt

Nonlinear periodic problems with a jumping reaction

Aizicovici, Sergiu, Papageorgiou, Nikolaos S., Staicu, Vasile

American Romanian Academy of Arts and Sciences

We consider a periodic problem driven by the scalar $p-$Laplacian and with a jumping (asymmetric) reaction. We prove two multiplicity theorems. The first concerns the nonlinear problem ($1 ria.ua.pt


Efficient domination through eigenvalues

Cardoso, Domingos M., Lozin, V. V., Luz, C. J., Pacheco, M. F.

Elsevier

The paper begins with a new characterization of (k,τ)(k,τ)-regular sets. Then, using this result as well as the theory of star complements, we derive a simplex-like algorithm for determining whether or not a graph contains a (0,τ)(0,τ)-regular set. When τ=1τ=1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NP-complete. If −1−1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it does not work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs.

ria.ua.pt

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Abreu, N., Cardoso, Domingos M., Carvalho, P., Vinagres, C. T. M.

Elsevier

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.

ria.ua.pt

Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators

Ferreira, Milton dos Santos, Vieira, Nelson Felipe Loureiro

Elsevier

In this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order $beta in ]0,2].$ Applying operational techniques via Fourier and Mellin transforms we obtain an integral representation of the fundamental solution (FS) of the time fractional diffusion-wave operator. Series representations of the FS are explicitly obtained for any dimension. From these we derive the FS for the time fractional parabolic Dirac operator in the form of integral and series representation. Fractional moments of arbitrary order $gamma>0$ are also computed. To illustrate our results we present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameter.

ria.ua.pt

On MDS convolutional codes over Z_p^r

Pinto, Raquel, Napp, Diego, Toste, Marisa

Springer

Maximum distance separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Zpr was recently discovered in Oued and Sole (IEEE Trans Inf Theory 59(11):7305–7313, 2013) via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Zpr from a new perspective. We introduce the notions of p-standard form and r-optimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over Zpr for any given set of parameters.

ria.ua.pt

Nonlinear, nonhomogeneous parametric Neumann problems

Aizicovici, S., Papageorgiou, Nikolaos S., Staicu, Vasile

Juliusz Schauder University Centre for Nonlinear Studies; Nicolaus Copernicus University in Toruń

We consider a parametric nonlinear Neumann problem driven by a nonlinear nonhomogeneous differential operator and with a Caratheodory reaction $fleft( t,xright) $ which is $p-$superlinear in $x$ without satisfying the usual in such cases Ambrosetti-Rabinowitz condition. We prove a bifurcation type result describing the dependence of the positive solutions on the parameter $lambda>0,$ we show the existence of a smallest positive solution $overline{u}_{lambda}$ and investigate the properties of the map $lambdarightarrowoverline{u}_{lambda}.$ Finally we also show the existence of nodal solutions.

ria.ua.pt

Fractional differential equations with dependence on the Caputo-Katugampola derivative

Almeida, R., Malinowska, A. B., Odzijewicz, T.

American Society of Mechanical Engineers (ASME)

In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation.

ria.ua.pt

Modeling some real phenomena by fractional differential equations

Almeida, Ricardo, Bastos, Nuno R. O., Monteiro, M. Teresa T.

Wiley

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.

ria.ua.pt

Higher-order variational problems of Herglotz type

Santos, S. P. S., Martins, N., Torres, D. F. M.

Springer

We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

ria.ua.pt

Extremal graphs for the sum of the two largest signless Laplacian eigenvalues

Oliveira, Carla Silva, Lima, Leonado de, Rama, Paula, Carvalho, Paula

ILAS–the International Linear Algebra Society (ILAS)

Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A, where A is the adjacency matrix and D is the diagonal matrix of the vertices degree of G. Let q1(G) and q2(G) be the first and the second largest eigenvalues of Q(G), respectively, and denote by S+ n the star graph with an additional edge. It is proved that inequality q1(G)+q2(G) e(G)+3 is tighter for the graph S+ n among all firefly graphs and also tighter to S+ n than to the graphs Kk _ Kn−k recently presented by Ashraf, Omidi and Tayfeh-Rezaie. Also, it is conjectured that S+ n minimizes f(G) = e(G) − q1(G) − q2(G) among all graphs G on n vertices.

ria.ua.pt

Packing of R^2 by Crosses

Cruz, Catarina Neto, Breda, Ana, Pinto, Raquel

De Gruyter

A cross in Rn is a cluster of unit cubes comprising a central one and 2n arms. In their monograph Algebra and Tiling, Stein and Szabó suggested that tilings of ℝn by crosses should be studied. The question of the existence of such a tiling has been answered by various authors for many special cases. In this paper we completely solve the problem for ℝ2. In fact we do not only characterize crosses for which there exists a tiling of ℝ2 but for each cross we determine its maximum packing density.

ria.ua.pt

Brief report: preliminary proposal of a conceptual model of a digital environment for developing mathematical reasoning in students with Autism Spectrum Disorders

Santos, M. Isabel, Breda, Ana, Almeida, Ana Margarida

Springer

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a preliminary proposal of a digital environment, specifically targeted to promote the development of mathematical reasoning in students with ASD. Given the diversity of ASD, the prototyping of this environment requires the study of dynamic adaptation processes and the development of activities adjusted to each user’s profile. We present the results obtained during the first phase of this ongoing research, describing a conceptual model of the proposed digital environment. Guidelines for future research are also discussed.

ria.ua.pt

The Riemann sphere in GeoGebra

Santos, José Manuel dos Santos dos, Breda, Ana

InED – Centro de Investigação e Inovação em Educação, Escola Superior de Educação, Instituto Politécnico do Porto

The stereographic projection is a bijective smooth map which allows us to think the sphere as the extended complex plane. Among its properties it should be emphasized the remarkable property of being angle conformal that is, it is an angle measure preserving map. Unfortunately, this projection map does not preserve areas. Besides being conformal it has also the property of projecting spherical circles in either circles or straight lines in the plane This type of projection maps seems to have been known since ancient times by Hipparchus (150 BC), being Ptolemy (AD 140) who, in his work entitled "The Planisphaerium", provided a detailed description of such a map. Nonetheless, it is worthwhile to mention that the property of the invariance of angle measure has only been established much later, in the seventeenth century, by Thomas Harriot. In fact, it was exactly in that century that the Jesuit François d’Aguilon introduced the terminology "stereographic projection" for this type of maps, which remained up to our days. Here, we shall show how we create in GeoGebra, the PRiemannz tool and its potential concerning the visualization and analysis of the properties of the stereographic projection, in addition to the viewing of the amazing relations between Möbius Transformations and stereographic projections.

ria.ua.pt

Some results on open-edge and open mobile guarding of polygons and triangulations

Bajuelos, Antonio Leslie, Canales, Santiago, Hernández, Gregorio, Martins, Mafalda, Matos, Inês

Oxford University Press

This paper focuses on a variation of the Art Gallery problem that considers open-edge guards and open mobile-guards. A mobile guard can be placed on edges and diagonals of a polygon, and the ‘open’ prefix means that the endpoints of such an edge or diagonal are not taken into account for visibility purposes. This paper studies the number of guards that are sufficient and sometimes necessary to guard some classes of simple polygons for both open-edge and open mobile-guards. A wide range of polygons is studied, which include orthogonal polygons with or without holes, spirals, orthogonal spirals and monotone polygons. Moreover, this problem is also considered for planar triangulation graphs using open-edge guards.

ria.ua.pt

Difference factorizations and monotonicity in inverse medium scattering for contrasts with fixed sign on the boundary

Lechleiter, Armin, Lakshtanov, Evgeny

Society for Industrial and Applied Mathematics

We generalize the factorization method for inverse medium scattering using a particular factorization of the difference of two far field operators. While the factorization method has been used so far mainly to identify the shape of a scatterer's support, we show that factorizations based on Dirichlet-to-Neumann operators can be used to compute bounds for numerical values of the medium on the boundary of its support. To this end, we generalize ideas from inside-outside duality to obtain a monotonicity principle that allows for alternative uniqueness proofs for particular inverse scattering problems (e.g., when obstacles are present inside the medium). This monotonicity principle indeed is our most important technical tool: It further directly shows that the boundary values of the medium's contrast function are uniquely determined by the corresponding far field operator. Our particular factorization of far field operators additionally implies that the factorization method rigorously characterizes the support of an inhomogeneous medium if the contrast function takes merely positive or negative values on the boundary of its support independently of the contrast's values inside its support. Finally, the monotonicity principle yields a simple algorithm to compute upper and lower bounds for these boundary values, assuming the support of the contrast is known. Numerical experiments show feasibility of a resulting numerical algorithm.

ria.ua.pt

Eigenfunctions and fundamental solutions for the Fractional Laplacian in 3 dimensions

Ferreira, Milton dos Santos, Vieira, Nelson Felipe Loureiro

Bauhaus-University Weimar

Recently there has been a surge of interest in PDEs involving fractional derivatives in different fields of engineering. In this extended abstract we present some of the results developed in cite{FV}. We compute the fundamental solution for the three-parameter fractional Laplace operator $Delta^{(alpha,beta,gamma)}$ with $(alpha, beta, gamma) in ,]0,1]^3$ by transforming the eigenfunction equation into an integral equation and applying the method of separation of variables. The obtained solutions are expressed in terms of Mittag-Leffer functions. For more details we refer the interested reader to cite{FV} where it is also presented an operational approach based on the two Laplace transform.

ria.ua.pt

On Exponentiable Morphisms in Classical Algebra

Clementino, Maria Manuel, Hofmann, Dirk, Janelidze, George

Springer Verlag

We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an ``almost folklore" general result, we present a purely algebraic proof of ``'{e}tale implies exponentiable", alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphisms in ideal determined varieties and extend this to ideal determined categories. Finally, we give a complete characterization of exponential homomorphisms of semimodules over semirings.

ria.ua.pt

Two-Step-SDP approach to clustering and dimensionality reduction

Macedo, Eloísa

International Academic Press

Inspired by the recently proposed statistical technique called clustering and disjoint principal component analysis (CDPCA), this paper presents a new algorithm for clustering objects and dimensionality reduction, based on Semidefinite Programming (SDP) models. The Two-Step-SDP algorithm is based on SDP relaxations of two clustering problems and on a K-means step in a reduced space. The Two-Step-SDP algorithm was implemented and tested in R, a widely used open source software. Besides returning clusters of both objects and attributes, the Two-Step-SDP algorithm returns the variance explained by each component and the component loadings. The numerical experiments on different data sets show that the algorithm is quite efficient and fast. Comparing to other known iterative algorithms for clustering, namely, the K-means and ALS algorithms, the computational time of the Two-Step-SDP algorithm is comparable to the K-means algorithm, and it is faster than the ALS algorithm.

ria.ua.pt

Application of SIR epidemiological model: new trends

Rodrigues, Helena Sofia

North Atlantic University Union

The simplest epidemiologic model composed by mutually exclusive compartments SIR (susceptible-infectedsusceptible) is presented to describe a reality. From health concerns to situations related with marketing, informatics or even sociology, several are the fields that are using this epidemiological model as a first approach to better understand a situation. In this paper, the basic transmission model is analyzed, as well as simple tools that allows us to extract a great deal of information about possible solutions. A set of applications - traditional and new ones - is described to show the importance of this model.

ria.ua.pt

Dengue disease: a multiobjective viewpoint

Denysiuk, Roman, Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Costa, Lino, Espírito Santo, Isabel, Torres, Delfim F. M.

JMA

During the last decades, the global prevalence of dengue progressed dramatically. It is a disease that is now endemic in more than one hundred countries of Africa, America, Asia, and the Western Pacific. In this paper, we present a mathematical model for the dengue disease transmission described by a system of ordinary differential equations and propose a multiobjective approach to find the most effective ways of controlling the disease. We use evolutionary multiobjective optimization (EMO) algorithms to solve the resulting optimization problem, providing the performance comparison of different algorithms. The obtained results show that the multiobjective approach is an effective tool to solve the problem, giving higher quality and wider range of solutions compared to the traditional technique. The obtained trade-offs provide a valuable information about the dynamics of infection transmissions and can be used as an input in the process of planning the intervention measures by the health authorities. Additionally, a suggested hybrid EMO algorithm produces highly superior performance compared to five other state-of-the-art EMO algorithms, being indispensable to efficiently optimize the proposed model.

ria.ua.pt

On the Schrödinger–Poisson system with a general indefinite nonlinearity

Lirong Huang, Rocha, Eugénio M., Jianqing Chen

Elsevier

We study the existence and multiplicity of positive solutions of a class of Schrödinger–Poisson system: [View the MathML source Turn MathJax on] where k∈C(R3) changes sign in R3, lim∣x∣→∞k(x)=k∞<0, and the nonlinearity g behaves like a power at zero and at infinity. We mainly prove the existence of at least two positive solutions in the case that μ>μ1 and near μ1, where μ1 is the first eigenvalue of −Δ+id in H1(R3) with weight function h, whose corresponding positive eigenfunction is denoted by e1. An interesting phenomenon here is that we do not need the condition View the MathML source, which has been shown to be a sufficient condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity (see e.g. Costa and Tehrani, 2001).

ria.ua.pt

Sign changing solutions of a semilinear equation on Heisenberg group

Jianqing Chen, Rocha, Eugénio M.

Yokohama Publishers

Here, we studied an elliptic semilinear equation on a non-commutative manifold (the Heisenberg group) with a Dirichlet boundary condition. By using variational methods adapted to this setting, we prove that this problem possesses at least one positive solution and one sign changing solution for some values of the parameters.

ria.ua.pt

Seasonality effects on dengue: basic reproduction number, sensitivity analysis and otpimal control

Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Torres, Delfim F. M.

Wiley Online Library

Dengue is a vector-borne disease transmitted from an infected human to an Aedes mosquito, during a blood-meal. Dengue is still a major public health problem. A model for the disease transmission is presented, composed by human and mosquitoes compartments. The aim is to simulate the effects of seasonality, on the vectorial capacity and, consequently, on the disease development. Using entomological information about the mosquito behavior under different temperatures and rainfall, simulations are carried out and the repercussions analyzed. The basic reproduction number of the model is given, as well as a sensitivity analysis of model's parameters. Finally, an optimal control problem is proposed and solved, illustrating the difficulty of making a trade-off between reduction of infected individuals and costs with insecticide.

ria.ua.pt

Coexistence of two dengue virus serotypes and forecasting for Madeira Island

Rocha, Filipa Portugal, Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Torres, Delfim F. M.

Elsevier

The first outbreak of dengue occurred in Madeira Island in 2012, featuring one virus serotype. Aedes aegypti was the vector of the disease and it is unlikely that it will be eliminated from the island. Therefore, a new outbreak of dengue fever can occur and, if it happens, risk to the population increases if two serotypes coexist. In this paper, mathematical modeling and numerical simulations are carried out to forecast what may happen in Madeira Island in such a scenario.

ria.ua.pt

Multiobjective approach to optimal control for a dengue transmission model

Denysiuk, Roman, Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Costa, Lino, Espírito Santo, Isabel, Torres, Delfim F. M.

International Academic Press

During the last decades, the global prevalence of dengue progressed dramatically. It is a disease which is now endemic in more than one hundred countries of Africa, America, Asia and the Western Pacific. This study addresses a mathematical model for the dengue disease transmission and finding the most effective ways of controlling the disease. The model is described by a system of ordinary differential equations representing human and vector dynamics. Multiobjective optimization is applied to find the optimal control strategies, considering the simultaneous minimization of infected humans and costs due to insecticide application. The obtained results show that multiobjective optimization is an effective tool for finding the optimal control. The set of trade-off solutions encompasses a whole range of optimal scenarios, providing valuable information about the dynamics of infection transmissions. The results are discussed for different values of model parameters.

ria.ua.pt

Approximating the maximum size of a k-regular induced subgraph by an upper bound on the co-k-plex number

Luz, C.J.

Springer Verlag

Let α_{k} and α_{k} denote respectively the maximum cardinality k-regular induced subgraph and the co-k-plex number of a given graph. In this paper a convex quadratic programming upper bound on α_{k} which is also an upper bound on α_{k} will be introduced. The new bound, denoted by υ_{k}, improves on the bound υ_{k} given in CardKamLoz. For regular graphs, a necessary and sufficient condition under which υ_{k} equals υ_{k} is proved. It is also shown that the graphs for which α_{k} equals υ_{k} coincide with those such that α_{k} equals υ_{k}. Next, an improvement of υ_{k} denoted by ϑ_{k} is proposed, which is not worse than the upper bound ϑ_{k} for α_{k} introduced in Luzkind. Finally, some computational experiments perfomed to appraise the gains brought by ϑ_{k} are reported.

ria.ua.pt

Variational methods for the solution of fractional discrete/continuous Sturm-Liouville problems

Almeida, Ricardo, Malinowska, Agnieszka B., Morgado, M. Luísa, Odzijewicz, Tatiana

Mathematical Sciences Publishers

The fractional Sturm–Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions to this problem is of great importance. Here, we describe how the fractional Sturm–Liouville eigenvalue problem can be formulated as a constrained fractional variational principle and show how such formulation can be used in order to approximate the solutions. Numerical examples are given, to illustrate the method.

ria.ua.pt

Compliance to radiation therapy of head and neck cancer patients and impact on treatment outcome

Ferreira, B. C., Sá-Couto, P., Lopes, M. C., Khouri, L.

Springer Verlag

AIMS: The aims of the study were to evaluate head and neck cancer (HNC) patient's compliance to the planned radiation therapy (RT) using the department policy established in 2005 at IPOCFG and to estimate the impact on treatment outcome due to failure in receiving RT as prescribed. MATERIALS AND METHODS: 359 HNC patients irradiated from 2007 to 2013 were included in this study. Patient cohort was divided into Group 1: patients receiving RT as prescribed and Group 2: patients that interrupted or suspended RT. Group Tox is the subgroup of patients that interrupted RT due to toxicity or intercurrent disease. Number and causes for treatment interruptions were assessed. The cumulative incidence of locoregional control (LRC), disease-free survival (DFS) and overall survival for Groups 1 and 2 was determined. Cox regression was performed to investigate potential hazard factors and logistic regression was made to determine risk factors related to treatment interruptions. RESULTS: Major causes for treatment interruptions were toxicity plus intercurrent disease (41.7 %) and public holidays (30.1 %). 10.3 % of the patients interrupted 3-9 days. Significant differences in survival distributions of the LRC between Groups 1 and 2, of up to 19 %, were found in the subgroup of patients with N2-3 tumours, for post-operative RT and for concomitant RT. Treatment breaks larger than two days had an almost fourfold increased risk of poorer LRC and DFS. CONCLUSIONS: Twin accelerators and treating on public holidays are effective measures minimizing RT breaks. For HNC, patient compliance is mostly limited by RT side-effects. Efforts to maintain RT biological effective dose in HNC must be always undertaken.

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Nurse perception of care of hospitalized older adults: a comparative study between northern and central regions of Portugal

Tavares, João Paulo de Almeida, Silva, Alcione Leite da, Sá-Couto, Pedro, Boltz, Marie, Capezuti, Elizabeth

Universidade de São Paulo

Objective: to analyze the relationship between the perceptions of nurses about geriatric care (GC) environment and geriatric nurses’ knowledge and attitudes according to unit type considering the northern and central regions of Portugal. Method: a cross-sectional study was developed among 1,068 Portuguese’s nurses in five hospitals. The instrument was Geriatric Institutional Assessment Profile – Portuguese version. The independent samples t-test was when the assumption of normality was verified, otherwise, the Mann-Whitney U test was used. The level of significance was 5%. Results: the profile of perceptions of GC showed a relatively homogeneous pattern (no statistically significant results were found). For the geriatric care environment scale, only the CC/ED units presented significant differences in all considered subscales (resource availability; aging-sensitive care; institutional values; and continuity of care), with more positive perceptions among nurses in the northern region. In Professional Issues scales, only the scale perception of burden related with upsetting behaviors revealed significant differences between regions in all specialties. Conclusion: the findings suggest the need for increased investment by hospital leaders to promote a geriatric nursing practice environment that supports the specialized needs of hospitalized older adults.

ria.ua.pt

Edge perturbation on graphs with clusters: Adjacency, Laplacian and signless Laplacian eigenvalues

Cardoso, Domingos M., Rojo, Oscar

Elsevier

Let G be a simple undirected graph of order n. A cluster in G of order c and degree s, is a pair of vertex subsets (C, S), where C is a set of cardinality |C| =c ≥2 of pairwise co-neighbor vertices sharing the same set S of s neighbors. Assuming that the graph G has k≥1 clusters (C_1, S_1), ..., (C_k, S_k), consider a family of k graphs H_1, ..., H_k and the graph G(H_1, ..., H_k) which is obtained from G after adding the edges of the graphs H_1, ..., H_ k whose vertex set of each H_j is identified with C_j, for j=1, ..., k. The Laplacian eigenvalues of G(H_1, ..., H_k)remain the same, independently of the graphs H_1, ..., H_k, with the exception of |C_1| +···+|C_k| −k of them. These new Laplacian eigenvalues are determined using a unified approach which can also be applied to the determination of a same number of adjacency and signless Laplacian eigenvalues when the graphs H_1, ..., H_k are regular. The Faria’s lower bound on the multiplicity of the Laplacian eigenvalue 1 of a graph with pendant vertices is generalized. Furthermore, the algebraic connectivity and the Laplacian index of G(H_1, ..., H_k) remain the same, independently of the graphs H_1, ..., H_k.

ria.ua.pt

Implicit cover inequalities

Agra, Agostinho, Requejo, Cristina, Santos, Eulália

Springer Verlag

In this paper we consider combinatorial optimization problems whose feasible sets are simultaneously restricted by a binary knapsack constraint and a cardinality constraint imposing the exact number of selected variables. In particular, such sets arise when the feasible set corresponds to the bases of a matroid with a side knapsack constraint, for instance the weighted spanning tree problem and the multiple choice knapsack problem. We introduce the family of implicit cover inequalities which generalize the well-known cover inequalities for such feasible sets and discuss the lifting of the implicit cover inequalities. A computational study for the weighted spanning tree problem is reported.

ria.ua.pt

A dynamic programming approach for a class of robust optimization problems

Agra, Agostinho, Santos, Márcio Costa, Nace, Dritan, Poss, Michael

Society for Industrial and Applied Mathematics

Common approaches to solving a robust optimization problem decompose the problem into a master problem (MP) and adversarial problems (APs). The MP contains the original robust constraints, written, however, only for nite numbers of scenarios. Additional scenarios are generated on the y by solving the APs. We consider in this work the budgeted uncertainty polytope from Bertsimas and Sim, widely used in the literature, and propose new dynamic programming algorithms to solve the APs that are based on the maximum number of deviations allowed and on the size of the deviations. Our algorithms can be applied to robust constraints that occur in various applications such as lot-sizing, the traveling salesman problem with time windows, scheduling problems, and inventory routing problems, among many others. We show how the simple version of the algorithms leads to a fully polynomial time approximation scheme when the deterministic problem is convex. We assess numerically our approach on a lot-sizing problem, showing a comparison with the classical mixed integer linear programming reformulation of the AP.

ria.ua.pt

On reconstruction of complex-valued once differentiable conductivities

Lakshtanov, Evgeny, Vainberg, Boris

European Mathematical Society

The classical ∂-method has been generalized recently ([13] and [14]) to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on smoothness of potentials. As a consequence, this provides an effective method of reconstruction of complex-valued one time differentiable conductivities in the inverse impedance tomography problem.

ria.ua.pt

Problems of maximal mean resistance on the plane

Plakhov, A., Gouveia, P. D. F.

A two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic. The body performs both translational and slow rotational motion. It is required to select the body, from a given class of bodies, such that the average force of resistance of the medium to its motion is maximal. Numerical and analytical results concerning this problem are presented. In particular, the maximum resistance in the class of bodies contained in a convex body K is proved to be 1.5 times the resistance of K. The maximum is attained on a sequence of bodies with a very complicated boundary. The numerical study was made for somewhat more restricted classes of bodies. The obtained values of resistance are slightly lower, but the boundary of obtained bodies is much simpler, as compared with the analytical solutions. © 2007 IOP Publishing Ltd and London Mathematical Society.

ria.ua.pt

An expansion formula with higher-order derivatives for fractional operators of variable order

Almeida, R., Torres, D.F.M.

Hindawi

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.

ria.ua.pt

On the Laplacian and signless Laplacian spectrum of a graph with k pairwise co-neighbor vertices

Abreu, Nair M.M., Cardoso, Domingos Moreira, Martins, Enide A., Robbiano, Maria, San Martin, B.

Elsevier

Consider the Laplacian and signless Laplacian spectrum of a graph G of order n, with k pairwise co-neighbor vertices. We prove that the number of shared neighbors is a Laplacian and a signless Laplacian eigenvalue of G with multiplicity at least k− 1. Additionally, considering a connected graph Gk with a vertex set defined by the k pairwise co-neighbor vertices of G, the Laplacian spectrum of Gk, obtained from G adding the edges of Gk, includes l + β for each nonzero Laplacian eigenvalue β of Gk. The Laplacian spectrum of G overlaps the Laplacian spectrum of Gk in at least n − k + 1 places.

ria.ua.pt

An extension of Markov's Theorem

Branquinho, Amilcar, Fidalgo Prieto, Ulises, Foulquie Moreno, Ana

American Mathematical Society

We give a general sufficient condition for the uniform convergence of sequences of type II Hermite-Padé approximants associated with Nikishin systems of functions.

ria.ua.pt

On the full Kostant-Toda system and the discrete Korteweg-de Vries equations

Barrios Rolanía, Dolores, Branquinho, Amilcar, Foulquie Moreno, Ana

Elsevier

The relation between the solutions of the full Kostant–Toda lattice and the discrete Korteweg–de Vries equation is analyzed. A method for constructing solutions of these systems is given. As a consequence of the matricial interpretation of this method, the transform of Darboux is extended for general Hessenberg banded matrices.

ria.ua.pt

Eigenvalues of a H-generalized join graph operation constrained by vertex subsets

Cardoso, Domingos M., Martins, Enide A., Robbiano, Maria, Rojo, Oscar

Elsevier

A generalized H-join operation of a family of graphs G1, . . . , Gp, where H has order p, constrained by a family of vertex subsets Si ⊆V(Gi), i = 1, . . . , p, is introduced. When each vertex subset Si is (ki, τi)-regular, it is deduced that all non-main adjacency eigenvalues of Gi , different from ki−τi , remain as eigenvalues of the graph G obtained by this operation. If each Gi is ki-regular and all the vertex subsets are such that Si = V(Gi), the H-generalized join constrained by these vertex subsets coincides with the H-join operation. Furthermore, some applications on the spread of graphs are presented.

ria.ua.pt

The minimum weight t-composition of an integer

Cardoso, D. M., Cerdeira, J. O.

Springer

Let p and t, p ≥ t, be positive integers. A t-composition of p is an ordered t-tuple of positive integers summing p. If T = (s_1, s_2, . . . , s_t) is a t-composition p and W is a (p − (t − 1)) × t matrix, then W(T) = w_(s_1)+ w_(s_2)2... + w_(s_k)k is called the weight of the t-composition T. We show that finding a minimum weight t-composition of p can be reduced to the determination of the shortest path in a certain digraph with O(tp) vertices. This study was motivated by a problem arising from the automobile industry, and the presented result is useful when dealing with huge location problems.

ria.ua.pt

On hereditary properties of the class of graphs with convex quadratic stability number

Cardoso, D. M., Lozin, V. V.

Springer

We show that the class of graphs with quadratic stability number is not hereditary. Then we prove that this class contains a unique maximal hereditary subclass and, finally, we characterize this subclass by two forbidden induced subgraphs.

ria.ua.pt

A generalization of chromatic polynomial of a graph subdivision

Cardoso, D. M., Silva, M. E., Szymanski, J.

Springer

Considering the partitions of a set into nonempty subsets, we obtain an expression for the number of all partitions of a given type. The chromatic polynomial of a graph subdivision is generalized, considering two sets of colors, and a general explicit expression is obtained for this generalization. Using these results, we determine the generalized chromatic polynomial for the particular case of complete graph subdivision.

ria.ua.pt

Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case

Castro, L. P., Rojas, E. M., Saitoh, S., Tuan, N. M., Tuan, P. D.

World Scientific Publishing

By means of Riemann boundary value problems and of certain convenient systems of linear algebraic equations, this paper deals with the solvability of a class of singular integral equations with rotations and degenerate kernel within the case of a coefficient vanishing on the unit circle. All the possibilities about the index of the coefficients in the corresponding equations are considered and described in detail, and explicit formulas for their solutions are obtained. An example of application of the method is shown at the end of the last section.

ria.ua.pt

Wave diffraction by wedges having arbitrary aperture angle

Castro, L. P., Kapanadze, D.

Elsevier

The problem of plane wave diffraction by a wedge sector having arbitrary aperture angle has a very long and interesting research background. In fact, we may recognize significant research on this topic for more than one century. Despite this fact, up to now no clear unified approach was implemented to treat such a problem from a rigourous mathematical way and in a consequent appropriate Sobolev space setting. In the present paper, we are considering the corresponding boundary value problems for the Helmholtz equation, with complex wave number, admitting combinations of Dirichlet and Neumann boundary conditions. The main ideas are based on a convenient combination of potential representation formulas associated with (weighted) Mellin pseudo-differential operators in appropriate Sobolev spaces, and a detailed Fredholm analysis. Thus, we prove that the problems have unique solutions (with continuous dependence on the data), which are represented by the single and double layer potentials, where the densities are solutions of derived pseudo-differential equations on the half-line.

ria.ua.pt

Interplay of Wiener-Hopf and Hankel operators with almost periodic Fourier symbols on standard and variable exponent Lebesgue spaces

Castro, L. P., Silva, A. S.

Duke University Press, Tusi Mathematical Research Group

Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators in both frameworks of standard and variable exponent Lebesgue spaces are considered in this paper. The main aim is to describe certain dependencies between the Fredholm property of some Wiener-Hopf operators acting between variable exponent Lebesgue spaces and the invertibility of Wiener-Hopf plus and minus Hankel operators on all the standard Lebesgue spaces. Different types of Fourier symbols will be used but special focus will be considered on the Wiener subclass of almost periodic matrix functions. In the first part of the paper we will give a survey of investigations on related results. This will be useful at the end of the paper to derive the above mentioned dependencies between the operators under study.

ria.ua.pt

Cauchy-Kovalevskaya extension theorem in fractional Clifford analysis

Vieira, Nelson

Springer

In this paper, we establish the fractional Cauchy-Kovalevskaya extension (FCK-extension) theorem for fractional monogenic functions defined on R^d. Based on this extension principle, fractional Fueter polynomials, forming a basis of the space of fractional spherical monogenics, i.e. fractional homogeneous polynomials, are introduced. We studied the connection between the FCK-extension of functions of the form x^alpha P_l and the classical Gegenbauer polynomials. Finally we present two examples of FCK-extension.

ria.ua.pt

Harmonic analysis on the Möbius gyrogroup

Ferreira, Milton

Springer

In this paper we propose to develop harmonic analysis on the Poincaré ball $B_t^n$, a model of the n-dimensional real hyperbolic space. The Poincaré ball $B_t^n$ is the open ball of the Euclidean n-space $R^n$ with radius $t>0$, centered at the origin of $R^n$ and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in $mathbb{R}^n$. For any $t>0$ and an arbitrary parameter $sigma in R$ we study the $(sigma,t)$-translation, the $( sigma,t)$-convolution, the eigenfunctions of the $(sigma,t)$-Laplace-Beltrami operator, the $(sigma,t)$-Helgason Fourier transform, its inverse transform and the associated Plancherel's Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic harmonic analysis. Moreover, when $t rightarrow +infty$ the resulting hyperbolic harmonic analysis on $B_t^n$ tends to the standard Euclidean harmonic analysis on $R^n$, thus unifying hyperbolic and Euclidean harmonic analysis. As an application we construct diffusive wavelets on $B_t^n$.

ria.ua.pt

Harmonic analysis on the Einstein gyrogroup

Ferreira, Milton

JGSP

In this paper we study harmonic analysis on the Einstein gyrogroup of the open ball of R$^n$, $n in N,$ centered at the origin and with arbitrary radius $t in R^+,$ associated to the generalised Laplace-Beltrami operator $$ L_{sigma,t} = disp left( 1 - frac{|x|^2}{t^2} right) !left( Delta - sum_{i,j=1}^n frac{x_i x_j}{t^2} frac{partial^2}{partial x_i partial x_j} - frac{kappa}{t^2} sum_{i=1}^n x_i frac{partial}{partial x_i} + frac{kappa(2-kappa)}{4t^2} right)$$ where $kappa=n+sigma$ and $sigma in {mathbb R}$ is an arbitrary parameter. The generalised harmonic analysis for $L_{sigma,t}$ gives rise to the $(sigma,t)$-translation, the $(sigma,t)$-convolution, the $(sigma,t)$-spherical Fourier transform, the $(sigma,t)$-Poisson transform, the $(sigma,t)$-Helgason Fourier transform, its inverse transform and Plancherel's Theorem. In the limit of large $t,$ $t rightarrow +infty,$ the resulting hyperbolic harmonic analysis tends to the standard Euclidean harmonic analysis on $R^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.

ria.ua.pt

A new frontier approach to model the eco-efficiency in European countries

Robaina-Alves, Margarita, Moutinho, Victor, Macedo, Pedro

Elsevier

This study aims to evaluate the resource and environment efficiency problem of European countries. We specify a new stochastic frontier model where Gross Domestic Product (GDP) is considered as the desirable output and Greenhouse Gases (GHG) emissions as the undesirable output. Capital, Labour, Fossil fuels and Renewable Energy consumption are regarded as inputs. GDP/GHG ratio is maximized given the values of the other four variables. The study is divided into two distinct periods: 2000-2004 and 2005-2011. This division is related to the implementation of the Kyoto Protocol in 2005, and will allow us to evaluate the difference between the levels of efficiency before and after the establishment of environmental targets. Since stochastic frontier models are typically ill-posed, a new maximum entropy approach to assess technical efficiency, which combines information from the data envelopment analysis and the structure of composed error from the stochastic frontier approach without requiring distributional assumptions, is presented in this work.

ria.ua.pt

Relaxed quaternionic Gabor expansions at critical density

Hartmann, Stefan

Wiley

Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique l2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion.

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A discrete method to solve fractional optimal control problems

Almeida, R., Torres, D. F. M.

Springer Verlag

We present a method to solve fractional optimal control problems, where the dynamic control system depends on integer order and Caputo fractional derivatives. Our approach consists in approximating the initial fractional order problem with a new one that involves integer order derivatives only. The latter problem is then discretized, by application of finite differences, and solved numerically. We illustrate the effectiveness of the procedure with an example.

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Computing Hadamard type operators of variable fractional order

Almeida, R., Torres, D. F. M.

Elsevier

We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these operators as series of terms involving integer-order derivatives only, and then approximate the fractional operators by a finite sum. An upper bound formula for the error is provided. We exemplify our method by applying the proposed numerical procedure to the solution of a fractional differential equation and a fractional variational problem with dependence on the Hadamard-Marchaud fractional derivative.

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Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure

Razminia, K., Razminia, A., Torres, D. F. M.

Elsevier

We obtain an analytical solution for the pressure-transient behavior of a vertically hydraulic fractured well in a heterogeneous reservoir. The heterogeneity of the reservoir is modeled by using the concept of fractal geometry. Such reservoirs are called fractal reservoirs. According to the theory of fractional calculus, a temporal fractional derivative is applied to incorporate the memory properties of the fractal reservoir. The effect of different parameters on the computed wellbore pressure is fully investigated by various synthetic examples.

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Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order

Tavares, D., Almeida, R., Torres, D. F. M.

Taylor & Francis

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are proved. Several particular cases are considered illustrating the new results.

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A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration

Benkhettou, N., Brito da Cruz, A. M. C., Torres, D. F. M.

Elsevier

We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then developed. As particular cases, one obtains the usual time-scale Hilger derivative when the order of differentiation is one, and a local approach to fractional calculus when the time scale is chosen to be the set of real numbers.

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Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem

Santos, S. P. S., Martins, N., Torres, D. F. M.

American Institute of Mathematical Sciences (AIMS)

We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the first Noether theorem for variational problems with time delay recently proved in [Numer. Algebra Control Optim. 2(2012), no. 3, 619-630]. Our main result is also a generalization of the first Noether-type theorem for the generalized variational principle of Herglotz proved in [Topol. Methods Nonlinear Anal. 20(2002), no. 2, 261-273].

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A general delta-nabla calculus of variations on time scales with application to economics

Dryl, M., Torres, D. F. M.

Inderscience

We consider a general problem of the calculus of variations on time scales with a cost functional that is the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange delta-nabla differential equations are proved, which lead to important insights in the process of discretisation. Application of the obtained results to a firm that wants to program its production and investment policies to reach a given production rate and to maximise its future market competitiveness is discussed.

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Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa

Rachah, A., Torres, D. F. M.

Hindawi Publishing Corporation

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone, and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

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Solving Abel integral equations of first kind via fractional calculus

Jahanshahi, S., Babolian, E., Torres, D. F. M., Vahidi, A.

Elsevier

We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed approach.

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Multiobjective approach to optimal control for a tuberculosis model

Denysiuk, R., Silva, C. J., Torres, D. F. M.

Taylor & Francis

Mathematical modelling can help to explain the nature and dynamics of infection transmissions, as well as support a policy for implementing those strategies that are most likely to bring public health and economic benefits. The paper addresses the application of optimal control strategies in a tuberculosis model. The model consists of a system of ordinary differential equations, which considers reinfection and post-exposure interventions. We propose a multiobjective optimization approach to find optimal control strategies for the minimization of active infectious and persistent latent individuals, as well as the cost associated to the implementation of the control strategies. Optimal control strategies are investigated for different values of the model parameters. The obtained numerical results cover a whole range of the optimal control strategies, providing valuable information about the tuberculosis dynamics and showing the usefulness of the proposed approach.

ria.ua.pt

A TB-HIV/AIDS coinfection model and optimal control treatment

Silva, C. J., Torres, D. F. M.

American Institute of Mathematical Sciences (AIMS)

We propose a population model for TB-HIV/AIDS coinfection transmission dynamics, which considers antiretroviral therapy for HIV infection and treatments for latent and active tuberculosis. The HIV-only and TB-only sub-models are analyzed separately, as well as the TB-HIV/AIDS full model. The respective basic reproduction numbers are computed, equilibria and stability are studied. Optimal control theory is applied to the TB-HIV/AIDS model and optimal treatment strategies for co-infected individuals with HIV and TB are derived. Numerical simulations to the optimal control problem show that non intuitive measures can lead to the reduction of the number of individuals with active TB and AIDS.

ria.ua.pt

Optimal control with time delays via the penalty method

Benharrat, M., Torres, D. F. M.

Hindawi Publishing Corporation

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

ria.ua.pt

The diamond integral on time scales

Brito da Cruz, A. M. C., Martins, N., Torres, D. F. M.

Springer

We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder’s, Cauchy–Schwarz’s, and Minkowski’s inequalities.

ria.ua.pt

Crack impedance-Dirichlet boundary value problems of diffraction in a half-plane

Castro, L. P., Kapanadze, D.

Cambridge Scientific Publishers

We study two wave diffraction problems modeled by the Helmholtz equation in a half-plane with a crack characterized by Dirichlet and impedance boundary conditions. The existence and uniqueness of solutions is proved by an appropriate combination of general operator theory, Fredholm theory, potential theory and boundary integral equation methods. This combination of methods leads also to integral representations of solutions. Moreover, in Sobolev spaces, a range of smoothness parameters is obtained in which the solutions of the problems are valid.

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Interactive and multimedia contents associated with a system for computer-aided assessment

Paiva, Rui C., Ferreira, Milton, Mendes, Ana G., Eusébio, Augusto M. J.

SAGE Journals

This paper presents a research study addressing the development, implementation, evaluation and use of Interactive Modules for Online Training (MITO) of mathematics in higher education. This work was carried out in the context of the MITO project, which combined several features of the learning and management system Moodle, the computer-aided assessment for mathematics STACK, the mathematical software GeoGebra, several packages from the type-setting program LaTeX, and tutorial videos. A total of 1962 students participated in this study. Two groups of students taking a Calculus course were selected for a deeper analysis. In regard to usability and functionality, the results indicate that MITO scored well in almost all aspects, which is fundamental for their introduction into formal university courses. The analysis of the data reveals that the use of MITO educational contents by students mainly occurs about one week and a half prior the evaluations. Moreover, there is a strong correlation between the results of online assessments on MITO in a continuous assessment model and the final grade on the course.

ria.ua.pt

Embeddings of Besov spaces on fractal h-sets

Caetano, António, Haroske, Dorothee

Duke University Press

Let $Gamma$ be a fractal $h$-set and ${mathbb{B}}^{{sigma}}_{p,q}(Gamma)$ be a trace space of Besov type defined on $Gamma$. While we dealt in [9] with growth envelopes of such spaces mainly and investigated the existence of traces in detail in [12], we now study continuous embeddings between different spaces of that type on $Gamma$. We obtain necessary and sufficient conditions for such an embedding to hold, and can prove in some cases complete characterisations. It also includes the situation when the target space is of type $L_r(Gamma)$ and, as a by-product, under mild assumptions on the $h$-set $Gamma$ we obtain the exact conditions on $sigma$, $p$ and $q$ for which the trace space ${mathbb{B}}^{{sigma}}_{p,q}(Gamma)$ exists. We can also refine some embedding results for spaces of generalised smoothness on $mathbb R^n$.

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Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

Almeida, Alexandre, Harjulehto, P., Hästö, P., Lukkari, T.

Springer

We prove optimal integrability results for solutions of the p(x)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L1 to variable exponent weak Lebesgue spaces.

ria.ua.pt

Exponential Kleisli monoids as Eilenberg-Moore algebras

Hofmann, Dirk, Mynard, Frédéric, Seal, Gavin J.

Springer Verlag

Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.

ria.ua.pt

Dualities for modal algebras from the point of view of triples

Hofmann, Dirk, Nora, Pedro

Springer Verlag

In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by Cartesian product on the relational side and show that in some cases the corresponding operation on the algebraic side represents bimorphisms.

ria.ua.pt

Exponentiable approach spaces

Hofmann, Dirk, Seal, Gavin J.

University of Houston

In this note we present a characterisation of exponentiable approach spaces in terms of ultrafilter convergence.

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A cottage industry of lax extensions

Hofmann, Dirk, Seal, Gavin J.

Shahid Beheshti University

In this work, we describe an adjunction between the comma category of Set-based monads under the V-powerset monad and the category of associative lax extensions of Set-based monads to the category of V-relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

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Sign changes of error terms related to arithmetical functions

Almeida, Paulo J.

Institut de Mathématiques de Bordeaux

Resumo indisponível.

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A new class of superregular matrices and MDP convolutional codes

Almeida, Paulo J., Pinto, Raquel, Napp, Diego

Elsevier

This paper deals with the problem of constructing superregular matrices that lead to MDP convolutional codes. These matrices are a type of lower block triangular Toeplitz matrices with the property that all the square submatrices that can possibly be nonsingular due to the lower block triangular structure are nonsingular. We present a new class of matrices that are superregular over a sufficiently large finite field F . Such construction works for any given choice of characteristic of the field F and code parameters ( n , k ,δ) such that ( n − k ) | δ . We also discuss the size of F needed so that the proposed matrices are superregular.

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Maps of Archimedean class and operations on dessins

Catalano, Domenico, d'Azevedo, António Breda, Karábas, Ján, Nedela, Roman

Elsevier

In the present paper we introduce a family of functors (called operations) of the category of hypermaps (dessins) preserving the underlying Riemann surface. The considered family of functors include as particular instances the operations considered by Magot and Zvonkin (2000), Singerman and Syddall (2003), and Girondo (2003). We identify a set of 10 operations in the above infinite family which produce vertex-transitive dessins out of regular ones. This set is complete in the following sense: if a vertex-transitive map arises from a regular dessin H applying an operation, then it can be obtained from a regular dessin on the same surface (possibly different from H) applying one of the 10 operations. The statement includes the classical case when the underlying surface is the sphere.

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A 2D Hopfield Neural Network approach to mechanical beam damage detection

Almeida, Juliana, Alonso, Hugo, Ribeiro, Pedro, Rocha, Paula

Springer

The aim of this paper is to present a method based on a 2D Hopfield Neural Network for online damage detection in beams subjected to external forces. The underlying idea of the method is that a significant change in the beam model parameters can be taken as a sign of damage occurrence in the structural system. In this way, damage detection can be associated to an identification problem. More concretely, a 2D Hopfield Neural Network uses information about the way the beam vibrates and the external forces that are applied to it to obtain time-evolving estimates of the beam parameters at the different beam points. The neural network organizes its input information based on the Euler-Bernoulli model for beam vibrations. Its performance is tested with vibration data generated by means of a different model, namely Timonshenko's, in order to produce more realistic simulation conditions.

ria.ua.pt

On integral operators generated by the Fourier transform and a reflection

Castro, L. P., Guerra, R. C., Tuan, N. M.

Georgian National Academy of Sciences; A. Razmadze Mathematical Institute

We present a detailed study of structural properties for certain algebraic operators generated by the Fourier transform and a reflection. First, we focus on the determination of the characteristic polynomials of such algebraic operators, which, e.g., exhibit structural differences when compared with those of the Fourier transform. Then, this leads us to the conditions that allow one to identify the spectrum, eigenfunctions, and the invertibility of this class of operators. A Parseval type identity is also obtained, as well as the solvability of integral equations generated by those operators. Moreover, new convolutions are generated and introduced for the operators under consideration.

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