Publications 2020

Book Chapters

11.  A new mathematical model for the efficiency calculation

Galindro, Aníbal and Santos, Micael and Torres, Delfim F. M. and Marta-Costa, Ana

Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control

Springer Nature

During the past sixty years, a lot of effort has been made regarding the productive efficiency. Such endeavours provided an extensive bibliography on this subject, culminating in two main methods, named the Stochastic Frontier Analysis (parametric) and Data Envelopment Analysis (non-parametric). The literature states this methodology also as the benchmark approach, since the techniques compare the sample upon a chosen “more-efficient” reference. This article intends to disrupt such premise, suggesting a mathematical model that relies on the optimal input combination, provided by a differential equation system instead of an observable sample. A numerical example is given, illustrating the application of our model’s features. | doi | Peer Reviewed

10.  Parametric identification of the dynamics of inter-sectoral balance: modelling and forecasting

Kostylenko, Olena and Rodrigues, Helena Sofia and Torres, Delfim F. M.

Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control


This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identification of a weakly formalized dynamical system is developed. A matching procedure for parameters of a linear stationary Cauchy problem with a decomposition of its upshot trend and a periodic component, is proposed. Moreover, an approach for detection of significant harmonic waves, which are inherent to real macroeconomic dynamical systems, is developed. | doi | Peer Reviewed


9.  Extremal graphs for Estrada indices

Andrade, Enide and Lenes, Eber and Mallea-Zepeda, Exequiel and Robbiano, María and Rodríguez Z., Jonnathan

Linear Algebra and its Applications


Let $mathcal{G}$ be a simple undirected connected graph. The signless Laplacian Estrada, Laplacian Estrada and Estrada indices of a graph $mathcal{G}$ is the sum of the exponentials of the signless Laplacian eigenvalues, Laplacian eigenvalues and eigenvalues of $mathcal{G}$, respectively. The present work derives an upper bound for the Estrada index of a graph as a function of its chromatic number, in the family of graphs whose color classes have order not less than a fixed positive integer. The graphs for which the upper bound is tight is obtained. Additionally, an upper bound for the Estrada Index of the complement of a graph in the previous family of graphs with two color classes is given. A Nordhaus-Gaddum type inequality for the Laplacian Estrada index when {$mathcal{G}$ is a bipartite} graph with color classes of order not less than $2$, is presented. Moreover, a sharp upper bound for the Estrada index of the line graph and for the signless Laplacian index of a graph in terms of connectivity is obtained. | doi | Peer Reviewed

8.  Matrix Toda and Volterra lattices

Moreno, Ana Foulquié and Branquinho, Amílcar and García-Ardila, Juan C.

Applied Mathematics and Computation


We consider matrix Toda and Volterra lattice equations and their relation with matrix biorthogonal polynomials. From that relation, we give a method for constructing a new solution of these systems from another given one. An illustrative example is presented. | doi | Peer Reviewed

7.  Maximal commutators and commutators of potential operators in new vanishing Morrey spaces

Almeida, Alexandre

Nonlinear Analysis


We study mapping properties of commutators in certain vanishing subspaces of Morrey spaces, which were recently used to solve the delicate problem of describing the closure of nice functions in Morrey norm. We show that the vanishing properties defining those subspaces are preserved under the action of maximal commutators and commutators of fractional integral operators. | doi | Peer Reviewed

6.  Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense

Teodoro, A. Di and Ferreira, M. and Vieira, N.

Advances in Applied Clifford Algebras


In this paper, we study the fundamental solution for natural powers of the $n$-parameter fractional Laplace and Dirac operators defined via Riemann-Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace $Delta_{a^+}^alpha$ and Dirac $D_{a^+}^alpha$ operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag-Leffler function. | doi | Peer Reviewed

5.  Variable exponent Triebel-Lizorkin-Morrey spaces

Caetano, António and Kempka, Henning

Journal of Mathematical Analysis and Applications


We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Littlewood maximal inequality in the fully variable setting. Using it we obtain characterizations by means of Peetre maximal functions and use them to show the independence of the introduced spaces from the admissible system used. | doi | Peer Reviewed

4.  On the energy of singular and non singular graphs

Andrade, Enide and Carmona, Juan R. and Poveda, Alex and Robbiano, María

MATCH Communications in Mathematical and in Computer Chemistry

University of Kragujevac

Let $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $rho$ and nullity $kappa$. The energy of $G,$ $mathcal{E}(G)$ is the sum of its singular values. In this work lower bounds for $mathcal{E}(G)$ in terms of the coefficient of $mu^{kappa}$ in the expansion of characteristic polynomial, $p(mu)=det{(mu I-A)}$ are obtained. In particular one of the bounds generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in $2013$ to the case of graphs with given nullity. The bipartite case is also studied obtaining in this case, a sufficient condition to improve the spectral lower bound $2rho.$ Considering an increasing sequence convergent to $rho$ a convergent increasing sequence of lower bounds for the energy of $G$ is constructed. | doi | Peer Reviewed

3.  Numerical optimal control of HIV transmission in Octave/MATLAB

Campos, Carlos and Silva, Cristiana J. and Torres, Delfim F. M.

Mathematical and Computational Applications


We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article. | doi | Peer Reviewed

2.  Regional enlarged observability of Caputo fractional differential equations

Zouiten, Hayat and Boutoulout, Ali and Torres, Delfim F. M.

Discrete and Continuous Dynamical Systems - Series S

American Institute of Mathematical Sciences (AIMS)

We consider the regional enlarged observability problem for fractional evolution differential equations involving Caputo derivatives. Using the Hilbert Uniqueness Method, we show that it is possible to rebuild the initial state between two prescribed functions only in an internal subregion of the whole domain. Finally, an example is provided to illustrate the theory. | doi | Peer Reviewed

1.  Graphs with clusters perturbed by regular graphs: Aα-spectrum and applications

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

Discussiones Mathematicae Graph Theory

De Gruyter

Given a graph $G$, its adjacency matrix $A(G)$ and its diagonal matrix of vertex degrees $D(G)$, consider the matrix $A_{alpha}left( Gright) = alpha Dleft( Gright) +(1-alpha)Aleft(Gright)$, where $alpha inleft[ 0,1right)$. The $A_{alpha}-$ spectrum of $G$ is the multiset of eigenvalues of $A_{alpha}(G)$ and these eigenvalues are the $alpha-$ eigenvalues of $G$. A cluster in $G$ is a pair of vertex subsets $(C,S)$, where $C$ is a set of cardinality $|C| ge 2$ of pairwise co-neighbor vertices sharing the same set $S$ of $|S|$ neighbors. Assuming that $G$ is connected and it has a cluster $(C,S)$, $G(H)$ is obtained from $G$ and an $r-$ regular graph $H$ of order $|C|$ by identifying its vertices with the vertices in $C$, eigenvalues of $A_{alpha}(G)$ and $A_{alpha}(G(H))$ are deduced and if $A_{alpha}(H)$ is positive semidefinite then the $i$-th eigenvalue of $A_{alpha}(G(H))$ is greater than or equal to $i$-th eigenvalue of $A_{alpha}(G)$. These results are extended to graphs with several pairwise disjoint clusters $(C_1,S_1), ldots, (C_k,S_k)$. As an application, the effect on the energy, $alpha$-Estrada index and $alpha$-index of a graph $G$ with clusters when the edges of regular graphs are added to $G$ are analyzed. Finally, the $A_{alpha}-$ spectrum of the corona product $G circ H$ of a connected graph $G$ and a regular graph $H$ is determined. | doi | Peer Reviewed
(latest changes on 2020-01-27 17:44)

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