Analytic solution for a class of discrete-time Riccati equations arising in Nash games

Explicit solutions for second-order operator differential equations with two boundary-value conditions. II

AbstractBoundary-value problems for second-order operator differential equations with two boundary-value conditions are studied for the case where the companion operator is similar to a block-diagonal operator. This case is strictly more general than the one treated in an earlier paper, and it provides explicit closed-form solutions of boundary-value problem in terms of data without increasing the dimension of the problem.

A discrete mathematical model for addictive buying: Predicting the affected population evolution

This paper deals with the construction of a discrete mathematical model for addictive buying. Firstly, identifications of consumers buying behavior are performed by using multivariate statistical techniques based on real data bases and sociological approaches. Then the population is divided into appropriate groups according to the level of overbuying and a discrete compartmental model is constructed. The future short term addicted population is computed assuming several future economic scenarios. © 2010 Elsevier Ltd.

Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization

In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut A(t)uxx B(t)u=0; 0 0, u(0;t)=u(p;t)=0; u(x;0)=f(x);06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given >0 and t0;t1; with 0<t0<t1 and D(t0;t1)=f(x;t); 06x6p; t06t6t1g the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0;t1). An algorithm is also included. c 1999 Elsevier Science B.V. All rights reserved. AMS classication: 65M15, 34A50, 35C10, 35A50

Solving coupled Riccati matrix differential systems

Abstract We start by noting that coupled Riccati matrix differential systems appearing in differential games may be considered as a single rectangular Riccati equation. An explicit solution of the coupled differential system in terms of a solution of the associated algebraic Riccati equation is given.

Explicit solutions of two-point boundary value operator problems

Soit H un espace de Hilbert, complexe, separable et soit L(H) l'algebre de tous les operateurs lineaires bornes sur H. On etudie des conditions d'existence non triviales pour le probleme aux valeurs limites operateurs: t 2 X (2) +tA 1 X (1) +A 0 X=0; M 11 X(a)+N 11 X(b)+M 12 X (1) (a)+N 12 X (1) (b)=0, M 21 X(a)+N 21 X(b)+M 22 X (1) (a)+N 22 X (1) (b)=0, 0<a≤t≤b ou M ij , N ij , pour 1≤i, j≤2 et A 0 , A 1 sont des operateurs de L(H). Sous certaines hypotheses concernant l'existence des solutions d'une equation operateur algebrique X 2 +B 1 X+B 0 =0, on obtient des solutions explicites au probleme aux limites

Computing continuous numerical solutions of matrix differential equations

Abstract In this paper, we construct analytical approximate solutions of initial value problems for the matrix differential equation X ′( t ) = A ( t ) X ( t ) + X ( t ) B ( t ) + L ( t ), with twice continuously differentiable functions A ( t ), B ( t ), and L ( t ), continuous. We determine, in terms of the data, the existence interval of the problem. Given an admissible error e, we construct an approximate solution whose error is smaller than e uniformly, in all the domain.

Explicit closed form solutions of boundary value problems for systems of difference equations

In this paper boundary value problems for systems of difference equations of the type , where A j ∈ C p×p and bn y j+n ∈ C p , for 0≤j≤k − 1, are studied from an algebraic point of view. Existence conditions and closed form solutions are given in terms of co-solutions of the algebraic matrix equation .

Explicit expressions for Sturm-Liouville operator problems

Throughout this paper H will denote a complex separable Hilbert space and L(H) denotes the algebra of all bounded linear operators on H. If T lies in L(H), its spectrum σ(T) is the set of all complex numbers z such zI–T is not invertible in L(H) and its compression spectrum σcomp(T) is the set of all complex numbers z such that the range (zI-T)(H) is not dense in H ([3, p. 240]). This paper is concerned with the Sturm–Liouville operator problemwhere λ is a complex parameter and X(t), Q, Ei, Fi for i = l,2, and t∈[0,a], are bounded operators in L(H). For the scalar case, the classical Sturm-Liouville theory yields a complete solution of the problem, see [4], and [7]. For the finite-dimension…

Explicit solutions of Riccati equations appearing in differential games

Abstract In this paper an explicit closed form solution of Riccati differential matrix equations appearing in games theory is given.

Modeling Political Corruption in Spain

Political corruption is a universal phenomenon. Even though it is a cross-country reality, its level of intensity and the manner of its effect vary worldwide. In Spain, the demonstrated political corruption cases that have been echoed by the media in recent years for their economic, judicial and social significance are merely the tip of the iceberg as regards a problem hidden by many interested parties, plus the shortage of the means to fight against it. This study models and quantifies the population at risk of committing political corruption in Spain by identifying and quantifying the drivers that explain political corruption. Having quantified the problem, the model allows changes to be …

On complete set of solutions for polynomial matrix equations

Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.

Explaining shopping behavior in a market economy country: A short-term mathematical model applied to the case of Spain

[EN] In recent decades, pathological consumption has become a growing behavioral misbehavior. Impulsive consumption is governed by two internal behavioral mechanisms that respond fundamentally to the hedonism or Pascal effect and to the emulation or Veblen effect. Today's development of technology acts as a catalyst of consumption by increasing access and availability to products, as well as the advertisement impact. This paper presents a compartmental discrete matrix mathematical model that allows short-term estimates of ordinary, impulsive, and pathological buyers in Spain in three different economic scenarios. The results show that impulsive and pathological buyers will increase in all t…

An algorithm for solving generalized algebraic Lyapunov equations in Hilbert space, applications to boundary value problems

Let L(H) be the algebra of all bounded linear operators on a separable complex Hubert space H. In a recent paper [7], explicit expressions for solutions of a boundary value problem in the Hubert space H, of the typeare given in terms of solutions of an algebraic operator equation

Mathematical modelling of social obesity epidemic in the region of Valencia, Spain

In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic. We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general stra…