A tropical extremal problem with nonlinear objective function and linear inequality constraints

We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear inequality constraints. An efficient solution approach is developed which reduces the problem to that of solving a linear inequality with an extended set of unknown variables. We use the approach to obtain a complete solution to the problem in a closed form under quite general assumptions. To illustrate the obtained results, a two-dimensional problem is examined and its numerical solution is given.Comment: The 6th WSEAS European Computing Conference (ECC'12), Prague, Czech Republic, September 24-26, 2012; Advances in Computer Science: Proc. 6th WSEAS European Computing Conf. (ECC '12), WSEAS Press. ISBN 978-1-61804-126-5; RACES 5, ISSN 1790-510

An optimal control problem for the systems with integral boundary conditions

In this paper, we consider an optimal control problem with a «pure», integral boundary condition. The Green’s function is constructed. Using contracting Banach mappings, a sufficient condition for the existence and uniqueness of a solution to one class of integral boundary value problems for fixed admissible controls is established. Using the functional increment method, the Pontryagin‘s maximum principle is proved. The first and second variations of the functional are calculated. Further, various necessary conditions for optimality of the second order are obtained by using variations of controls

Computation of the inverse Laplace Transform based on a Collocation method which uses only real values

We develop a numerical algorithm for inverting a Laplace transform (LT), based on Laguerre polynomial series expansion of the inverse function under the assumption that the LT is known on the real axis only. The method belongs to the class of Collocation methods (C-methods), and is applicable when the LT function is regular at infinity. Difficulties associated with these problems are due to their intrinsic ill-posedness. The main contribution of this paper is to provide computable estimates of truncation, discretization, conditioning and roundoff errors introduced by numerical computations. Moreover, we introduce the pseudoaccuracy which will be used by the numerical algorithm in order to provide uniform scaled accuracy of the computed approximation for any x with respect to ex . These estimates are then employed to dynamically truncate the series expansion. In other words, the number of the terms of the series acts like the regularization parameter which provides the trade-off between errors. With the aim to validate the reliability and usability of the algorithm experiments were carried out on several test functions

High-order full discretization for anisotropic wave equations

Two-dimensional linear wave equation in anisotropic media, on a rectangular domain with initial conditions and periodic boundary conditions, is considered. The energy of the problem is contemplated. The space discretization is reached by means of finite differences on a uniform grid, paying attention to the mixed derivative of the equation. The discrete energy of the semi-discrete problem is introduced. For the time integration of the system of ordinary differential equations obtained, a fourth order exponential splitting method, which is a geometric integrator, is proposed. This time integrator is efficient and easy to implement. The stability condition for time step and space step ratio is deduced. Numerical experiments displaying the good behavior in the long time integration and the efficiency of the numerical solution are provided.MTM2015-66837-P del Ministerio de Economía y Competitivida

¿Existen diferencias en las emociones de los alumnos de eso hacia algunas materias según el género?

El presente trabajo analiza las emociones de los estudiantes en su paso por Educación Secundaria, en relación al aprendizaje de diversas materias relacionadas con las ciencias, intentando encontrar posibles diferencias en función del género del sujeto. Para ello, se elaboró un cuestionario que incluye diferentes emociones donde el estudiante debía señalar con que frecuencia experimentaban esas emociones en el aprendizaje de las asignaturas científicas. La muestra está constituida por 510 alumnos de primero de Grado de diferentes carreras y ramas de conocimiento de la Universidad de Extremadura (España) durante el curso académico 2012/2013. Los resultados muestran, principalmente, que los chicos experimentaron emociones positivas hacia la Física, las Matemáticas y la Tecnología a diferencia de las mujeres que manifestaron con mayor frecuencia nerviosismo, preocupación o ansiedad.This paper analyzes the emotions of students on their way through Secondary Education, in relation to learning various subjects related to science, trying to find possible differences by gender of the student. To do this, we developed a questionnaire that includes different emotions where the student should note how often they experienced those emotions in learning science subjects. The sample consists of 510 students from first grade of different races and branches of knowledge of the University of Extremadura (Spain) during the academic year 2012/2013. The results show, mainly, that the boys experienced positive emotions toward Physics, Mathematics and Technology, unlike women who reported more often of nervousness, worry or anxiety.peerReviewe