Francisco Criado-Aldeanueva

The dynamical boundary value problem for viscoelastic half-space with cut in the form of a strip is considered. The problem is reduced to the singular integral equation of first kind. Using the method of orthogonal polynomials, the integral equation is reduced to an infinite system of linear algebraic equations. The quasi-completely regularity of the obtained system is proved and the reduction method for approximate solution is developed.

In the present paper, the models of structural analysis and evaluation of efficiency indicators (reliability, fault tolerance, viability, and flexibility) of a multi-core processor with variable structure, equipped with multi-functional cores, are considered. Using logical–probabilistic methods, the following has been developed: models for evaluating the reliability and fault tolerance of processor cores as multi-functional elements; logical–probabilistic models of the shortest paths, flexibility, and performance conditions for successful operation of multi-core processors based on multi-functional cores; and models for estimating the reliability, fault tolerance, and lifetime of multi-core processors considering all possible states of performance. The results of the structural analysis of two-core and four-core processors and the trends of increasing the efficiency indicators of multi-core processors are presented.

The dynamical boundary value problem for viscoelastic half-space with cut in the form of a strip is considered. The problem is reduced to the singular integral equation of first kind. Using the method of orthogonal polynomials, the integral equation is reduced to an infinite system of linear algebraic equations. The quasi-completely regularity of the obtained system is proved and the reduction method for approximate solution is developed.

This paper describes the application of the method of probabilistic solutions (MPS) to numerically solve the Dirichlet generalized and classical harmonic problems for irregular $ n $-sided pyramidal domains. Here, "generalized" means that the boundary function has a finite number of first-kind discontinuity curves, with the pyramid edges acting as these curves. The pyramid's base is a convex polygon, and its vertex projection lies within the base. The proposed algorithm for solving boundary problems numerically includes the following steps: a) applying MPS, which relies on computer modeling of the Wiener process; b) determining the intersection point between the simulated Wiener process path and the pyramid surface; c) developing a code for numerical implementation and verifying the accuracy of the results; d) calculating the desired function's value at any chosen point. Two examples are provided for illustration, and the results of the numerical experiments are presented and discussed.

Este trabajo tiene como objetivo el desarrollo del prototipo de un sistema de posicionamiento que permita validar los modelos numéricos de predicción de aparición de residuos sólidos en las costas. Para ello, se ha realizado el diseño e implementación de un sistema de radiofrecuencia que permite el trazado de las trayectorias de boyas Lagrangianas. El sistema se compone de dos tipos de dispositivos: boyas de deriva superficial y receptores que permitan la extracción de los datos de las trayectorias de las boyas en tiempo real. Las boyas incorporan un receptor GNSS que registra su posición y se comunican con tecnología LoRa con un transceptor que se encuentre en su área de cobertura. Este sistema puede servir no sólo como herramienta de validación de modelos hidrodinámicos numéricos, también representa una metodología escalable, con amplio potencial de uso en el campo de la Oceanografía observacional.

A contact problem of the theory of electroelasticity for piecewise-homogeneous plate of piezo-electric material with infinite cut and elastic finite inclusion of variable bending rigidity is considered. By using methods of the theory of analytic function, the problem is reduced to a system of singular integro-differential equation with fixed singularity. Using an integral transformation a Riemann problem is obtained, the solution of which is presented in explicit form.

This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do not always cause the normal solvability of formulated exterior elliptic problems in the sense of Noether.Nevertheless, from the system of differential equations with partial derivatives of elliptic type it is possible to choose, under certain additional conditions, classes which are normally solvable in the sense of Noether.This paper also shows that for the so-called decomposed system of differential equations, with partial derivatives of an elliptic type in the case of exterior regions, the Noether theorems are valid.

In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where “generalized” indicates that a boundary function has a finite number of first kind discontinuity curves. The algorithm consists of the following main stages: (1) the transition from an infinite domain to a finite domain by an inversion; (2) the consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin’s theorem for the obtained finite domain; (3) the numerical solution of the new problem for the finite domain by the MPS, which in turn is based on a computer simulation of the Weiner process; (4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration, numerical examples are considered and results are presented.