Lagrangean Approximation for Combinatorial Inverse Problems

Various combinatorial problems are effectively modelled in terms of (0,1) matrices. Origins are coming from n-cube geometry, hypergraph theory, inverse tomography problems, or directly from different models of application problems. Basically these problems are NP-complete. The paper considers a set of such problems and introduces approximation algorithms for their solutions applying Lagragean relaxation and related set of techniques.

Inverse Problems Involving Generalized Axial-Symmetric Helmholtz Equation

MSC 2010: 35J05, 33C10, 45D05

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity

2000 Mathematics Subject Classification: 53C24, 53C65, 53C21.

On a Direct Approach to the Solution of Inverse Optical Problems

The evaluation from experimental data, of physical quantities, which enter into the electromagnetic Maxwell equations, is described as inverse optical problem. The functional relations between the dependent and independent variables are of transcendental character and numeric procedures for evaluation of the unknowns are largely used. Herein, we discuss a direct approach to the solution, illustrated by a specific example of determination of thin films optical constants from spectrophotometric data. New algorithm is proposed for the parameters evaluation, which does not need an initial guess of the unknowns and does not use iterative procedures. Thus we overcome the intrinsic deficiency of minimization techniques, such as gradient search methods, Simplex methods, etc. The price of it is a need of more computing power, but our algorithm is easily implemented in structures such as grid clusters. We show the advantages of this approach and its potential for generalization to other inverse optical problems.

Interface Engineering and Design: Adaptibility Problems

* The research work reviewed in this paper has been carried out in the context of the Russian Foundation for Basic Research funded project “Adaptable Intelligent Interfaces Research and Development for Distance Learning Systems”(grant N 02-01-81019). The authors wish to acknowledge the co-operation with the Byelorussian partners of this project.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Electronic Education in the Field of Electrical Engineering Disciplines. Combined Didactic Interactive Program System

At present in the educational process of electrical engineering disciplines electronic learning program, providing control over reproductive educational-cognitive activity (the decision of standard problems) and universal modeling program systems, for instance Electronics Workbench, giving a chance of organizing productive, in particular research activity are basically used. However universal modeling program systems can not provide auto control over educational-cognitive activity because of the absence of the feedback with students. The combined didactic interactive program system, providing the closed directed auto control over both the reproductive and productive heuristic educational-cognitive activity of the student is offered.

Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Static and Dynamic Integrated Expert Systems: State of the Art, Problems and Trends

Systemized analysis of trends towards integration and hybridization in contemporary expert systems is conducted, and a particular class of applied expert systems, integrated expert systems, is considered. For this purpose, terminology, classification, and models, proposed by the author, are employed. As examples of integrated expert systems, Russian systems designed in this field and available to the majority of specialists are analyzed.

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

The Notion of Model in Software Engineering

Милослав A. Средков - Понятията модел и моделиране се използват толкова интензивно в много дисциплини, че е трудно да им се придаде конретно значение. Дори в Софтуерните технологии, разбирането на тези понятия силно зависи от контекста. Ние смятаме, че това допринася за неконсистентността между подходите за моделиране там. В тази статия посочваме някои от произтичащите проблеми, както и важността да има подходяща дефиниция, съчетана с подходящи инструменти. Преглеждаме по-общите дефиниции на модел отвъд границите на Софтуерните технологии. Минаваме през моделирането на различни вторични продукти на процесите от Софтуерните технологии. Накрая представяме нашата визия относно използването на такава обща основа за наша полза.

Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.