# Computer Sciences

## About closed queuing networks with variable number of queues

Consider a closed queueing network with the possibility of breakdowns at each server. When a breakdown occurs at one server, all customers there are transferred in queue with operational server immediately, and the server is then sent for repair. Steady- state probability of the queue sizes is obtained, and is shown to have a product form solution.

## Some interval problems of the theory of discrete linear systems

Artificial neural networks can be used effectively for a quite general class of problems. Still there exists no formal foundation of some important constructions used in the theory. In this paper an

attempt is undertaken to formalize some concepts of neuroinformatics and consider their properties from the point of view of applied universal algebra. It is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems on homomorphisms and congruences.

## Modeling the Dynamics of Massless Charge Carries is Two-Dimensional System

The paper presents the results obtained in the process of developing a system for simulating the generation of massless charge carriers with a photon-like spectrum by an external electric field for two-dimensional media. The basis of the system is a physical model of the process, built in the formalism of a kinetic equation for an adequate quantum-field theory. It does not use simplifying assumptions, including expansions in some small parameters (perturbation theory). In this sense, the model used is accurate.

## The Study of the Statistical Characteristics of the Text Based on the Graph Model of the Linguistic Corpus

The article is devoted to the study of the statistical characteristics of the text, which are calculated on the basis of the graph model of the text from the linguistic corpus. The introduction describes

## Construction of All Minimal Edge Extensions of the Graph with Isomorphism Rejection

In 1993 Frank Harary and John P. Hayes proposed a graph model for investigating edge fault tolerance of discrete systems. The technical system is mapped to a graph. The elements of the system correspond to the vertices of the graph, and links between the elements correspond to edges or arcs of the graph. Failure of a system element refers to the removal of the corresponding vertex from the system graph along with all its edges. The formalization of a fault tolerant system implementation is the extension of the graph.

## Geometrical images of finite state machines

In this work a new way of defining finite state machines (FSM) is being suggested. The discrete word geometry is built for that purpose, in which machine image is expressed as a set of lines. The methods of synthesis and analysis of geometrical images of FSMs and their features are researched. The new way of defining the FSMs allows analyzing the machine's behavior, excluding the exhausting recursive procedure of defining the initial fragments of machine functioning.

## Algebraic properties of recurrent neural networks of discrete time

Artificial neural networks can be used effectively for a quite general class of problems. Still there exists no formal foundation of some important constructions used in the theory. In this paper an attempt is undertaken to formalize some concepts of neuroinformatics and consider their properties from the point of view of applied universal algebra. It is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems on homomorphisms and congruences.

## T-irreducible extension for unions of complete graphs

T-irreducible extension is one of kinds of optimal extensions of graphs. Constructions of optimal extensions are used in diagnosis of discrete systems and in cryptography. A graph H with n+1 vertices is called an extension of a graph G with n vertices if G can be embedded in every maximal subgraph of H. Any graph Ghas the trivial extension that is the join ng+of G with some outer vertex v. T-irreducible extensions are obtained from the trivial extension by removal of maximal number of edges in such a way that the extension property is preserved.

## Критерии универсальности конечного детерминированного автомата для класса КДА без потери информации

Finite determined machine is one of the most popular mathematical models of complex discrete systems.

## Construction of All Nonisomorphic Minimal Vertex Extensions of the Graph by the Method of Canonical Representatives

In 1976 John P. Hayes proposed a graph model for investigating the fault tolerance of discrete systems. The technical system is mapped to a graph. The elements of the system correspond to the vertices of the graph, and links between the elements correspond to edges or arcs of the graph. Failure of a system element refers to the removal of the corresponding vertex from the system graph along with all its edges. Later together with Frank Harary the model was extended to links failures. The formalization of a fault-tolerant system implementation is the extension of the graph.