An approach to the parallel solution of a high-dimensional basic flow problem

The body of mathematics of modified systems of algorithmic algebras (SAA-M) is used to formalize the Edmonds–Karp algorithm of finding the maximum flow in a network. With allowance made for the distributed system features that are usually used for solving complicated problems, optimization criteria are formulated and used to obtain parallel SAA-M-schemes. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 146–152, March–April 2009.     

An asymptotic estimate of the error of eigenvalues in the method of finite elements for the sturm-liouville problem

A scheme of the second order of accuracy for the Sturm—Liouville problem is constructed by the method of finite elements with the use of a special basic system of compact functions. The convergence of the method of finite elements is proved. An exact formula for estimating errors of eigenvalues is obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 28–36, March–Apni, 2000.     

Direct methods of solving systems of linear algebraic ef ions with complex a-matrices

Algorithms of computer algebra are proposed for solving systems of linear algebraic equations with complex á- matrices. An analysis of roundoff errors for the computational schemes considered is given. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 144–156, March–April, 2000.     

Remarks on stability of solutions of the property domination problem

A class of combinatorial problems is considered whose investigation and solution require the notions of the theory of fuzzy sets. The necessary and sufficient conditions of stability are given. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 36–40, July–August, 1999.     

Investigation and development of the atlas of chromaticity for formation of raster elements and basic link fragments in synthesizing color halftone images

A direction of improvement of a method for formation of color images on offset plates is proposed. The method and tools developed for synthesizing color images are experimentally tested. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 99–109, May–June, 2000.     

Vector optimization of a dynamic standard-size product series

A model and an algorithm of optimization of a standard-size product series on the basis of a two-criterion statement are described and their use for the determination of rational types of trucks in Ukraine is considered. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 157–163, March–April, 2000.     

Partition of a metric space into continuous components

The fact that each discrete metric space is uniquely decomposed into continuous components is elegantly proved. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 185–186, September–October, 1999.     

Accuracy of Approximation of a Solution to an Abstract Cauchy Problem

A constructive image of the solution to a homogeneous Cauchy problem in a Banach space with a densely specified linear closed logarithmically-sector operator is investigated. The uniform accuracy of estimation of an approximate solution in t ≥ 0 is proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 145–152, May–June 2005.     

Estimation and Ranking of Alternatives under Interval Uncertainty

A method is proposed to estimate and rank alternative decisions with interval representation of their characteristics. The method is verified experimentally. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 148–153, July–August 2005.     

Solution of systems of linear algebraic equations with preliminary flattening

A method of improving computing properties of matrices of systems of linear algebraic equations is considered. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 144–149, September–October, 1999.     

Relative rate of change of a function

A quantity is examined that characterizes the relative deviation of a derivative of a function from a specified reference value. This quantity is shown to be interpreted as a derivative of a function in some field constructed using a new operation. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 160–165, July–August, 1999.     

A method of designing cam mechanisms by means of piecewise-circular curves

An algorithm is obtained that permits one to describe cam mechanisms with flat pushers by smooth piecewise curves constructed from arcs of circles. The algorithm is based on the approximation of periodic functions by Hermitian local trigonometrical splines. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 78–86, November–December, 1999.     

Number of cyclically irreducible words in the alphabet of a free group of finite rank

It is shown that a formula that was independently obtained earlier for the number of cyclically irreducible words of length n in a symmetric alphabet of a finitely generated free group of rank k and the Whitney formula for a chromatic polynomial of a simple nonself-intersecting cycle of length n with a variable λ are mutually deducible from one another when λ = 2k. The necessary bijections differ for even and odd values of n. To the memory of William T. Tutte (05.14.1917–05.02.2002) __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 39–48, July–August 2007.     

Foundations of programmology

An explication of the intuitive concept of programming is given in the form of explicative programming, which is a modern form of composition programming. It is based on a pragmatically finite system of principles. On this basis, an explication of the concept of composition is obtained. A hierarchical composition structure of programmology is constructed. Translated from Kibemetika i Sistemnyi Analiz, No. 1, pp. 35–57, January–February, 2000.     

Optimality of software resource structurization in distributed processing

Efficiency and optimality criteria of block structurization of software resources taking account of overhead expenses is obtained for a class of uniformly distributed competing processes. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 59–62, November–December, 1999.     

Algorithm for construction of parametric vectors for solution of classification problems by a feed-forward neural network

A universal heuristic algorithm is considered that constructs the vector of properties of an object that are distributed among heterogeneous groups. This algorithm is based on a feed-forward neural network. An automatic system for objects classification is described. The use of the automatic classification system for a literary authorship attribution problem is considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 3–14, March–April 2007.     

Using categorical methods in computer science

Some categorical methods used in developing computer programs are considered. Relevant theorems are proved. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–11, July–August, 2000.     

Adaptive diagnostic system based on fuzzy relations

Causes (diagnoses) are retrieved and identified using observed effects (symptoms) based on fuzzy relations and Zadeh’s compositional rule of inference. An approach to designing adaptive fuzzy diagnostic systems is proposed. It allows solving fuzzy logic equations and designing and adjusting fuzzy relations using expert and experimental information. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 135–150, July–August 2009.     

Elimination of unknown flows running along intermediate and terminal subgraphs

A new condition that has a real technological significance is imposed on the coefficients of a system of inequalities with graph structure. Methods of elimination of groups of unknown flows along edges of a definite subgraph are considered. The emphasis is placed on the method of elimination of intermediate and terminal subgraphs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 174–177, January–February 2006.     

A generalization of the Jensen inequality

A new approach for estimating functions and functionals based on the concept of function superconvexity and a generalization of the Jensen inequality is proposed. A new concept is introduced and the associated analytical results are substantiated. Some nontrivial estimates of functions are derived. Translated from Kibemetika i Sistemnyi Analiz, No. 2, pp. 89–99, March–April, 2000.