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.     

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.     

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.     

The initial stage of the well-founded design of computer in the context of the comprehensive approach

Two initial forms are considered to substantiate the choice of suitable versions of a computer being designed. The comprehensive approach is used for this purpose. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 174–179, March–April, 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.     

Fast retraining of SDM

The functioning of Kanerva’s Sparse Distributed Memory is examined under conditions of changes in data that are to be written at an address. To improve the efficiency of retraining, a modification of the Kanerva writing procedure is proposed. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 40–49, July–August, 1999.     

Formalization of algorithmic knowledge of object domains in terms of the algebra of algorithmics

Clones of algebras of n-relations are examined. These clones include algebras equipotent to Codd’s algebra. The results obtained earlier for semigroup (grammatical and algorithmic) clones are extended to clones of algebras of functional n-relations. One-dimensional and multidimensional computing structures and related object domains are outlined. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 3–17, November–December 2007.     

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.     

Neurolinguistic identification of nonlinear dependences

A method is proposed for the identification of nonlinear dependences on the basis of a composition of a fuzzy knowledge base and a neural network. The structure of a neurofuzzy network that is isomorphic to a system of linguistic statements of the form “if-then” is specified, and analytical models for training are obtained. The efficiency of the proposed method of identification is illustrated by a computer experiment. Translatedfrom Kibernetika i Sistemnyi Analiz, No. 2, pp. 37–44, March–April, 2000     

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.     

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.     

Combinatorial properties of noninteger vertices of a polytope in a three-index axial assignment problem

It is proved that, for any r ∈ { 2n, 2n + 1,…, 3n−2} and only for such r, the polytope of a three-index axial assignment problem of order n, n ≥ 2, contains completely r-noninteger vertices (r-CNVs), i.e., vertices such that all their positive components are fractional and their number equals r. For each r ∈ {2n, 2n + 1,…, 3n −2}, all the types of r-CNVs are characterized and the combinatorial properties of completely r-noninteger vertices of the polytope are studied. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 33–44, January–February 2007.     

Object Model as the Basis of the Information Technology of Designing Complex Socio-Economic Systems

A method of modeling complex socio-economic systems based on the object-oriented approach is considered. The method is the basis for the information technology of design and allows creating a hierarchical model of a complex system. The results of applying the approach to developing a regional energy efficiency program are given. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 136–146, September–October 2005.     

Simulation of Motion of a Collection of Rigid Bodies,Taking into Account Their Collisions and Joints

Existing methods of simulation of motion of rigid bodies are considered that take into account collisions and joints of such bodies. A new fast universal fixed-step-size algorithm of speed constraints is proposed. This algorithm combines all the advantages of well-known algorithms and is deprived of their drawbacks. Using a modified Dantzig method, the upper time estimate equal to O(4k) is obtained for the algorithm. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 29–38, July–August 2005.     

Investigation and development of an atlas of optimal configurations, standard sizes, and areas of raster elements and basic link fragments for the synthesis of color halftone images

Results of investigation and development of methods for the synthesis of halftone images and computer and laser modern information technologies are presented. A completely new technology is proposed. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 134–143, March–April, 2000.     

Isomorphism of regular NM-graphs of degree 4

An analysis of the problem of isomorphism of natural modular graphs is continued. New results are obtained for regular graphs of degree 4. The general approach to the analysis of arbitrary regular NM-graphs is developed, which brings close to solving the isomorphism problem for a given class of numerical graphs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 95–103, January–February 2006.     

Solving systems of linear equations with Boolean variables

The paper presents a method to solve systems of linear equations with Boolean variables, which implements an enumeration strategy. Necessary and sufficient conditions for the existence of feasible plans are formalized. A formal procedure to analyze subsets of alternatives is described. The structure of an algorithm that possesses the property of completeness is presented. Special cases of systems of equations are examined. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 42–50, September–October 2006.     

Construction and analysis of a model of a discrete oscillatory system

A model is proposed for a discrete oscillatory system that operates in the modes of generation of harmonic, quasiharmonic, and chaotic signals. The domains of existence of the signals generated are shown. The results obtained are supported by computer simulation. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 161–165, July–August, 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.     

Polynomial expansions of boolean functions in images of nonhomogeneous operators

To represent the functions in terms of which expansions are constructed, the so-called dp-, pt -, and dt -operators are used. The existence of polynomial expansions of Boolean functions in functions obtained by applying heterogeneous operators of the above-mentioned types to a nondegenerate Boolean function is proved. Some methods of finding coefficients of these expansions are also considered. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 40–55, May–June, 2000.