Regularization of a lexicographic vector problem of integer programming

A stability criterion for a vector integer linear problem of lexicographic optimization is obtained. A regularization method is proposed that allows us to reduce a possible unstable output problem to a sequence of perturbed stable equivalent problems. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 125–130, November–December, 1999.     

Stability and regularization of the lexicographic vector problem of quadratic discrete programming

The paper studies the bounds of variation of input parameters for a vector quadratic discrete optimization problem, which do not expand the set of lexicographic optima. A stability criterion is described and a regularization method is presented, which makes it possible to pass from a possibly unstable problem to a series of perturbed stable problems with a previous set of lexicographic optima. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 54–62, March–April, 2000.     

Stability criterion for a lexicographic Boolean optimization problem

A vector Boolean sequential minimization problem for absolute values of linear functions is considered. Necessary and sufficient condition for stability of this type that is a discrete analogue of the upper Hausdorff semicontinuity of a point-to-set mapping is established. This mapping associates a set of lexicographic optima with each set of problem parameters. The study was sponsored by the Fundamental and Applied Research Interuniversity Program of the Republic of Belarus (Grant 492/28). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 127–132, July–August 2007.     

Solution of a problem of geometric programming

The convergence of a method of solution of a geometric programming problem with one forced constraint is studied. The algorithm proposed can be used in searching for chemical equilibrium of an ideal system of gases. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 172–175, November–December 2005.     

A Partial Inverse Linear-Quadratic Optimization Problem

A partial linear-quadratic problem is considered. It is formulated as the determination of the perturbation of a matrix that belongs to a control block under the constraint that the perturbation is such that an extreme value of a quadratic functional has a preassigned form in the “perturbed system” obtained. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 183–188, May–June 2005.     

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.     

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.     

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.     

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.     

Solution of Euclidean combinatorial optimization problems by the method of construction of a lexicographic equivalence

A method of space partition based on an equivalence relation is considered. Based on a lexicographic exhaustive search for equivalence classes, algorithms are developed for solution of a new class of optimization problems, namely, linear conditional Euclidean problems of lexicographic combinatorial optimization.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 155–125, September–October 2004.     

Efficient difference scheme for numerical solution of a convective diffusion problem

Problems of modeling of atmospheric circulation are investigated. A new method for solution of a one-dimensional nonstationary inhomogeneous initial-boundary-value problem of convective diffusion is considered. The problem is solved using a new unconditionally stable and efficient difference scheme. The results of a theoretical analysis of the scheme are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 64–74, May–June 2007. An erratum to this article is available at .     

Invariance theorems for a class of systems of random nonlinear equations over an arbitrary finite ring with left unity

A class of homogenous systems of random nonlinear equations over an arbitrary finite ring with left unity is considered. The author analyzes the invariance boundaries for limit factorial moments of nonzero solutions, the limit distribution of the number of nonzero solutions, and the geometrical structure of the set of nonzero solutions of the system as the number of unknowns tends to infinity. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 106–115, November–December 2008.     

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.     

Statement and solution of some problems on a mathematical safe

The problem on a mathematical safe is formulated and studied in terms of graph theory. The cases of simplest digraphs such as paths, contours, and doubly connected components are analyzed. A number of statements on the existence of solutions to these problems are proved. The results obtained are extended to the case of corresponding nondirected graphs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–14, May–June 2006.     

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.     

Algorithms for solution of systems of linear diophantine equations in residue fields

Algorithms are proposed for computing the basis of the solution set of a system of linear Diophantine homogeneous or inhomogeneous equations in the residue field modulo a prime number. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 15–23, March–April 2007.     

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.     

An approximate solution of the problem of optimal control over elliptic systems in domains of arbitrary form

A combination of the net method and method of fictitious domains is used for solving the problem of optimal control over elliptic systems in domains of arbitrary form. As is shown, the proposed difference scheme has the order of accuracy O(h^1/2) in the net norm W^1/2 (ω). Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 3–8, November–December, 1999.     

Checking the satisfiability of formulas represented in disjunctive normal form in the language <Emphasis Type="Italic">L</Emphasis>. II

This paper concentrates on issues of implementation of the method proposed for checking the consistency of formulae of the language L and described in the first part of this work. Upper-bound estimates of time complexity of the corresponding algorithms are obtained. Part I of this article is published in No. 4 (2005). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 11–19, November–December 2005.     

Field interactions and distinctive features of development of devices for diagnostics and correction of states of biologically active points

Based on a model of field interactions of thermochemical potentials, the possibility of correlation between the conductance and other parameters of biologically active points (BAPs) is investigated. New methods are described for diagnostics and correction of physiological systems by mild actions on BAPs. These methods can be taken into account in developing new devices for reflexotherapy. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 157–165, March–April 2006.