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Збірник наукових праць  Заснований в 1967 р.  Виходить 1 раз на рік  2016
Abstracts of articles in English
O.S. Samosonok, G.D. Bila, A.P. Knopov
USAGE OF MARKOV RANDOM FIELDS FOR ROOT COUSE DETERMINATION OF
NETWORK FAULT
The model of the communication network based on Markov fields is considered along with the
problem of identification of hidden network’s fault based on Bayesian principle of recognition. A
recursive algorithm for identifying the root causes of communication system faults is suggested
based on analysis of the fault messages registered in the neighboring nodes of the network
topological graph.
G.A. Donets, A.N. Naghirna
OPTIMIZATION OF QUADRATIC FUNCTION ON A SET OF PERMUTATIONS
Approach to the solution of optimization problems with quadratic function of the purpose is
considered on the combinatorial set of permutations, represented as a graph. The numerical example
is given.
L.F. Hulianytskyi, I.I. Riasna
ON FORMALIZATION OF COMBINATORIAL OPTIMIZATION PROBLEMS
ON FUZZY SETS
The article considers an approach to formalizing the concept "fuzzy combinatorial object" that
allows to formalize both known, and new classes of problems of combinatorial optimization on
fuzzy sets. We classify fuzzy combinatorial objects. Examples of such fuzzy combinatorial objects
as fuzzy arrangements, fuzzy combinations, fuzzy permutations, and fuzzy graphs are given.
M.F. Semeniuta
ON DISTANCE ANTIMAGIC LABELING OF GRAPHS
We studied the antimagic type of a vertex labeling of the graph. We have found necessary condition
for existence of (a, d)-distance antimagic labelling for circulation graphs, as well as necessary and
sufficient conditions for existence of (a, d)-distance antimagic labelling for a Dutch windmill graph.
V.K. Chikriy
ONE GAME MODEL OF THE SPORT SINGLE COMBAT
A game problem on the sport single combat is explored on the basis of the method of resolving
functions. Sufficient conditions for winning of each of the players are established, expressed in the
terms of parameters of the conflict-controlled process under study.
I.E. Shulinok, G.A. Shulinok
ABOUT NUMERIC GRAPHS NODES MATCHING
Natural arithmetic and natural modular graphs are considered. The graphs qualities for cover
problem are solved. The algorithms to allow compute coverability of NA- and NM-graphs were
developed. Also algorithms to compute minimal cover for any NA- and NM-graph were made and
appropriate statements were proved.
I.S. Rappoport
ON THE REGULARIZATION OF INTEGRANTS
Minimum conditions of reguiar integrants for the existence of integral functionals and the
possibility of regularization of integrants while maintaining extreme value of integral functionals
is established.
M.M. Kopets, S. F. Sabol
OPTIMAL CONTROL BY PROCESS OF VIBRATION OF THE PRISMATIC BEAM
In the present paper the linear-quadratic optimal control problem for vibration process of the
prismatic is considered. The necessary optimality conditions are obtained by using the Lagrange
multiplier method. The system of integro-differential Riccati equations is derived from this
conditions. The solution of obtained system permits to write the closed formula for optimal control.
S.I. Dotsenko
ON EXPENSES DISTRIBUTION IN CONVEYING PROBLEM
The expenses distributions in conveying problem is considered at the conditions, that the total
customers demand doesn't exceed vehicle bearing capacity. The acceptable decision is found with
the help of cooperative game theory technique.
V.I. Biletsky, E.I. Nenakhov
ALGORITHMS OF SEARCHING FOR TWO ACTIVE BALLS ON GIVEN SETS
The problems of searching for two active balls on given sets for n=63, 89. We some give theorems
that allow calculating the minimal number of trials needed to find two active balls among the
elements of the given set. For every case, the specific step-by-step algorithms are provided.
A.N. Khimich, A.V. Popov, А.Y. Baranov, A.V. Chystyakov
HYBRID ALGORITHM FOR SOLVING EIGENVALUES PROBLEM FOR BAND MATRICES
This paper proposes an algorithm for solving partial generalized algebraic eigenvalue problem with
band symmetric matrices on hybrid computers. The results of testing of the algorithm on a personal
hybrid supercomputer Inparkom_pg are shown.
P.І. Stetsyuk, E.S. Dolynskyi, I.I. Parasiuk
ON THE SHORTEST K-NODE PATH IN A DIRECTED GRAPH
We present the formulation of the mixed Boolean linear programming problem for the shortest path,
which passes through the given number of nodes of the digraph. The results of numerical
experiments of solution of discrete programming problems using NEOS-solver are given. We
discuss the formulation of the problem for finding the shortest Hamiltonian path in a directed graph.
Yu.N. Bazilevich
ON THE REDUCING OF SEMIDEFINITE PROGRAMMING PROBLEM
The method, which allows to reducing some symmetric matrices to the same block-diagonal form,
either to establishing that such a reduction is impossible for these matrices, is considered. This can
be useful in solving semidefinite programming problems. We taken into account the demand — the
transformation matrix must be orthogonal.
O.P. Lykhovyd, O.V. Fesyuk
MPI-REALIZATION OF AN ALGORITHM FOR SOLVING THE PROBLEM OF FINDING
LOAD OF POWER SYSTEM
The problem of finding optimal load of power units with a non-smooth nonlinear fuel cost function,
which takes into account the valve point loading effect, is considered. Parallel MPI-realization of an
algorithm for solving the problem and the results of computational experiments are presented.
V.I. Norkin, I.G. Magdenko, B.V. Norkin
NUMERICAL SIMULATION OF THE INSURANCE BUSINESS BY MEANS
OF MARKOV CHAINS
A model of evolution of an insurance company's capital in the form of a Markov chain with a large
number (thousands) of states is developed. To construct the transition probability matrix quarterly or
annual statistics of the company’s premiums and claims is used. This statistic accounts for
correlation of premiums and claims. Markov chains method allows effectively compute not only the
probability of ruin of the company as a function of time, but also visually track the evolution of the
distribution of company’s capital over time.
A.G. Donets, S.P. Zagordniuk
CONSTRUCTING A TWO-DIMENSIONAL MOSAIC BY MEANS OF ONE PATTERN
We consider the problem of constructing discrete images on a rectangular field by means of
patterns. A notion of pattern self-sufficiency is introduced, which means that one can construct there
identity image by means of the pattern. We prove several statements about necessary and sufficient
conditions for patterns possessing this property.
V.M. Kuzmenko, E.I. Nenakhov
A REDUCTION OF SUPERQUANTILE ERROR TO ROCKAFELLAR ERROR
IN REGRESSION ANALISYS
An opportunity of reduction of superquantile error to Rockafellar error for uniform discrete
distribution is considered. Two variants of reduction are shown and a question of equivalence of
using superquantile error and reductions is analyzed.
N.G. Zhurbenko
THE CONSTRUCTION OF LINEAR CLASSIFIERS ON THE BASIS OF SUPPORT
FUNCTIONS
An algorithm for construction of linear binary classifiers is proposed. The objects of recognition are
presented by convex compacts of Euclidean space. The algorithm is based on the use of support
functions of convex compacts and nonsmooth optimization methods.
G.A. Donets, L.N. Kolechkina
AN APPROACH SOLUTION EXTREME PROBLEMS ON COMBINATORIAL
CONFIGURATIONS IN GRAPHS
We consider the optimization problem of combinatorial optimization configurations permutations,
describes the approach to the solution of these problems on the basis of graph theory to the
properties and structure of the set of permutations. An algorithm for solving such problems.
O.E. Skukis
INFORMATION TECHNOLOGIES AND SYSTEMS OF VEHICLE LOGISTICS
Analysis of information systems (IS) of vehicle logistics. The structure and composition of IS
designed for automation of manufacturing processes of enterprises operating in the segment of
logistics and transportation management.
V.M. Gorbachuk, G.O. Shulinok, O.O. Morozov
NETWORK EFFICIENCY ESTIMATION
It is shown the efficiency of networks is estimated on the basis of their organization as decentralized
systems.