G.A. Donets, L.N. Kolechkina
ALGORITHM OF SEARCH OF LINEAR FUNCTION VALUES
ON LEXICOGRAPHIC ORDERING TRANSPOSITIONS
Algorithms of search of linear function values on lexicographic ordering transpositions are considered. The investigation
serves to clarify the issue of possible application the graph theory to construct algorithms of finding a transposition
under the basis of certain number and vice versa.
F.A. Sharifov
METHODS TO SOLVE THE SHEDULING CHOICE PROBLEM FOR POWER SYSTEMS JOINTED BY ACTIVE
STATE
We propose methods for finding an approximation solution the design minimum cost scheduling for choosing an active
state of power systems that must be operated in a short time or for given time. The methods are based on approaches
that are used in solving nonlinear programming problems.
S.I. Dotsenko
ON NASH EQUILIBRIUM IS SUCCESSIVE PURSUIT PROBLEM
The problem of successive pursuit with one pursuer and two escapers is considered. It is assumed< that each escaper can
choose his speed between zero and given value u. For different relations between pursuer and escaper Nash equilibrium
situations are considered.
V.V. Boyko, B.I. Goldengorin, V.M. Kuzmenko
ABOUT ESTIMATION IN P-MEDIAN PROBLEM
The paper considers lower bounds building for solving p-median problem. Authors use Hammer-Beresnev function as an
objective while investigate properties of p-median problems and bounds building. This way permits use particularities of
the function such as positive coefficients and pseudo Boolean property for data aggregation and decreasing problem size.
The results of computational experiments are given.
K.G. Dziubenko
СONTINUITY OF LINEAR FUNCTIONAL AND STOCHASTIC INTEGRAL
General criterion of continuity for linear random functional is established. Continuity of stochastic integral with respect to
integrable function is proved. Differential form of stochastic integral increments is obtained.
T.V. Pepeljaeva
ABOUT SOME CONTROL PROBLEM OF THE STOCHASTIC DYNAMIC SYSTEM
The stochastic differential equation with the fractional Wiener sheet is investigated. The existence theorem of optimal
control of the corresponding equation solution is proved.
E.P. Karpets, G.F.Kikot, S.V. Panasenko
PROBLEMS OF PROGNOSTICATION OF THE BALANCED ECONOMIC STRUCTURE
In this article the principles of the use of model of interspecific cooperations are described in prognostication of
structure of budgetary proportions. The got results enable not only to define the extreme variants of structure of economy
but also outline the possible scenarios of structural balanced for the basic types of economic activity.
V.I. Biletsky
ON A PROBLEM OF SOIL MASS DISTRIBUTION AND THE
ALGORITHM OF ITS SOLUTION
We consider a problem of soil mass distribution, when the soil from the groove is inappropriate for levee construction and
the soil is taken from borrows, located along the road at a certain distance from it. We point out peculiarities of the borrov
soil mass distribution problem, describe the algorithm of its solution using the method of sequential analysis of variants.
A.V. Chikrii
ON MULTIPLE CAPTURE OF THE EVADER
Conflict-controlled processes with group of pursuers and single evader are studied. Sufficient conditions for multiple
capture in a finite quaranteed time are obtained.
G.A. Shulinok
ABOUT MINIMAL GENERATRIXES SET FOR COMPLETE SUBGRAPH
OF THE NA-GRAPH
Natural arithmetic graphs are considered. Minimal generatrixes set for existence of complete graph of appropriate level is
investigated. A number of proposition was proved to determine existence of complete subgraph in the target natural
arithmetic graph.
O.V. Mironenko
THE EXISTENCE OF T-FACTORIZATION OF ODD ORDER FOR SYMMETRICAL TREES
In this paper we explore the problem of the existence of T-factorization of complete graph Кn of odd order n = 2k + 1. The
research in this direction is confirm the hypothesis «For each symmetrical tree of odd order T-factorization is possible» for
tress of order n = 13, n = 15, n = 17 with the help of a half-turned method. The results of studies are presented in the form
of table.
S.I. Sirenko
ON THEORETICAL STUDY OF AN ACO-H METHOD
Рaper considers a hybrid metaheuristic method of combinatorial optimization ОМК-Н and studies its convergence. A class
of method’s algorithms is formally described. A convergence in value to an optimal solution for the algorithms from this
class is shown.
L.B.Vovk, O.P. Knopov
MODELING AND CREATING ALGORITHMS FOR FINANCIAL MODELS
Some algorithmic approaches to the random values and processes modeling for obtaining the calculated estimators for
stock, options and other kinds of valuable papers are investigated.
Z.V Nekrylova
ABOUT THE MODELS WITH BOTH DISCRETE AND CONTINUOUS PARTS DEPENDENT VARIABLE
The models that have both discrete and continuous parts dependent variable are investigated. One important model is the
Tobit. It is an extansion of the probit, but it is one approach the problem of censored data. Two possible solutions for
consistent estimations even in the face of heteroscedasticity are discussed. A class of problems involving a treatment and
an outcome and two-step method for them are discribed.
E.I. Nenakhov
ON LINE LINEAR EXCHANGE MODEL
An exchange model with variable budgets is considered. The linear utilities functions of the traders is proposed.
Investigation of the model is based on it’s reducing to finite system of inequalities. Given model, that has periodic points,
has a vector of equilibrium prices.
V.B. Bigdan
MODELS OF DATA FLOWS CONTROL IN THE PROCESSES OF THE DISTRIBUTED SEARCH OF OPTIMAL
DECISIONS
The features of realisation are considered in regard to some basic aspects of Data Mining technology in the frame of
optimisation-simulation system NEDISOPT_D developed at V.M.Glushkov Institute of cybernetics of NAS of Ukraine.
The emphasis is made upon the models of data flows control in the processes of the distributed search of optimal decisions
with the subsequent search results accumulation in warehouses of experience of modelling.
Yu.M. Tchornyy
RELIABILITY EVALUATION FOR THE RESULTS OF DIRECTED SEARCH OF OPTIMAL DECISIONS
The possible approach to the problem of reliability evaluation for the results of directed search of optimal decisions is
considered. This approach is based on the conception of replications runs and was implemented in the optimizationsimulation system NEDISOPT_D.
W.M. Gorbachuk
THE COMPARATIVE ANALYSIS OF COURNOT–NASH AND BERTRAND–NASH EQUILIBRIA FOR
DIFFERENTIATED PRODUCTS
In the case of heterogeneous duopoly, the fact of substitutability or complementarity of differentiated products is more
improtant for profits’ difference at Cournot–Nash and Bertrand–Nash equilibria, than the degree of their uniformity. For
substitutes (complements) the price and the profit of each firm at Cournot–Nash equilibrium are higher (lower), than ones
at Bertrand–Nash equilibrium, and the output is lesser (larger).
Yu.P.Laptin, D.L.Kroshko
SOME NETWORK NONLINEAR OPTIMIZATION PROBLEMS
The problems under consideration are described by a set of interconnected functional blocks. Some block outputs may be
used as inputs for other blocks. Functional dependencies of blocks are defined on bounded areas. Problem solving
approach is based on function redefining at full space.
P.I. Stetsyuk, O.P. Lykhovyd, O.V. Pylypovskiy
OPTIMIZATION PROBLEMS FOR CHOICE OF ELECTRIC LOADS IN A POWER SYSTEM
A family of mathematical models for finding optimal (for total costs) load of power units in a power system for planning
period is considered. Constraints for ecological factors and a possibility of manoeuvring for load levels of power units are
taken into account in these models. The mathematical models are formulated in the form of linear and nonlinear
programming problems.
N.G.Gurbenko, B.M.Chumakov
METHOD OF MODEL HEAT-EXCHANGERS IN CALCULATIONS OF THE THERMAL SCHEMES
A method for calculation the thermal schemes is proposed. The method is based on the construction of model heatexchangers. Calculation of thermal schemes consists of the iterative procedure. The main iteration operation is the solution
of system of linear equations. The results of solving the system of equations are used to adjust the parameters of the model
heat exchangers. The algorithm is used for software engineering of the tasks of optimum projection of steam boiler
A.V. Popov
OPTIMIZATION OF PARALLEL ALGORITHMS OF PROBLEMS WITH SPARSE MATRICES SOLVING
The problems of organization of solving of the systems of linear algebraic equations and partial generalized eigenvalue
algebraic problem with sparse symmetric matrices are considered. Modification of parallel algorithms of solving of the
systems of linear algebraic equations with sparse triangular matrices is offered for the rise of efficiency.
T.A. Lazebna
ON SOME ASPECTS OF MODELLING OF HUMORAL IMMUNE REACTION
The aspects of existence and uniqueness of equations system solutions have been investigated. The system presented
describes model of humoral immune reaction on non-reproducting molecular-disperse antigen, which is based on relative
approach for described reactions of B-lymphocytes and its products with antigen.