We consider a distributed system represented by a weighted bipartite graph G=(I∪J,ε). Each vertex i∈I ("agent i") possesses a certain amount of resource and distributes it among adjacent vertices j∈J ("fields of interaction"). Agent i evaluates the efficiency of allocation of its resource to the field j according to the value of a given function c_<ij>(x_<ij>, X_j). Here x_<ij> is the quantity of resource assigned to j by i and X_j is the total amount of resources allocated to j by all the adjacent agents. At each time step, every agent redistributes its resource in order to "optimize" the allocation. In this paper, we study the process of resource redistribution in systems with linear functions c_<ij> and represented by different kinds of graphs. We formulate sufficient conditions for convergence of the process and obtain explicit expressions for limit and equilibrium states.

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The main wholesale electricity spot market characteristics and appropriate oligopoly microeconomic models of strategic interactions of producers in such a market are discussed in the paper. Equilibrium supply strategies and market outcomes for Cournot, Linear Supply Function equilibrium and Price Leadership models are obtained. Conjectured supply function approach that generalizes all these models is discussed. The bilevel model of producers' strategic interaction with network constraints is discussed and the most practically attractive approaches to its solution based on review of available publications are presented.

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We consider a vertical control distribution channel in which a manufacturer sells a single kind of good to a retailer. We assume that a wholesale price discount increases the retailer's sale motivation thus improving sales. The optimal control of manufacturer's profit via trade discounts is embedded in a differential game framework; in the special case of constant controls we compare the Stackelberg equilibria obtained considering manufacturer and retailer respectively as leaders of the game with Nash equilibrium points.

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We consider a linear optimal control model for the marketing of seasonal products which are produced by the same firm and sold by retailers in different market segments The horizon is divided in two consecutive non-intersecting intervals, called production and selling periods, respectively. The production period state variables are the inventory levels and two kinds of goodwills (consumers' and retailers' goodwill, respectively) while the selling period state variables are the sales levels and the two kinds of goodwills. In the production interval there are three kinds of controls: on production, quality and advertising, while in the selling one the controls are on communication via advertising, promotion addressed to consumers and incentives given to retailers. We consider the case of several kinds of communications. The optimal control problem is transformed into an equivalent nonlinear programming problem.

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We deal with characteristics weight determination in cluster analysis. Our aim is to arrange characteristics used to construct some cluster partition in order that correspond strength of their influence to a clusters structure. To manage this, we propose a numerical coefficient presenting a degree of one fixed characteristic's impact on clusters. When we have located the characteristics in increasing order with a respect to the proposed coefficient, we get a proper solution for the post-hoc analysis problem.

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This paper introduces generalization of Gauss-Seidel iterations interval algorithm on complex sets. Presented method can be used for computer calculations in case of interval uncertainty in data. We prove boundaries of this method.

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We consider an infinite n-personal extensive game defined by Kuhn, with the restriction that for every vertex the set of successors is finite. We want build its normal form and study sufficient conditions in the payoff functions that make it continuous. The main result obtained is that the normal form is continuous if each player payoff function and each profile of pure strategies satisfy: (1) The function is integrable with respect to the determined distribution by the profile; (2) the measure (determined by the profile) of the set of discontinuities of the function is zero and (3) there is a Lebesgue-integrable function that locally bounds the payoff function in a special sense.

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We start from the infinite n-personal extensive games defined by Kuhn, with the restriction that for every vertex the set of successors is finite. We find sufficient conditions which the payoff functions of the extensive game have to satisfy in order to grant the existence of at least one Nash equilibrium in the game. Our search consists of proceeding as usual in the finite extensive games. That is, when the game is reduced to its normal form, we build the sets of mixed strategies and the expected payoff functions, to finally apply a fixed point theorem (a Schauder's one. The fundamental result we obtained is that there exists at least a Nash Equilibrium if each player payoff function and each profile of pure strategies satisfy: (1) The function is integrable with respect to the distribution determined by the profile (2) the measure of the set of discontinuities of the function is zero and (3) there is a Lebesgue-integrable function that locally bounds the payoff function in a special sense.

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In the present article there are grounds of model basis of discount basis system of regional development, which is presented as the complex of interrelated modules, mainly: the module of assessment and analysis of inequality of social-economic development (SED) of Ukrainian regions; the module of management of scenarios of social-economic development (SED) of regions. One of the main components of systems has been considered, mainly: models of assessment of inequality and skewness of regions development. Proposed complex is based on Barro's model, and Sala-i-Martina, Baumolya, Solou-Svana, Cuadrado-Roura, and analysis technique on panel data, which allows to reveal the existence of global and cluster convergence (divergence) effects of levels of social-economic development (SED) regions; to make assessments of level of adaptability of components of cluster structures to factors, which cause instability effect on economy of regions.

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A quadratic-linear bilevel optimization problem with pessimistic (guaranteed) solution is considered. It is reduced to a series of optimistic bilevel optimization problems, which are further reduced to nonconvex optimization problems. Global and local search algorithms for the latter problems are developed. The results of computational solving randomly generated test problems are given and analyzed.

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A new approach for finding optimistic solutions in quadratic-linear bilevel problems is considered. First, we investigate the interrelations between these problems and problems with constraint which is represented as a difference of two convex functions (d.c. constraint). Further on the basis of the global search strategy for d.c. constraint problems a special global method for quadratic-linear bilevel problems is developed.

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The P-complete problem of logic deduction in classical propositional and first order predicate calculus is considered. The suggested method is alternative to the traditional methods of direct and inverse logic deduction in particular to the Robinson's resolution principle. The deterministic algorithm of polynomial complexity based on Boolean algebra of cubic functions for differentiation between two classes of formulas: valid and satisfiable, or unsatisfiable and satisfiable, is suggested.

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the article presents proposed by authors Knowledge Management System Model which can be used while creating the System of Knowledge Management at the System of Consumer Cooperatives in Ukraine. It describes the content of each component of the proposed Model.

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The paper deals with a description and generation of new combinatorial sets. An approach for constructing special types of combinatorial sets having complex structure based on primary combinatorial sets and special mappings is developed. The investigation is devoted to a development of constructive means of creation of combinatorial sets on the ground of the concept of composition k-images of combinatorial sets. The concept uses configurations proposed by C. Berge for description of the combinatorial sets, and special combinatorial operations defined on the sets. The properties of the sets are investigated. A number of examples is given.

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