The competition of two firms on the market of one product with regard to import is considered. The particular volume of product supplied to the market by the importer is unknown to both producers. They know only restrictions about volume of import defined by the market. Non-cooperative game of two persons under uncertainty will serve as a mathematical model where "the role"of uncertainty "plays"the quantity of export goods, "the role"of players strategy - the quantity of goods supplied by them on the sale, payoff function - the income of the player.
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In the present work, we consider the integral equation
$$y(t) = x_0 - iJ\int_{[a, t)} d\textbf{p}(s)y(s) - iJ\int_{[a, t)}d\textbf{m}(s)f(s)$$
where $t \in [a, b], b > a; y$ is a unknown function; $\textbf{p}, \textbf{m}$ are operator-valued measures defined on Borel sets $\Delta \subset [a, b]$ and taking values in the set of linear bounded operators acting in a separable Hilbert space $H$; $J$ is a linear operator in
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In recent years, there is an active formation of the mathematical theory of Berge equilibrium, proposed in 1994, by Russian mathematician, K.S. Vaisman (who died in 1998, did not live up to 36 years). However, the use of this balance is not beyond the scope of matrix games of two persons. This article, apparently for the first time, breaks this tradition.
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Source of the Golden Rule: «Do with respect to someone in such way as you would like him to do with respect to you» one can find in New Testament.
Such approach in economics results to altruistic rules of behavior «help others, forgetting about yourself». The concept of Berge equilibrium strictly formalized in Russia in 1994 in thesis and first articles of Vaisman K.S. fully meets such approach. Then this method of conflict balancing began to be used in works of western colleagues.
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In this paper new solution for portfolio selection problem under uncertainty is formalized. It is based on three concepts: guaranteed result, regret function, Pareto optimal solution.
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The study of completely positive linear maps is motivated by applications of the theory of completely positive linear maps to quantum information theory, where operator valued completely positive linear maps on $C^\ast$-algebras are used as a mathematical model for quantum operations and quantum probability.
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In this paper we analyze the stability of the two-parametric secant type method to errors calculations for solving nonlinear equations and estimate the total error.
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Parameter estimation for Levy processes has generated much research effort lately with a strong injection of interest coming from finance. Within this context the problem can be framed as estimation using increments from an infinitely divisible distribution, for which empirical characteristic functions (ecf) are convenient tools. However convergence of ecf’s to Gaussian processes has not been exploited as fully as it might have been.
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Estimates for the convergence speed models isotropic random fields on the sphere in the norms of Orlich space. The resulting estimates are used to construct models of random fields on the sphere. Models approximate the random field with given accuracy and reliability.
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This paper contains the substantiation of the scheme of partial averaging for one class of hybrid systems where one equation is a differential equation with Hukuhara derivative and the other one is an ordinary differential equation.
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The creation and justification of the methods for guaranteed estimation of linear functionals from solutions to the boundary value problems for linearized stationary Navier-Stokes equations in bounded open Lipschitzian domains are considered.
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In this paper, we discuss a method of auxiliary controlled models and the application of this method to solving some problems of robust control for differential equations. As objects for the approbation of the method, a system of nonlinear differential equations describing some ecological and economic processes is used. A solving algorithm, which is stable with respect to informational noises and computational errors, is presented.
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The concept of languages similarity of Petri nets is introduced. It is determined, that mapping of languages similarity of Petri nets is a surjective homomorphism. The similarity of languages of component Petri net and original detailed Petri model of the investigated parallel distributed system is considered. The work reveals that the language of the original detailed Petri net model can always be restored using the language of its component model.
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In the article the theoretical and practical results of researches are generalized on the problem of intellectualization of decision-making in the conditions of global informatively-communication environment. Results are got within the framework of implementation of the proper scientific programs and realization of the different (including international) applied projects.
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In this paper consider the optimal control problem on infinite time interval with quadratic cost functional. State of this problem is defined by the evolutionary inclusion of reaction-diffusion type. We prove the solvability of such a problem. In the case of rapidly oscillating coefficients in coefficients of differential operator and multivalued interaction function we prove the convergence of $\varepsilon $-dependent optimal process to optimal process of the corresponding averaged problem.
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A model of oscillations of Earth’s poles is constructed on the basis of the analysis of the gravitational torques from Sun and Moon. The model reflects physical processes and does not imply using curve fitting techniques, based, for example, on the polynomial approximation. Within the framework of this model, the Chandler frequency is interpreted as the fundamental frequency of oscillations of the mechanical system and the annual frequency as the frequency of the excitation force.
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The first part of the paper designs a deterministic model to describe cancer prevalence and mortality in a population. Next the asymptotic properties of the model are investigated. In the second part, the model is applied to real-world data. For selected model data, a numerical solution is found to the differential equations describing the model, a long-term prediction is made with its results compared with those of predictions made by regression analysis, which are often used to model the prevalence and mortality in the present literature.
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The algorithm of reduction of the number of carrier elements of a discrete fuzzy number with the realization of an opportunity to save the information about values is proposed in the article. It is proposed that the information is given by the fuzzy number.
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Problem of grouping information: recovering function, represented by its observations, and the of classification (problem) clusterization problem, is of great importance for applied research. Choice of math object which represent the object under investigations largely determines the effectiveness: scalars, vectors or objects of other kinds. Such choice is determined by the richness of mathematical structures within which “representatives” are investigated. Euclidean spaces $R^{n}$ are common in this choosing.
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Finding the Nash equilibrium situation in linear-quadratic differential game of three persons reduces to construction of explicit form solving of matrix system of Riccati model differential equations. The question is that the existence of such solution, its properties is the unsolved problem. In proposed article this problem is solved only for the game of one player.
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The paper introduces the classification of informational situations for a zero-sum game with incomplete information based on uncertainty level. For each case the possible ways to deal with uncertainty are considered.
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The article discusses the implementation of the algorithms based on mortar-method and Schwarz alternating method for solving contact problems of elasticity theory. Solving such problems is often associated with necessity of using mismatched grids. Their joining can be carried out both with the help of iterative procedures that form the so-called Schwarz alternating methods, and with the help of the Lagrange multipliers method or the penalty method. The algorithm constructed in the article uses the mortar method for matching the finite elements on the contact line.
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In the paper we develop solve-operator methods for high order modelling, simulation and optimization of risk controlled stochastic processes described by general graph-operator control systems with incomplete data.
Optimization problems with partial derivatives and algorithms for constructing generalized solutions
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In the paper we define generalized solutions of the optimization problems for control systems with partial derivatives and develop two types of numerical algorithms for calculating the generalized solutions.
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The concept of a weakly guaranteed simultaneously under payoffs and risks solution of a one-criterion problem under uncertainty (OCPU) is proposed. Formalization is based on the concept of a vector saddle point from the theory of multicriteria problems with uncertainty.
Keywords: strategy, uncertainty, criterion, Slater optimum, vector saddle point.
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A discrete model of optimal advertising for a monopolist-seller of a new goods
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Linear operators with partial integrals are studied. Using Banach’s closed graph
theorem, a general theorem on the continuity acting from a space $X$ to a space $Y$ of linear operator
$K$ with partial integrals is proved. Here $X$ and $Y$ are complete metric spaces of measurable
functions with a shift-invariant metric, and the space $X$ contains, together with each function,
its modulus. With the application of this theorem, the continuity acting of the operator $K$ in
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The sufficient conditions of the existence of Berge equilibrium situation in noncooperative
game of many persons in normal form are established. On the basis of these conditions the
existence of Berge equilibrium situation in mixed strategies (by compact sets of strategies of
players and continuity of their payoff functions) is proved. Let us consider the history of the
appearance of the Berge equilibrium notion.
In 1949 the 21-years-old PhD student of Prinston University, John F. Nash (jun.), formalized
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Physical objects, describes the distribution of self-oscillating system is the
combustion front propagates in a homogeneous medium. Experimental studies conducted
Merzhanov, Borovinskaya showed that the stationary mode of propagation of the front becomes
unstable if the activation energy of the exothermic reaction exceeds a certain value. In the
instability of the stationary mode combustion front, staying flat, moving in an oscillatory mode. In
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The complex interactions between the processes of disturbed ecosystems are
often difficult to predict. The classical dynamic model may include a limited number of factors,
which act on the population balance just directly. In the common case of the transition to a
chaotic regime of discrete models are limited in predictive capabilities. Graph scheme allows
us to structure the information on the relationship between the factors in the subject field of