Decision-making in the economy should take into account the uncertainty, incompleteness of information, contingency, inconsistency, conflict, competition, multicriteria, alternatives and the resulting economic risk. As a game-theoretic model of decision-making in the economy with incomplete information, a model based on the concept of combined application of statistical and antagonistic games is proposed.
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The branch of analysis, connected with the study of functions of an infinite-dimensional argument, has been recently intensively developing. This is due both to internal causes and to applications to theoretical and mathematical physics. It is well known which role in classical mathematical physics is played by distributions — linear continuous functionals on smooth basic functions. Therefore, it is natural to develop such a theory in infinite-dimensional spaces.
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Procedure is shown hermeneutics nonparametric Ansari-Bradley test by facilities of Mathcad. Hermeneutics procedure is built on the analysis of typical methodical errors of calculation of criterion. The similar technique of penetration in essence of statistical criterion is in an equal degree useful as for beginners so for more experience researchers.
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Mathematical model of consolidation of soil has been improved taking into account their salinity and chemical erosion. Numerical solution of the corresponding three-dimensional boundary value problem has been found by the radial basis functions method.
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This article describes definition of exponential estimation of linear stationary system with delay solution by functional Liapunova-Krasovskogo.
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The system under consideration consists of two unreliable lines. The first line is more effective then the second one. Both lines have Poisson failure flow. If the lines are in good working order, failure rate of the first line is $\alpha _{1}$, failure rate of the second line is $\beta _{1}$. If one of the lines is down, failure rate of the other equals $\alpha_{2}$ or $\beta_{2}$ espectively. The system is serviced by a single repairman.
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The algorithm of creation of a component Petri net with ingibitor arcs ($CN_I$ -nets) is resulted. Possible methods of creation $CN_I$ -nets are considered on examples. An established fact of usage of the component analysis of $CN_I$ -nets for research of properties of detailed model of researched system.
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Kolmogorov’s definition of algorithmic complexity of constructive objects [7] is applicable not only to character strings, but also to the functions, function collections, and many other objects. If we define Kolmogorov complexity of a family of recursive functions, it will be its entropy characteristics. Introduced by different ways measures of a complexity of families of functions are of great theoretical and practical interest.
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In article is proposed the maximum flow problem with additional combinatorial restrictions. This problem is generalization of the classical maximum flow problem. In article NP-hard of a problem is proved.
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This article discusses the pencil of ordinary differential operators generated on $[0,1]$ by a linear differential expression of $n$-th order with constant coefficients, polynomially depending on spectral parameter $\lambda$ , and the two-point boundary conditions of a general form with coefficients which are polynomials of the spectral parameter $\lambda$.
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We consider a wide class of linear optimization problems with integer variables. In this paper, the lower and upper attainable bounds on the $T_2$-stability radius of the set of extremum solutions are obtained in the situation where solution space and criterion space are endowed with various Holder's norms. As corollaries, the $T_2$-stability criterion is formulated, and, furthermore, the $T_2$-stability radius formula is specified for the case where criterion space is endowed with Chebyshev's norm.
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Through the use of a suitable variant of dynamic programming, the explicit form of the situation of guaranteed equilibrium in a two-step positional mathematical model of Bertrand duopoly has been found. This research may be extended by examination of $N$-person games as well as applying the Berge equilibrium instead of the Nash equilibrium.
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Let $f$ be a real-valued $2\pi$-periodic function defined on $[-\pi,\pi]$, and for each open interval $I=(a,b)\subset [-\pi,\pi]$ set $f(I)=f(b)-f(a)$. We let $\Lambda=\{\lambda_k\}_{k=1}^\infty$ denote non-decreasing sequence of real numbers such that
\begin{equation*}
\sum_{k=1}^\infty \frac{1}{\lambda_k}=+\infty.
\end{equation*}
Then $f$ is said to be of $\Lambda$-bounded variation $(\Lambda BV)$ on $[-\pi,\pi]$ if
\begin{equation}
V(\Lambda,f):=\sum_{k=1}^\infty \frac{f(I_k)}{\lambda_k}\,{<}\,\infty,
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Let $G$ be a physical pendulum of mass $m$. Suppose that it has a cavity filled with a system of three homogeneous immiscible viscous fluids situated in domains $\Omega _{1}, \Omega _{2}$ and $\Omega _{3}$ with free boundaries $\Gamma _{1}\left ( t \right ), \Gamma _{2}\left ( t \right )$ and rigid parts $S_{1},S_{2},S_{3}$. Let $\rho _{1}, \rho _{2}, \rho _{3}$ be densities of fluids, and $\mu _{1}, \mu _{2}, \mu _{3}$ be dynamical viscosities. We suppose that the system oscillates (with friction) near the fixed point $O$ of spherical hinge.
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We consider the $\mathrm{}n$-homogeneous $C^{*}$-algebras over a two-dimensional compact oriented connected manifold. Suppose $A$ be the $\mathrm{}n$-homogeneous $C^{*}$-algebra with space of primitive ideals homeomorphic to a two-dimensional connected oriented compact manifold $P(A)$. It is well known that the manifold $P(A)$ is homeomorphic to the sphere $P_k$ glued together with $k$ handles in the hull-kernel topology. On the other hand, the algebra $A$ is isomorphic to the algebra $Γ(E)$ of continuous sections for the appropriate algebraic bundle $E$.
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This paper continues the research within the paradigm of extracting or building optimization models from data (BOMD) for intelligent control systems. The obtained results are devoted to nonlinear models with real variables, generally speaking, of any functional complexity in the class of functions of arbitrary degree of smoothness and constraints represented by piecewise linear approximation. This is achieved through the use of neural networks as the main used mathematical apparatus.
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Purpose of work. For a given (partially, completely) complex network, it is necessary to find, consistent with the routing problem, the network layout for a certain number of clusters, which
provides high accuracy and speed of solving the corresponding extreme problems on the graphs.
The article considers graph clustering algorithms, as well as their application for discrete optimization problems on graphs, as an example of the problem for k traveling salesmen. The
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In the article, based on the analysis of the specifics of the problem of increasing the fault tolerance of combinational integrated circuits, the requirements for such a code are formulated by the methods of excessive coding. A linear non-cyclic code with parity checks satisfying these requirements is proposed. The code fixes single errors, detects double errors and has the advantages that are essential for the task at hand. The efficiency of the proposed code is estimated.
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This article is devoted to the boundary value problem for elliptic-parabolic equation with small parameters by the second-order derivatives. The aim of our work is to construct an effective numerical algorithm based on asymptotic approximation for the solution.
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In our days, interest to the class of inductors on the basis of decision trees does not weaken, especially in the context of Data Mining paradigm . At the same time most widespread Quinlan algorithms ID3 and C4.5, as we show in the paper, are not the best. It is therefore possible to see the successful attempts of creation another heuristic splitting criteria for the algorithms of synthesis of decision trees. Comparative definition of different splitting criteria used for the synthesis of binary decision trees is the purpose of the paper.
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It is consider a nonlinear integro-differential equation with nonlinear hyperbolic operator of the higher order with initial value conditions. It is proposed in this paper a technique based on the characteristics method. This technique allows, moving to a new variable, provide a partial differential equation as an ordinary differential equation describing the change of unknown function along the characteristics. The study of the Cauchy problem reduces to the study of nonlinear Volterra integral equation.
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It is found asymptotical average computational complexity of local algorithm for solving block-tree discrete optimization problems with additional constraints of univariate multiple choice in more general case.
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Semi-Markov model of operation of a single-server queue system with losses and unreliable server has been built. All the random values appearing in the problem definition are supposed to have general distribution functions. An explicit form of system stationary characteristics has been defined.
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In this paper the properties of optimal sets of initial conditions in the problem of practical stability of discrete set systems are considered. In the case of linear dynamic components Minkowski function, inverse Minkowski function, and support function of these sets are obtained.
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A queueing system of type M/M/1 with customers impatience is considered. The system as a whole suffers occasionally a disastrous breakdown, upon which all present customers are cleared from the system and lost. A repair process then starts immediately. The equilibrium probabilities of the system, expected number of customers in the system, proportion of customers served, mean sojourn time of a served customer are obtained in the article.
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Isomorphisms between the set of permutations without repetition and the set of graphs are introduced in this article. The operation of replacing graph vertices by a seeding agent for the graph, which corresponding to the permutations, is defined. This operation is defined in terms of permutations and substitutions too.
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The installation and configuration of the educational and methodical web-sites using by content management system Drupal are described. The basic elements of structure are viewed. The websites which are created by author are represented.
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Systems of linear integral equations are studied in spaces of continuous and continuously differentiable on the square of vector functions.
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In the middle of the last century, the American mathematician and statistician Professor of the University of Michigan Leonard Savage (1917- 1971) and the famous Swiss economist, Professor of the University of Zurich Jurg Niehans (1919–2007) independently proposed an approach to the choice of the solution in the one-criterion problem under uncertainty (OPU), called the principle of minimax regret (according to Niehans–Savage). This principle, along with the Wald’s principle of guaranteed result (maximin), plays a crucial role in making a guaranteed decision in OPU.
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The paper formalizes a new model of solution-making under the conditions of uncontrolled (uncertain) factors in the form of a hierarchical game.
The problem of solution-making under uncertainty in the form of a hierarchical game with nature is considered
$$\Gamma = \left \langle U,\left \{ Y\left [ u \right ] | u \in U \right \}, f_{0} \left ( u,y\left ( u \right ) \right ) \right \rangle.$$