The paper is dedicated to generic sets characterization in autonomous terms. In particular, it is shown
that a language $L$ is $t(n)$-generic if and only if there it no nite or innite autonomous automation $A_{L}$
generating the prefix $L|x$ of the characteristic function of the language $L$ in the $(2^n −1)t(2^n −1)$ time. By
using this result it is proved: if the language $L$ is partially recursively enumerable and the time complexity
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The Steiner problem for graph without cycles is considered in the paper. The algebraic approach is
used for the problem investigation and solution. The operations under simple chains sets are introduced
and the properties of this operations are considered. The notions of completeness, base, canonic base for
simple chains sets are defined. It is offered a simple algorithm for problem solution which uses previously
defined base chains. It is shown the polynomial complexity of the problem.
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In opinion of luminaries in mathematical game theory the equilibrium asacceptable solution of differential game is characterized by the property of stability: the deviation from it of individual player cannot increase the payoff of deviated one. The solution proposed in [22], [23] by the 25-years old post-graduate of Princeton university John Forbes Nash (Jr) and later on called Nash equilibrium (NE) completely responds to this condition. NE certainly gained «the reigning position» in economics, sociology, military sciences.
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The role of the Bernstein inequality in various problems of approximation theory in problems of differential equations well known books from MS Nikolsky [1], NI Bari [2] (p. 895), Sigmund [3] (p. 41), and others. Bernstein inequality in the simplest case, it follows from the Riesz interpolation
$T'_{n}(t) = \frac{1}{4\pi}\sum\limits_{k=1}^{2n}(−1)^{k+1} \frac{1}{sin^{2} \frac{θ_{k}}{2}}T_{n}(t + θ_{k}), θ_{k} =\frac{2k − 1}{2n}\pi$,
for trigonometric polynomials
$T_{n}(t) = \frac{a_{0}}{2}+\sum\limits^{n}_{k=1}(a_{k} sin kt + b_{k} cos kt)$.
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The efficient numerical method for solving the modified Orr - Sommerfeld problem has been elaborated. The govering equation defines the operator pencil of polynomial type with spectral parameter "$c$ " entering the equation and boundary condition. This equation describes long-wave stable and unstable perturbations of geostrophic currents with linear vertical shear. The model includes vertical density diffusion; it is used to study generation of large scale intrusions in the Arctic Ocean.
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In the paper [1], for the solution of Boolean equations of the form $F\left ( x_{1},x_{2},...,x_{k_{0}} \right )=1$ the method for allocation of variables was offered. This work aims at improving the efficiency of this method due to a decrease of the maximum volume of the intermediate forms which are obtained in the process of the variables selection.
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Calculation of special type numerical series generated by 4-th order recurrent sequences is considered in this article. All sequences are satisfying of equation $v_{n+2}=av_{n}+bv_{n-2}$, where $a>0$, $b\in \mathbb{R}$, $a^{2}-4b>0$. Initial conditions are connecting in some cases.
Let $\left \{ v_{n} \right \}_{n\geq 1}$ is indicated sequence. One is satisfying equalities:
$v_{2k+1}^{2}-v_{2k+3}v_{2k-1}=b^{k-1}\left ( v_{3}^{2}-v_{5}v_{1} \right )$, $v_{2k+2}^{2}-v_{2k+4}v_{2k}=b^{k-1}\left ( v_{4}^{2}-v_{6}v_{2} \right )$, $k\geq 1$.
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Throughout in this paper we assume that $A$ is a compact set in $\mathbb{R}^{n}$, $n>2$, of positive Lebesgue measure. As usual we denote by $M\left ( n \right )$ the group of Euclidean motions in $\mathbb{R}^{n}$. Under $\mathfrak{P}\left ( A,B \right )$ we mean the class of functions $L_{loc}\left ( B \right )$ such that the relation $\int _{\lambda A}f\left ( x \right )dx=0$, $\forall \lambda \in M\left ( n \right )$ is valid for any $\lambda \in M ot\left ( \overline{A} ,B\right )$.
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We study the problem of optimal investment the initial capital into two kinds of investments in order to get the most benefit. Change in share capital is described by system of two ordinary linear nonhomogeneous differential equations with the random coefficients
$\frac{\mathrm{d}x_{1} }{\mathrm{d} t}=\varepsilon _{1}\left ( t,\omega \right )x_{1}+\varepsilon _{3}\left ( t,\omega \right )$,
$\frac{\mathrm{d}x_{2} }{\mathrm{d} t}=\varepsilon _{2}\left ( t,\omega \right )x_{2}+\varepsilon _{4}\left ( t,\omega \right )$.
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The article discusses environmentally sound modifications for two popularpopulation models of Bazykin and Verhulst-Pearl for the task of describing particular and non- trivial changes in population processes. A variety of the extreme nature of the number dynamics of an invasive insect species — outbreak activity of pests is modeled. The problem of applied computational modeling of transient modes of oscillating and destructive invasions of alien pests is relevant for many cases of sporadic mass reproduction of insect pests without biological control.
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The method of verification of parallel and distributed system by Component Petry Nets is offered. The using of Component Petry Nets for the design of parallel and distributed systems considerably diminishes model sizes and abbreviates time of verification. The presented methodology is studied on the example of verification of task of five philosophers.
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The method of dilations is used in the study of the non-unitary operators. Herewith, the theory of the unitary dilations of the contractions has been full enough developed in the works of B. Szokefalvi-Nagy and Ch. Foyash. Further, the $J$-unitary dilation of an arbitrary bounded operator was constructed by Ch. Davis and A. V. Kuzhel.
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In work the general method of construction explosive a spline-interlination for rectangular element having the trapeze form for the purpose of their use for approach of explosive functions of two variables is offered, which too can have (and can and not have) ruptures of the first sort on the lines forming rectangular elements having the trapeze form. The constructed splines as a special case, explosive splines and continuous splines include. Are formulated and proved interlinational properties of such explosive designs.
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The main methods for solving optimization problems with incomplete (precedent) initial information are considered. Highlighted the problem of synthesis of optimization models with precedent initial information.
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A queueing system of type M/G/2/0 is considered. An only customer in service engages both servers. Two customers are served separately. There is a limit on service time. The equilibrium probabilities of the system are obtained in the article.
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Classification of pattern recognition problems is offered. This classification is founded on the basic properties of pattern recognition problems. It is shown, a choice of methods of decisions must be coordinated with features of classes of pattern recognition problems.
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In the present paper we consider essentially Caratheodory class of scalar functions. This class consists of the meromorphic functions $f(z)$ on the open unit disc $\mathbb{D}$ for which the kernel
$$K_f (z, \omega) = \frac{f(z) + f(\omega)^∗}{1 − z\omega^∗} , z, \omega ∈ \textbf{hol(f)}$$
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In this paper we consider the problem of identification problem for one-dimensional nonlinear stationary equation of quasi optics of determining the coeffcients in the class of squareintegrable functions, where the nonlinear part include purely imaginary coeffcient. This proved the existence and uniqueness of solution of the identifcation problem. In addition, the theorem of existence and uniqueness of solution of the corresponding direct problem is proved.
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Both in the chemical and metallurgy production there is a problem of exceeding the allowable concentration of harmful substances in the premises, shops and in the environment. If we consider cement production, we deal with dust, associated with a non-optimal operation of the dust-free ventilation system in the clinker burning department. The optimally organized ventilation system in any type of production ensures the microclimate of the production premises, corresponding to the sanitary norms and rules, which contributes to the increase of the staff’s efficiency.
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In the article, the concept of metastructural identification of a modeled system is formalized as the construction of a pair consisting of a neighborhood structure (graph) and the type of interactions between the nodes of this structure. In the language of metagraphs, two types of interactions are defined: vertex type, when the equations of the model correspond to the nodes of the structure, and the relational type, when the equations correspond to the edges of the structure. Structural identification of the modeled system, as a rule, can be divided into two stages.
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Evolution of mathematical methods of classification and regression based on building decision trees and forests allowed to apply these methods to solve more complex problems of non-classical information modeling — retrieval models selection of the best solutions from the data. In this approach, a mathematical model is not specified a priori but is synthesized automatically based on the available empirical information.
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In this paper the class of simplest not rough $\Omega$-stable flows on a sphere isconsidered. We call simplest not rough $\Omega$-stable flow an $\Omega$-stable flow with least number of fixed points, a single separatrix connecting saddle points and without limit cycles. For such flows we design the Morse energy function.
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For mining a natural language interface of the automatic control system (ACS) in the article the techniques synthesis of words Russian language is offered.
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The set of all quadratic irrationalities ($s$-discriminants) with decomposition $[q_{0},\overline{q_{1},q_{2},\ldots,q_{2},q_{1},sq_{0}}]$ $(s \ge 2$ — parameter) are described. Theory of Pell $s$-equation is constructed. The inverse problem (reconstruction of $s$-discriminant with the help from continued fraction period’s symmetric part) is solved.
Keywords: $s$-discriminants, Pell $s$-equation, partial periodic continuesfraction, quadratic irrationalities.
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We consider the following spectral problem:
$ \lambda^2u − \lambda \beta Ku − {\Delta} u = 0 (в\;\Omega), \frac{\delta u}{\delta n} + u = 0 (на\;Γ), K = K^∗ \gg 0 $ (1)
Here $\Omega \subset R^m$ is an domain with Lipschitz boundary $Γ = \delta \Omega$. The parameter $\beta > 0$ imitates the power of the internal dissipation of an energy.
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In this paper optimization of profitability functions of queueing systems is considered. It is shown that as a rule such functions are unimodal.
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This article is devoted to the generalized approach of the effective decision of problems of computing geometry which initial data are set of points in Euclidean planes. The basis of this approach is construction recursion-parallel algorithm by means of strategy «distribute and dominate». In particular, on an example of a problem of a finding of a convex environment of set of points, it is offered recursion-parallel algorithm of its decision.
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In this paper the finite element method is analyzed for nonlinear elliptic variational problem which is formally equivalent to a two-dimensional nonlinear elliptic boundary problem with mixed nonhomogeneous boundary conditions. The given problem is analyzed under the maximum angle condition and is solved in the case of a bounded domain $\Omega$ whose boundary $\delta \Omega$ consists of two circles $\Gamma_{1}$, $\Gamma_{2}$; of the same centre $S_{0}$. These circles have the radii $R_{1}$, $R_{2} = R_{1} +\varrho$, where $\varrho \ll R_{1}$.
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Obtain the sufficient conditions the converges the jumping stochastic approximation procedure in semi-Markoy media in the averaging scheme. By using the asymptotic representation the compensating operator for the three-components of Markov renewal process.
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Three concrete examples of strongly nonregular polynomial pencils of ordinary differential operators of the third order generated on $[0, 1]$ by a linear differential expression with constant coefficients, polynomially depending on spectral parameter $\lambda$, and by two-point not semisplitting boundary conditions are considered, namely:
$1)$ the pencil $L^{1}_{0}(\lambda)$ of the form
$y'''−\lambda y''+ \lambda^{2}y' − \lambda^{3}y=0$,
$y(0)+y(1)=y'(0)+iy'(1)=y''(0)−y''(1)=0$;
$2)$ the pencil $L^{2}_{0}(λ)$ of the form