The problem of stability of the zero solution of a nonlinear system of ordinary differential equations with impulse perturbation at fixed moments is considered. The system of linear approximation is supposed to be non-asymtotically stable. Sufficient conditions on the uniform asymptotic stability of the complete system are obtained.
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The paper discusses the classes of infinitely differentiable functions, the growth of derivatives are limited given the positive sequence. This sequence can behave arbitrarily, ie be a regular, but non-zero it should be the members of an infinite number. It offers a variety of regularization of these sequences, depending on the type of area in which we study classes of infinitely differentiable functions.
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In the present work, we prove the Lagrange formula for the integral equation
\begin{align}y(t)=y_{0}-iJ\int_{[a,t)}dp_{1}(s)y(s)-iJ\int_{[a,t)}dq(s)f(s),\end{align}
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Let A is dissipative densely defined operator in the space $\mathfrak{H}$ and $-i\in \rho (A)$. Let denote $R= (A+iI)^{-1}$ and consider the defect operators
\begin{align}
B = iR - iR^{*} - 2R^{*}R,\\
\widetilde{B} = iR - iR^{*} - 2RR^{*},\\
T = I - 2iR.\end{align}
A set of linear bounded operators acting from an entire Hilbert space $H_{1}$ into a Hilbert space $H_{2}$ will be denoted by $L(H_{1},H_{2}).$
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In the article the spectral decomposition of a skew-selfadjoint linear operator (including the unbounded case) acting on a quaternion Hilbert bimodule is obtained. Earlier the last results on this topic concerning in finite dimensional quaternion spaces had been obtained even in the beginning of 80's (see Viswanath K. Normal operators on quaternionic Hilbert spaces // Trans. Amer. Math. Soc. - 1971. - v. 162. - p. 337-350). We essentially develop ideas and results presented in Viswanath's work and in our earlier works.
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The study of nonlinear Noetherian matrix boundary value problems for ordinary differential equations is associated with numerous applications of such problems in the theory of nonlinear oscillations in mechanics, biology, electrical engineering, theory of management, theory of motion stability, particularly in problems associated with different cases of the parametric resonance. Research papers of Yu.A Mitropolskii, A.M. Samoilenko, N.A. Perestyuk, A.A. Boichuk, M.I. Ronto, I.G. Malkin, P.A. Proskuryakov, V.A. Yakubovich, V.M. Starzhinsky, D.I. Martynyuk, E.A.
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Lyapunov matrix equations and their generalizations — linear matrix Sylvester equation widely used in the theory of stability of motion, control theory, as well as the solution of differential Riccati and Bernoulli equations, partial differential equations and signal processing. If the structure of the general solution of the homogeneous part of the Lyapunov equation is well studied, the solution of the inhomogeneous equation Sylvester and, in particular, the Lyapunov equation is quite cumbersome.
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Let $X$ be $n$-dimensional linear space over field $\mathbb{R}$ of real numbers and let $GL(n,\mathbb{R})$ be the group of all invertible linear transformations of the space $X$. Two paths $x(t),y(t)\subset X,t\in (0,1),$ are called $G$-equivalent with respect to the action of the subgroup $G$ of the group $GL(n,\mathbb{R})$ if $g(x(t))=y(t)$ for some $g\in G$ and all $t\in (0,1)$. One of the important problems of differential geometry is finding necessary and sufficient conditions such that the paths $x(t), y(t)$ are $G$-equivalent.
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The Schauder theorem, which claims the existence of a fixed point of every mapping $f:B\rightarrow B$, where $B$ is a compact convex set in a normed space $E$ , is well known. If a convex set $B$ is closed and bounded in $E$, then the result remains valid for the case in which $f(B)$ is precompact.
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Author studies properties of the curl and gradient of divergence operators in the $\mathbf{L}_2(G)$ space, spectral decompositions, and boundary value problems for any bounded domain $G$ with smooth boundary $\Gamma$.
It turns out that the space $\mathbf{L}_2(G)$ has orthogonal subspaces $\mathbf{V}^0(G)$ and $\mathscr A_\gamma(G)$ such that the curl and gradient of divergence operators admit self-adjoint extensions.
Therefor, each of these operators has a complete system of eigenfunctions corresponding to non zero eigenvalues.
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In the article under consideration we study periodic at infinity functions from $C_{b} \left ( \mathbb{J},X \right )$, i. e. bounded continuous functions defined on an interval $\mathbb{J} = \left \{ \mathbb{R}_{+}; \mathbb{R} \right \}$ with their values in a complex Banach space $X$. Together with an ordinary subspace $C_{0} \subset C_{b}$ of functions vanishing at infinity we define a subspace $\left ( L^{1}C \right )_{0} \subset C_{b}$ of functions vanishing at infinity upon the average.
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The aim of this article is to consider some problems of the theory of orthogonally additive operators in vector lattices. Order bounded orthogonally additive operators acting between vector lattices were introduced and studied in 1990 by Maz$\acute{o}$n and Segura de Le$\acute{o}$n. Recently, a new class of orthogonally additive operators in vector lattices where the condition of order boundness of an operator is replaced with a much weaker property was investigated by the author of these notes and Ramdane.
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The paper concerns use of genetic algorithm to solve the problem of optimal selection of the subset of irredundant unconditional diagnostic tests. The presented experimental results obtained for the case of pseudorandom diagnostic tests matrices show high convergence and efficiency of the proposed approach.
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The communicative stress is considered as the pathological state which has developed as a result of disadaptation to educational process. For exploration of reasons producing of stress we used the model of decease. The questionnaire is conducted. Features space is formatted and structured. Different types of regularities are revealed. The intelligent technology of regularities revealing with use of statistical methods and test methods of recognition is offered. Results and ways of the further researches are discussed.
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The article contains the description of a new programs compression method based on the frequency characteristics of programs behavior. Also the results of the theoretical and experimental research are shown demonstrated the possibility of this method application to embedded real-time controlling systems.
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This paper is dedicated to expert-ranging methods utilization the decision-making procedures within the making of contracts for corporate clients complex servicing (by the example of insurance companies).
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This paper is dedicated to the utilization of data analysis structure-classification methods in order to estimate the enterprise functioning efficiency (by example of the passenger motor transport enterprises in the Moscow Region).
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The paper presents new results on computational complexity of the known Minimum Affine Separating Committee (MASC) combinatorial optimization problem that is closely connected with the problem of optimal learning for perceptrons. It is proved that the MASC problem remains intractable being formulated in $\mathbb{Q}$$^n$ within arbitrary $n$ > 1. Actually, it is proven that the MASC problem is intractable even if the sets A and B used in its setting being in a general position.
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For increase of a reliability of fault detection of electrical machines of high dynamics in the technique of diagnostics is offered.
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The problem of measuring group similarity of amino acid sequences is one of fundamental issues of modern bioinformatics. Existing algorithms for decision this problem (so called multiple alignment procedures) are not based on any formal problem definition and any model of evolution of proteins. In this paper we propose a new approach for measuring group similarity of proteins, which is founded on probabilistic evolutionary model of transformation of amino acid sequences.
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The method of the generalized interval estimations (GIE) developed by authors earlier is offered for using in scenario analysis of the theory of decision-making. GIE procedures to study problems with dependent parameters in the framework of the scenario approach are developed in addition to previous mathematical tools. An example of similar problems is the task of forecasting volumes of commercial developed reserves of ill-studied objects in dependence on prices for hydrocarbons.
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A framework of building a decision support system intended for functioning in a decentralized environment and supporting decentralized decision making based on the state of the current situation has developed. For situation modelling context model is used. An approach to producing a context that makes knowledge and information relevant to the current situation sharable by the resources; supplies the system to information provided by these resources; and serves as a functional tool in guiding the system users has been proposed.
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The task of interrelated features selection is considered. A lot of approaches assume that feature vector is unordered set of numerical coefficients. However in some tasks features are serial measurement along some axes, for example, counts of some kind of signal. The technique of feature selection using a priori information about one-dimensional order is suggested.
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In article the opportunity of application of methods of recognition of images for the analysis of communications between objective and subjective parameters of quality of life influencing on a socio economic situation in region is proved. The received results can be used at construction of decisive rules in tasks acceptance of the decision at the forecast of birth rate and death rate of the population. As the tool of the decision of the put task use of a method of linear directions – agreeing functions is offered.
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In article the intellectual system of recognition of prints of fingers is offered on the basis of the combined method. The hierarchical structure of the description of algorithm guarantees very high efficiency of the offered system.
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The basic conditions and directions of creation of an information society in Ukraine – features of the Ukrainian society, IT-market as well as corresponding problems and strategies are considered.
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In the paper the complex-organized data structural analysis methods and the results expert correction procedures in connection with of large-scale control systems efficiency problems are described. Algorithms of such structuring were developed on the base of range data analysis methods.
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In this paper the decision support methods within the passenger transportation strategic control problems in a large region are described (by example of passenger motor transportation in the Moscow Region). These methods were created on the
base of collective multivariate expertise technique, as well as on the base of algorithms and procedures, realizing the technique.
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Building integral (complex) indexes is considered as a problem of hierarchical ordinal classification of multiple criteria alternatives. Various ways for constructing integral (complex) indexes are compared. A new approach to ordinal classification of alternatives estimated upon many criteria with verbal scales, that uses an interactive procedure of attribute space dimension reduction, is suggested.
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The paper describes the approach to the accuracy increasing of classification rules, obtained by genetic clustering algorithm. Proposed approach uses the theory of fuzzy sets, allowing to lower the uncertainly during classification process. The approach permits to take decisions, considering the whole set of rules, activated by the experimental observation.