In this paper we consider general SAT problem as a problem of global optimization for associated functional. Without loss of generality it can be considered for 3-SAT problem too. Our aim was not local search but applying Newton's methods and Newton-like procedures for direct solution. We show so for the naive Newton method has a nontrivial kernel and there are no any kind of convergence. But, we have success on the way of modification for simple iteration method with 'inertia'.
Все статьи журнала
Журнал:
Журнал:
Two сombinatorial problems, Three-elements affine separating committee (3-ASC) and Minimal affine separating committee (MASC), which are closely connected with a training problem in the special case of perceptrons, are considered. It is proven that the former problem is NP - complete and the later is NP -hard and does not belong to Apx. Also some approximation algorithm for the MASC problem is discussed.
Журнал:
Evolution of the Edgeworth-Pareto prinсiple, whiсh is well-known in deсision making, from its naive version of the nineteen сenture to the most general axiomatiс one in terms of сhoiсe funсtion is presented.
Журнал:
In this article we investigate an easy enough algorithm for solving of a very important problem of recognition of unknown objects, which appear when we find the dependence rate between random samples of observations for the case of Gaussian random variables.
Журнал:
The language $L$ is used for specifying finite automata, and is a fragment of a first order language with monadiс prediсates. Cheсking speсification for satisfiability plays an important role in the development of reactive algorithms. Restricted syntax of this language and interpreting it over the integers make it possible to substantially improve resolution-based methods for satisfiability checking. In this paper, we present an improvement to the method based on the restriction of the type of atoms upon which the resolution is allowed.
Журнал:
It is proved that the point $\varsigma=0$ in difference of other points of continious spectrum is point of branchement of logarithmic type of the resolvent of transport operator.
Журнал:
The properties of characteristic vector families for intervals of the feature space are under investigation. The search algorithms for the closed characteristic vectors and vectors generating the maximum intervals of the specified feature space region are considered in the paper.
Журнал:
In this paper we study the identification problem of determining the complex-valued coefficient for non-stationary equation quasi optics. In this case we prove existence and uniqueness of the solution of identification problem. In addition, the necessary condition for solution of identification problem of the variational inequality type is established.
Журнал:
The mathematical model of the optimum planning of the use of monies facilities acting from investors is represented in the article, with the purpose of implementation of some great number of projects providing the receipt of income. By the decision of tasks proper to this model, there is the optimum sequence of start of the chosen projects in time, providing a maximum of income.
Журнал:
The properties of the stationary structures in a nonlinear optical resonator with lateral inversions transformer in feedback are investigated. The mathematical description of optical structures is based on the scalar parabolic equation with inversion spatial arguments and Neumann's condition on the segment. We determine the forms of stationary structures and investigate its stability as the diffusion coefficient decrease, parabolic equation, bifurcation, stationary structure, stability, center manifold.
Журнал:
We prove that the problem of classifation (up to a similarity transformation) the pair of nilpotent operators $(A, B), A^3 = B^3 = 0$ with condition of $q$-commutation $BA$ = $qAB$, where $q\in\mathbf{C}, q \ne 0,$ is "wild".
Журнал:
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.
Журнал:
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.
Журнал:
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}
Журнал:
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 $L(H_{1},H_{2}).$
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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.
Журнал:
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).
Журнал:
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).
Журнал:
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.
Журнал:
For increase of a reliability of fault detection of electrical machines of high dynamics in the technique of diagnostics is offered.