Search

This paper is devoted to solving the inverse problem of restoring the hydrometeor distribution function from radar measurements. We use the Tikhonov regularization algorithm based on the minimization of the residual functional by the conjugate gradient method. [ABSTRACT FROM AUTHOR]

Abstract. This paper deals with an extremal problem concerning hypergraph colorings. Let k be an integer. The problem is to find the value m( n) equal to the minimum number of edges in an n-uniform hypergraph not admitting two-colorings of the vertex set such that every edge of the hypergraph contains at least k vertices of each color. In this paper, we obtain upper bounds of m( n) for small k and n, the exact value of m(8), and a lower bound for m(7). [ABSTRACT FROM AUTHOR]

This paper continues another our work, which is the first of two parts where the approach to the processing of quantitative expert evaluations in the process of group decision-making under uncertainty is considered. In the second part, represented by this paper, an approach is proposed for the processing of qualitative expert evaluations in the process of group decision-making. The approach is based on the use of triangular fuzzy numbers. In group decision-making the opinions of experts are expressed by linguistic variables like very bad, not very bad, problematic, good, and so on. The technique of conversion of expert quantitative opinions to triangular fuzzy numbers is considered. A simple method of expressing expert opinions by triangular fuzzy numbers is introduced. A new approach to determining the expert degrees of importance is proposed. The proposed methodology is discussed in full detail and its algorithm is described. An illustrative example is given. [ABSTRACT FROM AUTHOR]

Let K be a nonsingular skew-symmetric matrix of even order n = 2m. For such a matrix, the paper proposes a finite algorithm for computing an m-dimensional neutral subspace, which uses arithmetic operations and quadratic radicals only. The necessity of computing neutral subspaces originates in the problem of solving quadratic matrix equations. [ABSTRACT FROM AUTHOR]

In this paper, we show that an overdetermined tropical linear system has a solution if and only if it contains a square subsystem having a stable solution that is a solution of the original system. This leads to a simple algorithm for solving tropical linear systems in time Onmn4, where m is the number of equations and n is the number of variables. For weakly overdetermined systems, this time is polynomial. [ABSTRACT FROM AUTHOR]

The paper proposes a mathematical formalism for describing artificial sense-of-touch systems. Mathematical models for obtaining, processing, and interpreting tactile information are provided. Problems of encoding and reproducing tactile information are formulated and algorithms for solving these problems are proposed. The problem of interpreting tactile information is considered, and the corresponding simple mathematical model is studied. Within the framework of this simple model, an exact solution of the interpretation problem is obtained for the case of finite deformations, and the insufficiency of the linear method (Hooke’s law) for describing problems of interpreting tactile data is shown. The presentation of mathematical models for the theory of artificial sense-of-touch systems in this paper is the first such detailed presentation in the Russian literature. These models are of interest to mathematicians, mechanicians, physicians, and engineers who construct or use artificial sense-of-touch systems. [ABSTRACT FROM AUTHOR]

In this paper, we discuss optimal control problems whose behavior is described by elliptic equations with Bitsadze-Samarski nonlocal boundary conditions. A necessary and sufficient optimality condition is given. The existence and uniqueness of a solution of the conjugate problem are proved. A numerical method of solution of an optimal problem by means of the Mathcad package is presented. [ABSTRACT FROM AUTHOR]

We consider approaches to making decisions for control problems in nonstandard situations in the absence of previous experience and incomplete knowledge of the considered problem. In such cases we usually cannot do without expert evaluations that lead to the process of group decisionmaking, and it becomes necessary to solve a problem of alternatives aggregation. It has been proposed to solve such problems by means of fuzzy sets. The material of the paper is divided into two parts. In Part 1, an approach is proposed for the processing of quantitative expert evaluations that are used in group decision-making. The approach is based on the coordination index and the similarity of finite collections of fuzzy sets and takes into account the specific character of the fuzzy aggregation operator. The approach is discussed in full detail and its algorithm is presented. An example of the application of the proposed method is given. [ABSTRACT FROM AUTHOR]

In this paper, we study optimal control problems whose behavior is described by second-order differential equations with nonlocal Bitsadze-Samarski boundary conditions. Necessary conditions of optimality are obtained in terms of the maximum principle; adjoint equations are constructed in the differential and integral form. Necessary and sufficient optimality conditions are obtained for a linear problem, a difference scheme is constructed and examined, and a numerical algorithm is proposed. [ABSTRACT FROM AUTHOR]

Study of many complex phenomena involves data sets of high dimension. This is typical for many medical and biological studies, especially in genetics and pharmacology. We treat binary response variable (showing, e.g., the state of patient's health) depending on n discrete factors (explanatory variables). To find the most significant among them is a very important problem. The aim of the paper is to establish necessary and sufficient conditions for the strong consistency of the specified estimates employing the cross-validation of the error arising in prediction algorithm for the response variable. The impact of the choice of a function is discussed as well. The obtained results provide a basis for the well-known MDR-method widely used in genetic data analysis. [ABSTRACT FROM AUTHOR]

The paper considers conditions under which rank factorizations of a two-parameter polynomial matrix can be affected with the use of unimodular matrices, as in the one-parameter case. Algorithms for computing such factorizations and a minimal basis of the null space of the corresponding matrix are presented. Also an algorithm for inverting unimodular two-parameter polynomial matrices is suggested. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

In the paper, formulas for comparing sparse matrix storage formats are derived. An iterative algorithm for solving linear systems using a sparse row format for storing prefiltered preconditioners is designed. A Modification of the sparse row format leading to 1.14-1.23 times speed up for matrices of order 1000 is suggested. It is demonstrated that as opposed to the usual storage format, the sparse row format provides for 1.5-1.6 times speed up in solving linear systems of orders 4800, 6000, and 8000. The use of the results obtained allows one to reduce both memory and time requirements in solving large-scale problems with dense matrices. Bibliography: 7 titles. [ABSTRACT FROM AUTHOR]

It is still not known whether the satisfiability problem (SAT), and hence the maximum satisdiability problem (MAX-SAT), can be solved in time poly(| F|) c for c < 2, where c is a constant, n is the number of variables, and F is the input formula. However, such bounds are known for some special cases of these problems where the clause length, the maximum number of variable occurrences, or the length of the formula is bounded. In this paper, we consider the ( n, 3)-MAX-SAT problem-the special case of MAX-SAT where each variable appears in a formula at most three times. We present a simple algorithm with running time O*(2). As a byproduct, we also obtain a polynomially sovable subclass that may be of independent interest. Bibliography: 13 titles. [ABSTRACT FROM AUTHOR]

We consider two closely related optimization problems: a problem of convex semi-infinite programming with multidimensional index set and a linear problem of semi-definite programming. In the study of these problems we apply the approach suggested in our recent paper [14] and based on the notions of immobile indices and their immobility orders. For the linear semi-definite problem, we define the subspace of immobile indices and formulate the first-order optimality conditions in terms of a basic matrix of this subspace. These conditions are explicit, do not use constraint qualifications, and have the form of a criterion. An algorithm determining a basis of the subspace of immobile indices in a finite number of steps is suggested. The optimality conditions obtained are compared with other known optimality conditions. [ABSTRACT FROM AUTHOR]

In this paper, we continue a series of previous articles and present a simple method of proving the correctness and self-adjointness of operators of the form B corresponding to some boundary value problems. We also give representations for the unique solutions of these problems. The algorithm is easy to implement via computer algebra systems. In our examples, Derive and Mathematica were used. Bibliography: 13 titles. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the properties of permutation binomials over finite fields and the possibility to use permutation binomials as encryption functions. We present an algorithm for enumeration of permutation binomials. Using this algorithm, all permutation binomials for finite fields up to order 15000 were generated. Using this data, we investigate the groups generated by the permutation binomials and discover that over some finite fields $$ {{\mathbb F}_q} $$, every bijective function on [1.. q − 1] can be represented as a composition of binomials. We study the problem of generating permutation binomials over large prime fields. We also prove that a generalization of RSA using permutation binomials is not secure. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

In this paper, we present three algorithms: the first one solves zero-dimensional parametric homogeneous polynomial systems within single exponential time in the number n of unknowns; it decomposes the parameter space into a finite number of constructible sets and computes the finite number of solutions by parametric rational representations uniformly in each constructible set. The second algorithm factirizes absolutely multivariate parametic polynomials within single exponential time in n and in the upper bound d on the degree of the factorized polynomials. The third algorithm decomposes algebraic varieties defined by parametric polynomial systems of positive dimension into absolutely irreducible components uniformly in the values of the parameters. The complexity bound for this algorithm is double exponential in n. On the other hand, the lower bound on the complexity of the problem of resolution of parametric polynomial systems is double exponential in n. Bibliography: 72 titles. [ABSTRACT FROM AUTHOR]

The authors study small vibrations of a mixture (emulsion) of two weakly viscous compressible fluids, construct a macroscopic (homogenized) model of emulsion, and establish convergence (with respect to a small parameter) of solutions of the original boundary value problem for a two-phase fluid to solutions of the corresponding homogenized problem. The paper also describes the results of qualitative analysis of the spectrum of the macroscopic acoustic equation (the dynamical Darcy's law), as well as typical spectral pictures obtained by numerical experiments. [ABSTRACT FROM AUTHOR]

The paper discusses the method of hereditary pencils for computing points of the regular and singular spectra of a general two-parameter polynomial matrix. The method allows one to reduce the spectral problems considered to eigenproblems for polynomial matrices and pencils of constant matrices. Algorithms realizing the method are suggested and justified. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

In this paper, we consider a solution of the space reorientation problem for a body by one plane rotation for the case where the number of flywheel engines can be arbitrary. The algorithm obtained for the solution of the problem defines the program of change of control influence at the entrance of flywheel engines. [ABSTRACT FROM AUTHOR]