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At least 1,207 records · Page 67
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DOE OSTI2016

Study of idempotents in cyclic group rings over F{sub 2}

The existence of an idempotent generator for group codes or group ring codes in F{sub q}G plays a very important role in determining the minimal distance of the respective code. Some necessary and sufficient conditions for a group ring element to be an idempotent in F{sub 2}C{sub n} are investigated in this paper. The main result in this paper is the affirmation of the existence of finitely many basis idempotents which gives a full identification of all idempotents in every binary cyclic group ring F{sub 2}C{sub n}. All the basis idempotents in F{sub 2}C{sub n} are able to be found by partitioning the largest idempotent’s support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

On a problem of reconstruction of a discontinuous function by its Radon transform

A problem of reconstruction of a discontinuous function by its Radon transform is considered. One of the approaches to the numerical solution for the problem consists in the next sequential steps: a visualization of a set of breaking points; an identification of this set; a determination of jump values; an elimination of discontinuities. We consider three of listed problems except the problem of jump values. The problems are investigated by mathematical modeling using numerical experiments. The results of simulation are satisfactory and allow to hope for the further development of the approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Granular crystals: Nonlinear dynamics meets materials engineering

In this article, the freedom to choose the size, stiffness, and spatial distribution of macroscopic particles in a lattice makes granular crystals easily tailored building blocks for shock-absorbing materials, sound-focusing devices, acoustic switches, and other exotica.

36 MATERIALS SCIENCE↗
DOE OSTI2013

On the structure of self-affine convex bodies

We study the structure of convex bodies in R{sup d} that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for d = 2 by Richter in 2011. In the present paper we disprove the conjecture for all d≥3 and derive a detailed description of self-affine bodies in R{sup 3}. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Infinitesimal and global rigidity and inflexibility of surfaces of revolution with flattening at the poles

The subject of this article is one of the most important questions of classical geometry: the theory of bendings and infinitesimal bendings of surfaces. These questions are studied for surfaces of revolution and, unlike previous well-known works, we make only minimal smoothness assumptions (the class C{sup 1}) in the initial part of our study. In this class we prove local existence and uniqueness theorems for infinitesimal bendings. We then consider the analytic class and establish simple criteria for rigidity and inflexibility of compact surfaces. These criteria depend on the values of certain integer characteristics related to the order of flattening of the surface at its poles. We also show that in the nonanalytic situation there exist nonrigid surfaces with any given order of flattening at the poles. Bibliography: 22 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

On large deviations for ensembles of distributions

The paper is concerned with the large deviations problem in the Freidlin-Wentzell formulation without the assumption of the uniqueness of the solution to the equation involving white noise. In other words, it is assumed that for each ε>0 the nonempty set P{sub ε} of weak solutions is not necessarily a singleton. Analogues of a number of concepts in the theory of large deviations are introduced for the set (P{sub ε}, ε>0), hereafter referred to as an ensemble of distributions. The ensembles of weak solutions of an n-dimensional stochastic Navier-Stokes system and stochastic wave equation with power-law nonlinearity are shown to be uniformly exponentially tight. An idempotent Wiener process in a Hilbert space and idempotent partial differential equations are defined. The accumulation points in the sense of large deviations of the ensembles in question are shown to be weak solutions of the corresponding idempotent equations. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Systems of elements preserving measure on varieties of groups

It is proved that for any l, 1≤l≤r, a system of elements (v{sub 1},…,v{sub l}) of a free metabelian group S of rank r≥2 is primitive if and only if it preserves measure on the variety of metabelian groups A{sup 2}. From this we obtain the result that a system of elements (v{sub 1},…,v{sub l}) is primitive in the group S if and only if it is primitive in its profinite completion S-hat . Furthermore, it is proved that there exist a variety M and a nonprimitive element v∈F{sub r}(M) such that v preserves measure on M. Bibliography: 13 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials

The paper concerns the approximation properties of the Bernstein-Stechkin summability method for trigonometric Fourier series. The Jackson-Stechkin theorem is refined. Moreover, for any continuous periodic function not only is the exact upper estimate for approximation found, a lower estimate of the same order is also put forward. To do this special moduli of smoothness and the K-functional are introduced. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group

The aim of this paper is to prove ergodic decomposition theorems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for σ-finite invariant measures. For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by the initial invariant measure. Bibliography: 21 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Rings whose p-ranks do not exceed 1

We consider associative torsion-free rings of finite rank whose p-ranks do not exceed 1. For these rings, certain analogues of Wedderburn's theorem on finite-dimensional algebras are found. Bibliography: 11 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A universal measure for a pencil of conics and the Great Poncelet Theorem

Borel measures on conics which are invariant under the Poncelet map are investigated. For a pencil of conics the existence of a universal measure, which is invariant with respect to each conic in the pencil, is proved. Using this measure a new proof of the Great Poncelet Theorem is given. A full description of invariant Borel measures is also presented. Bibliography: 10 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

The endotopism semigroups of an equivalence relation

In this work we investigate six types of endotopism semigroups for a given equivalence relation. Necessary and sufficient conditions for the existence of all such endotopisms are presented. Conditions for the regularity and coregularity of each of the endotopism semigroups of a given type are established. The notion of the endotype of a binary relation with respect to its endotopisms is introduced and the endotype of an arbitrary equivalence relation is calculated. Bibliography: 26 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Isometric deformations of planar quadrilaterals with constant index

We consider isometric deformations (motions) of polygons (so-called carpenter's rule problem) in the case of self-intersecting polygons with the additional condition that the index of the polygon is preserved by the motion. We provide general information about isometric deformations of planar polygons and give a complete solution of the carpenter's problem for quadrilaterals. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

On the cylindricity of submanifolds containing a line in Minkowski space

We consider Finsler submanifolds in Minkowski spaces, and in particular, in Randers spaces. We give generalizations of the Toponogov and Cheeger-Gromoll theorems to the case of Randers spaces. Sufficient conditions are obtained for complete Finsler submanifolds in Minkowski spaces to be cylindrical. We also find conditions under which the convexity of a hypersurface in a Randers space implies that the flag curvature is positive. Bibliography: 17 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Polynomial solutions of the Monge-Ampère equation

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Martingale Rosenthal inequalities in symmetric spaces

We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.

97 MATHEMATICS AND COMPUTING↗