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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,315 records · Page 73
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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↗
DOE OSTI2015

On the analogues of Szegő's theorem for ergodic operators

Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Extension of transformation groups of compact solvmanifolds

We indicate a way to extend connected simply connected soluble Lie groups acting transitively and locally effectively on a given compact solvmanifold. In 1973, Auslander posed the problem of describing all groups of this kind. The results obtained here lead to the conclusion that it is unlikely that this problem has an exhaustive solution. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics

A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On the exponent of G-spaces and isovariant extensors

The equivariant version of the Curtis-Schori-West theorem is investigated. It is proved that for a nondegenerate Peano G-continuum X with an action of the compact abelian Lie group G, the exponent expX is equimorphic to the maximal equivariant Hilbert cube if and only if the free part X{sub free} is dense in X. We also show that the latter is sufficient for the equimorphy of expX and Q in the case of an action of an arbitrary compact Lie group G. The key to the proof of these results lies in the theory of the universal G-space (in the sense of Palais). Bibliography: 28 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Topological classification of the Goryachev integrable case in rigid body dynamics

A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in other words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Approximation of functions and their conjugates in variable Lebesgue spaces

One-sided Steklov means are used to introduce moduli of continuity of natural order in variable L{sub 2π}{sup p(⋅)}-spaces. A direct theorem of Jackson- Stechkin type and an inverse theorem of Salem-Stechkin type are given. Similar results are obtained for the conjugate functions. Bibliography: 24 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Proper central and core polynomials of relatively free associative algebras with identity of Lie nilpotency of degrees 5 and 6

We study the centre of a relatively free associative algebra F{sup (n)} with the identity [x{sub 1},…,x{sub n}]=0 of Lie nilpotency of degree n=5,6 over a field of characteristic 0. It is proved that the core Z{sup ∗}(F{sup (5)}) of the algebra F{sup (5)} (the sum of all ideals of F{sup (5)} contained in its centre) is generated as a T-ideal by the weak Hall polynomial [[x,y]{sup 2},y]. It is also proved that every proper central polynomial of F{sup (5)} is contained in the sum of Z{sup ∗}(F{sup (5)}) and the T-space generated by [[x,y]{sup 2},z] and the commutator [x{sub 1},…,x{sub 4}] of degree 4. This implies that the centre of F{sup (5)} is contained in the T-ideal generated by the commutator of degree 4. Similar results are obtained for F{sup (6)}; in particular, it is proved that the core Z{sup ∗}(F{sup (6)}) is generated as a T-ideal by the commutator of degree 5. Bibliography: 15 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Quantization of the Sobolev space of half-differentiable functions

A quantization of the Sobolev space V=H{sub 0}{sup 1/2}(S{sup 1},R) of half- differentiable functions on the circle, which is closely connected with string theory, is constructed. The group QS(S{sup 1}) of quasisymmetric circle homeomorphisms acts on V by reparametrizations, but this action is not smooth. Nevertheless, a quantum infinitesimal action of QS(S{sup 1}) on V can be defined, which enables one to construct a quantum algebra of observables which is associated with the system (V,QS(S{sup 1})). Bibliography: 7 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On volumes of classical supermanifolds

We consider the volumes of classical supermanifolds (such as the supersphere, complex projective superspace, Stiefel and Grassmann supermanifolds) with respect to natural metrics or symplectic structures. We show that the formulae for the volumes of these supermanifolds can be obtained from the formulae for the volumes of the corresponding ordinary manifolds (under some universal normalization of the volume) by analytic continuation with respect to parameters. The volumes of nontrivial supermanifolds may be identically equal to zero. In the 1970s Berezin showed that the total Haar measure of the unitary supergroup U(n|m) vanishes except in the cases m=0 and n=0, when the supergroup is the ordinary unitary group U(n) or U(m). Some time ago Witten conjectured that the Liouville volume of a compact even symplectic supermanifold is always equal to zero (except for ordinary manifolds). We give counterexamples to this conjecture, present a simple explanation of Berezin's theorem, and generalize this theorem to the Stiefel supermanifold V{sub r|s}(C{sup n|m}). We mention a connection with recent work of Mkrtchyan and Veselov on universal formulae in Lie algebra theory. Bibliography: 32 titles. (paper)

97 MATHEMATICS AND COMPUTING↗