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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 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Global attractors of complete conformal foliations

We prove that every complete conformal foliation (M,F) of codimension q{>=}3 is either Riemannian or a (Conf(S{sup q}), S{sup q})-foliation. We further prove that if (M,F) is not Riemannian, it has a global attractor which is either a nontrivial minimal set or a closed leaf or a union of two closed leaves. In this theorem we do not assume that the manifold M is compact. In particular, every proper conformal non-Riemannian foliation (M,F) has a global attractor which is either a closed leaf or a union of two closed leaves, and the space of all nonclosed leaves is a connected q-dimensional orbifold. We show that every countable group of conformal transformations of the sphere S{sup q} can be realized as the global holonomy group of a complete conformal foliation. Examples of complete conformal foliations with exceptional and exotic minimal sets as global attractors are constructed. Bibliography: 20 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

On the geometric properties of Cesaro spaces

It is proved that the Cesaro space Ces{sub p}[0,1], 1{<=}p<{infinity}, contains a complemented subspace isomorphic to l{sup q} if and only if either q=1 or q=p. A class of subspaces of this space that contain complemented copies of the space l{sup p} is distinguished. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Subexponential estimates in Shirshov's theorem on height

Suppose that F{sub 2,m} is a free 2-generated associative ring with the identity x{sup m}=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F{sub 2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x{sup d}=0 is smaller than {Psi}(d,d,l), where {Psi}(n,d,l)=2{sup 18}l(nd){sup 3log}{sub 3}{sup (nd)+13}d{sup 2}. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d{>=}n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than {Psi}(n,d,l) are either n-divisible or contain x{sup d}; a word W is n-divisible if it can be represented in the form W=W{sub 0}W{sub 1} Horizontal-Ellipsis W{sub n} so that W{sub 1},...,W{sub n} are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<{Phi}(n,l) over the set of words of degree {<=}n-1, where {Phi}(n,l)=2{sup 87}l{center_dot}n{sup 12log}{sub 3}{sup n+48}. Bibliography: 40 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Criteria for compactness in L{sup p}-spaces, p {>=} 0

The paper puts forward new compactness criteria for spaces of summable and measurable functions on a metric space with measure satisfying the doubling condition. These criteria are formulated in terms of either local smoothness inequalities or maximal operators that measure local smoothness. Bibliography: 28 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Arrangements of codimension-one submanifolds

We study the number f of connected components in the complement to a finite set (arrangement) of closed submanifolds of codimension 1 in a closed manifold M. In the case of arrangements of closed geodesics on an isohedral tetrahedron, we find all possible values for the number fof connected components. We prove that the set of numbers that cannot be realized by the number f of an arrangement of n {>=} 71 projective planes in the three-dimensional real projective space is contained in the similar known set of numbers that are not realizable by arrangements of n lines on the projective plane. For Riemannian surfaces M we express the number f via a regular neighbourhood of a union of immersed circles and the multiplicities of their intersection points. For m-dimensional Lobachevskii space we find the set of all possible numbers f for hyperplane arrangements. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

On Selberg formulae related to Gram's law

In the paper, we obtain a new proof of Selberg formulae related to Gram's law in the theory of the Riemann zeta function. Bibliography: 12 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

On the homotopy type of spaces of Morse functions on surfaces

Let M be a smooth closed orientable surface. Let F be the space of Morse functions on M with a fixed number of critical points of each index such that at least {chi}(M)+1 critical points are labelled by different labels (numbered). The notion of a skew cylindric-polyhedral complex is introduced, which generalizes the notion of a polyhedral complex. The skew cylindric-polyhedral complex K-tilde ('the complex of framed Morse functions') associated with the space F is defined. In the case M=S{sup 2} the polytope K-tilde is finite; its Euler characteristic {chi}(K-tilde) is calculated and the Morse inequalities for its Betti numbers {beta}{sub j}(K-tilde) are obtained. The relation between the homotopy types of the polytope K-tilde and the space F of Morse functions equipped with the C{sup {infinity}}-topology is indicated. Bibliography: 51 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Topology of actions and homogeneous spaces

Topologization of a group of homeomorphisms and its action provide additional possibilities for studying the topological space, the group of homeomorphisms, and their interconnections. The subject of the paper is the use of the property of d-openness of an action (introduced by Ancel under the name of weak micro-transitivity) in the study of spaces with various forms of homogeneity. It is proved that a d-open action of a Cech-complete group is open. A characterization of Polish SLH spaces using d-openness is given, and it is established that any separable metrizable SLH space has an SLH completion that is a Polish space. Furthermore, the completion is realized in coordination with the completion of the acting group with respect to the two-sided uniformity. A sufficient condition is given for extension of a d-open action to the completion of the space with respect to the maximal equiuniformity with preservation of d-openness. A result of van Mill is generalized, namely, it is proved that any homogeneous CDH metrizable compactum is the only G-compactification of the space of rational numbers for the action of some Polish group. Bibliography: 39 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Hyperbolic tori in Hamiltonian systems with slowly varying parameter

This paper looks at a Hamiltonian system which depends periodically on a parameter. For each value of the parameter the system is assumed to have a hyperbolic periodic solution. Using the methods in KAM-theory it is proved that if the Hamiltonian is perturbed so that the value of the parameter varies with constant small frequency, then the nonautonomous system will have hyperbolic 2-tori in the extended phase space. Bibliography: 12 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Littlewood polynomials and applications of them in the spectral theory of dynamical systems

In this paper we establish the existence of character sums on the real line R that are {epsilon}-flat on any given compact subset K Subset-Of R Reverse-Solidus-Operator {l_brace}0{r_brace} with respect to the metric in the space L{sup 1}(K). A consequence of this analytic result is an affirmative answer to Banach's conjecture on the existence of a dynamical system with a simple Lebesgue spectrum in the class of actions of the group R. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

On the boundary of the group of transformations leaving a measure quasi-invariant

Let A be a Lebesgue measure space. We interpret measures on A×A×R{sup ×} as 'maps' from A to A, which 'spread' A along itself; their Radon-Nikodym derivatives are also spread. We discuss the basic properties of the semigroup of such maps and the action of this semigroup on the spaces L{sup p}(A). Bibliography: 26 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

On the existence of a stationary measure for the stochastic system of the Lorenz model describing a baroclinic atmosphere

The paper is concerned with a nonlinear system of partial differential equations with parameters. This system describes the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a rotating two-dimensional sphere. The right-hand side of the system is perturbed by white noise. Sufficient conditions on the parameters and the right-hand side are obtained for the existence of a stationary measure. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system

The distribution of the zeros of the Hermite-Padé polynomials of the first kind for a pair of functions with an arbitrary even number of common branch points lying on the real axis is investigated under the assumption that this pair of functions forms a generalized complex Nikishin system. It is proved (Theorem 1) that the zeros have a limiting distribution, which coincides with the equilibrium measure of a certain compact set having the S-property in a harmonic external field. The existence problem for S-compact sets is solved in Theorem 2. The main idea of the proof of Theorem 1 consists in replacing a vector equilibrium problem in potential theory by a scalar problem with an external field and then using the general Gonchar-Rakhmanov method, which was worked out in the solution of the '1/9'-conjecture. The relation of the result obtained here to some results and conjectures due to Nuttall is discussed. Bibliography: 51 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A decomposition theorem for the space of C{sup 1}-smooth skew products with complicated dynamics of the quotient map

We use the notions of the Ω-function and functions suitable to it, to give a detailed proof of a decomposition theorem for the space of C{sup 1}-smooth skew products of interval maps whose quotient maps have complicated dynamics and satisfy the additional condition of Ω-stability with respect to the C{sup 1}-norm. In our theorem, the space of C{sup 1}-smooth skew products is decomposed into a union of four nonempty, pairwise disjoint subspaces. We give examples of maps contained in each of the four subspaces. Bibliography: 46 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Intersections of adelic groups on a surface

We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers, one can associate with it an adelic group. We show that this operation commutes with taking intersections if the surface is defined over an uncountable field, and we provide a counterexample otherwise. Bibliography: 12 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Nonmaximality of known extremal metrics on torus and Klein bottle

The El Soufi-Ilias theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator. Recently, this connection was used to provide several explicit examples of extremal metrics. We investigate the properties of these metrics and prove that none of them is maximal. Bibliography: 24 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

On small values of the Riemann zeta-function at Gram points

In this paper, we prove the existence of a large set of Gram points t{sub n} such that the values ζ(0.5+it{sub n}) are 'anomalously' close to zero. A lower bound for the negative 'discrete' moment of the Riemann zeta-function on the critical line is also given. Bibliography: 13 titles.

97 MATHEMATICS AND COMPUTING↗