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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 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2014

Existence of standard models of conic fibrations over non-algebraically-closed fields

We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

On spectral synthesis on element-wise compact Abelian groups

Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace H⊆C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ{sub y}:f(x)↦f(xy), y∈G. By definition, an invariant subspace H⊆C(G) admits strict spectral synthesis if H coincides with the closure in C(G) of the linear span of all characters of G belonging to H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace H⊆C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Definability of semifields of continuous positive functions by the lattices of their subalgebras

We consider the lattice A(U(X)) of subalgebras of a semifield U(X) of continuous positive functions on an arbitrary topological space X and its sublattice A{sub 1}(U(X)) of subalgebras with unity. The main result of the paper is the proof of the definability of any semifield U(X) both by the lattice A(U(X)) and by its sublattice A{sub 1}(U(X)). Bibliography: 12 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots

We calculate the Chern-Simons invariants of twist-knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present concrete formulae and calculations. We use the Pythagorean Theorem, which was used by Ham, Mednykh and Petrov, to relate the complex length of the longitude and the complex distance between the two axes fixed by two generators. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic twist-knot orbifolds. We also derive some interesting results. The explicit formulae of the A-polynomials of twist knots are obtained from the complex distance polynomials. Hence the edge polynomials corresponding to the edges of the Newton polygons of the A-polynomials of twist knots can be obtained. In particular, the number of boundary components of every incompressible surface corresponding to slope −4n+2 turns out to be 2. Bibliography: 39 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Complexity of virtual 3-manifolds

Virtual 3-manifolds were introduced by Matveev in 2009 as natural generalizations of classical 3-manifolds. In this paper, we introduce a notion of complexity for a virtual 3-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two 2-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic 3-manifolds with totally geodesic boundary. Bibliography: 24 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Information and Statistics in Nuclear Experiment and Theory (ISNET)

As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Tripal, a community update after 10 years of supporting open source, standards-based genetic, genomic and breeding databases

Abstract Online, open access databases for biological knowledge serve as central repositories for research communities to store, find and analyze integrated, multi-disciplinary datasets. With increasing volumes, complexity and the need to integrate genomic, transcriptomic, metabolomic, proteomic, phenomic and environmental data, community databases face tremendous challenges in ongoing maintenance, expansion and upgrades. A common infrastructure framework using community standards shared by many databases can reduce development burden, provide interoperability, ensure use of common standards and support long-term sustainability. Tripal is a mature, open source platform built to meet this need. With ongoing improvement since its first release in 2009, Tripal provides full functionality for searching, browsing, loading and curating numerous types of data and is a primary technology powering at least 31 publicly available databases spanning plants, animals and human data, primarily storing genomics, genetics and breeding data. Tripal software development is managed by a shared, inclusive governance structure including both project management and advisory teams. Here, we report on the most important and innovative aspects of Tripal after 11 years development, including integration of diverse types of biological data, successful collaborative projects across member databases, and support for implementing FAIR principles.

59 BASIC BIOLOGICAL SCIENCES↗