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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 37 records · Page 2
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DOE OSTI2011

Nuclear Fission Investigation with Twin Ionization Chamber

The purpose of the present paper was to report the recent results, obtained in development of digital pulse processing mathematics for prompt fission neutron (PFN) investigation using twin ionization chamber (TIC) along with fast neutron time-of-flight detector (ND). Due to well known ambiguities in literature (see refs. [4, 6, 9 and 11]), concerning a pulse induction on TIC electrodes by FF ionization, we first presented detailed mathematical analysis of fission fragment (FF) signal formation on TIC anode. The analysis was done using Ramo-Shockley theorem, which gives relation between charged particle motion between TIC electrodes and so called weighting potential. Weighting potential was calculated by direct numerical solution of Laplace equation (neglecting space charge) for the TIC geometry and ionization, caused by FF. Formulae for grid inefficiency (GI) correction and digital pulse processing algorithms for PFN time-of-flight measurements and pulse shape analysis are presented and discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2011

Toward a Classical Thermodynamic Model for Retro-cognition

Retro-cognition--a human response before a randomly determined future stimulus--has always been part of our experience. Experiments over the last 80 years show a small but statistically significant effect. If this turns out to be true, then it suggests a form of macroscopic retro-causation. The 2nd Law of Thermodynamics provides an explanation for the apparent single direction of time at the macroscopic level although time is reversible at the microscopic level. In a preliminary study, I examined seven anomalous cognition (a.k.a., ESP) studies in which the entropic gradients and the entropy of their associated target systems were calculated, and the quality of the response was estimated by a rating system called the figure of merit. The combined Spearman's correlation coefficient for these variables for the seven studies was 0.211 (p = 6.4x10{sup -4}) with a 95% confidence interval for the correlation of [0.084, 0.332]; whereas, the same data for a correlation with the entropy itself was 0.028 (p = 0.36; 95% confidence interval of [-0.120-0.175]). This suggests that anomalous cognition is mediated via some kind of a sensory system in that all the normal sensory systems are more sensitive to changes than they are to inputs that are not changing. A standard relationship for the change of entropy of a binary sequence appears to provide an upper limit to anomalous cognition functioning for free response and for forced-choice Zener card guessing. This entropic relation and an apparent limit set by the entropy may provide a clue for understanding macroscopic retro-causation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2011

Existence and uniqueness of the measure of maximal entropy for the Teichmueller flow on the moduli space of Abelian differentials

The main result of the paper is the statement that the 'smooth' measure of Masur and Veech is the unique measure of maximal entropy for the Teichmueller flow on the moduli space of Abelian differentials. The proof is based on the symbolic representation of the flow in Veech's space of zippered rectangles. Bibliography: 29 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Curvature and Tachibana numbers

The aim of this paper is to define the rth Tachibana number t{sub r} of an n-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing r-forms, for r=1,2,...,n-1. We also describe properties of these numbers, by analogy with properties of the Betti numbers b{sub r} of a compact oriented Riemannian manifold. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Extremal properties of sequences of zeros of analytic functions in spaces with mixed norm

Functions whose sequences of absolute values of zeros have certain extremal properties are constructed in Bergmann spaces with powerlike weight and in more general spaces with mixed norm. These properties can be expressed in terms of subsequences with indices satisfying certain necessary and sufficient conditions. In particular, using these functions it is possible to distinguish between the zero sets of the spaces in question in some cases which have not previously been investigated. This reveals the significant role which subsequences of zeros in general play in the solution of this type of problems. Bibliography: 8 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Parabolically connected subgroups

All reductive spherical subgroups of the group SL(n) are found for which the intersections with every parabolic subgroup of SL(n) are connected. This condition guarantees that open equivariant embeddings of the corresponding homogeneous spaces into Moishezon spaces are algebraic. Bibliography: 6 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

The order of a homotopy invariant in the stable case

Let X, Y be cell complexes, let U be an Abelian group, and let f:[X,Y]{yields}U be a homotopy invariant. By definition, the invariant f has order at most r if the characteristic function of the rth Cartesian power of the graph of a continuous map a:X{yields}Y determines the value f([a]) Z-linearly. It is proved that, in the stable case (that is, when dimX<2n-1, and Y is (n-1)-connected for some natural number n), for a finite cell complex X the order of the invariant f is equal to its degree with respect to the Curtis filtration of the group [X,Y]. Bibliography: 9 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

On the structure of invariant measures for set-valued maps

Properties of measures invariant with respect to set-valued maps are studied. It is shown that an absolutely continuous invariant measure for a set-valued map need not be unique, and the set of all invariant measures need not be a Choquet simplex. The problem concerning the existence of invariant measures with respect to set-valued maps parametrized by single-valued and set-valued maps of the circle having various smoothness classes is studied. Bibliography: 13 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Framed 4-graphs: Euler tours, Gauss circuits and rotating circuits

We consider connected finite 4-valent graphs with the structure of opposite edges at each vertex (framed 4-graphs). For any of such graphs there exist Euler tours, in travelling along which at each vertex we turn from an edge to a nonopposite one (rotating circuits); and at the same time, it is not true that for any such graph there exists an Euler tour passing from an edge to the opposite one at each vertex (a Gauss circuit). The main result of the work is an explicit formula connecting the adjacency matrices of the Gauss circuit and an arbitrary Euler tour. This formula immediately gives us a criterion for the existence of a Gauss circuit on a given framed 4-graph. It turns out that the results are also valid for all symmetric matrices (not just for matrices realisable by a chord diagram). Bibliography: 24 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Direct and inverse theorems of rational approximation in the Bergman space

For positive numbers p and {mu} let A{sub p,{mu}} denote the Bergman space of analytic functions in the half-plane {Pi}:={l_brace}z element of C:Imz>0{r_brace}. For f element of A{sub p,{mu}} let R{sub n} (f){sub p,{mu}} be the best approximation by rational functions of degree at most n. Also let {alpha} element of R and {tau}>0 be numbers such that {alpha}+{mu}=1/{tau}-1/p and 1/p+{mu} not element of N. Then the main result of the paper claims that the set of functions f element of A{sub p,{mu}} such that {Sigma}{sub n=1}{sup {infinity}} 1/n (n{sup {alpha}}+{mu}R{sub n} (f){sub p,{mu}}){sup {tau}}<{infinity} is precisely the Besov space B{sub {tau}}{sup {alpha}} of analytic functions in {Pi}. Bibliography: 23 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane

The problem of a sphere rolling on a plane without twisting or slipping is considered. It is required to roll the sphere from one contact configuration to another so that the length of the curve described by the contact point is minimal. A parametrization of extremal trajectories is obtained. The asymptotics of extremal trajectories and the behaviour of the Maxwell time for the rolling of a sphere over sinusoids of small amplitude are studied; for such trajectories estimates for the so-called cut time are obtained. Bibliography: 21 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Self-affine polytopes. Applications to functional equations and matrix theory

A special kind of functional equation with compression of the argument--the affine self-similarity equation--is studied. The earlier known one-dimensional self-similarity equations are generalized to the multidimensional case of functions of several variables. A criterion for the existence and uniqueness of an L{sub p}-solution is established. Description of such equations involves classification of finite-dimensional convex self-affine compact sets. In this work properties of such objects are thoroughly analysed; in particular, a counterexample to the well-known conjecture about the structure of such bodies, which was put forward in 1991, is given. Applications of the results obtained include some facts about the convergence of products of stochastic matrices; also, criteria for the convergence of some subdivision algorithms are suggested. Bibliography: 39 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Neighbourly polytopes with few vertices

A family of neighbourly polytopes in R{sup 2d} with N=2d+4 vertices is constructed. All polytopes in the family have a planar Gale diagram of a special type, namely, with exactly d+3 black points in convex position. These Gale diagrams are parametrized by 3-trees (trees with a certain additional structure). For all polytopes in the family, the number of faces of dimension m containing a given vertex A depends only on d and m. Bibliography: 7 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Existence 'in the large' of a solution to the system of equations of large-scale ocean dynamics on a manifold

A theorem is presented proving the unique solvability 'in the large' of the system of primitive equations on an arbitrary smooth oriented Riemannian manifold in a cylindrical domain. Namely, it is shown for an arbitrary interval of time [0,T], in the 3d domain {Omega}{identical_to}{Omega}' Multiplication-Sign [-h,0], where h=const and {Omega}' is a compactly embedded subdomain of a 2-manifold M, for any viscosity coefficients {mu},{nu},{mu}{sub 1},{nu}{sub 1}>0 and initial conditions u{sub 0} element of W{sub 2}{sup 2}({Omega}), {integral}{sub -h}{sup 0}divu{sub 0} dz=0, and {rho}{sub 0} element of W{sub 2}{sup 2}({Omega}), there exists a unique generalized solution such that {partial_derivative}{sub z}u element of W{sub 2}{sup 1}(Q{sub T}), {partial_derivative}{sub z}{rho} element of W{sub 2}{sup 1}(Q{sub T}) (z is the vertical variable). Bibliography: 12 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

On the index of elliptic operators for the group of dilations

We investigate nonlocal operators associated with the operators of compression and expansion. We obtain an ellipticity condition, which implies that the problem has the Fredholm property, compute the index, and study how the index depends on the exponent of the Sobolev space in which the problem is considered. Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

The continuity of the output entropy of positive maps

Global and local continuity conditions for the output von Neumann entropy for positive maps between Banach spaces of trace-class operators in separable Hilbert spaces are obtained. Special attention is paid to completely positive maps: infinite dimensional quantum channels and operations. It is shown that as a result of some specific properties of the von Neumann entropy (as a function on the set of density operators) several results on the output entropy of positive maps can be obtained, which cannot be derived from the general properties of entropy type functions. In particular, it is proved that global continuity of the output entropy of a positive map follows from its finiteness. A characterization of positive linear maps preserving continuity of the entropy (in the following sense: continuity of the entropy on an arbitrary subset of input operators implies continuity of the output entropy on this subset) is obtained. A connection between the local continuity properties of two completely positive complementary maps is considered. Bibliography: 21 titles.

97 MATHEMATICS AND COMPUTING↗