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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 1,801 records · Page 100
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information

A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Some functional limit theorems for compound Cox processes

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Mathematical modelling of the beam under axial compression force applied at any point – the buckling problem

The study is devoted to stability of simply supported beam under axial compression. The beam is subjected to an axial load located at any point along the axis of the beam. The buckling problem has been desribed and solved mathematically. Critical loads have been calculated. In the particular case, the Euler’s buckling load is obtained. Explicit solutions are given. The values of critical loads are collected in tables and shown in figure. The relation between the point of the load application and the critical load is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On mixing of Markov measures associated with b−bistochastic QSOs

New majorization is in advantage as compared to the classical one since it can be defined as a partial order on sequences. We call it as b−order. Further, the defined order is used to establish a bistochasticity of nonlinear operators in which, in this study is restricted to the simplest case of nonlinear operators i.e quadratic operators. The discussions in this paper are based on bistochasticity of Quadratic Stochastic Operators (QSO) with respect to the b−order. In short, such operators are called b−bistochastic QSO. The main objectives in this paper are to show the construction of non-homogeneous Markov measures associated with QSO and to show the defined measures associated with the classes of b−bistochastic QSOs meet the mixing property.

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

Several versions of the compensated compactness principle

The convergence of the product of a solenoidal vector w{sub {epsilon}} and a gradient {nabla}u{sub {epsilon}} in L{sup 1}({Omega}) (where {Omega} is a region in R{sup d}) is investigated in the case when the factors converge weakly in the spaces L{sup {gamma}({Omega})}{sup d} and L{sup {alpha}({Omega})}{sup d}, respectively, with 1/{gamma}+1/{alpha}>1, which means that the main assumption of the classical div-curl lemma fails. Nevertheless, the same convergence (in the sense of distributions in {Omega}) as in the framework of the div-curl lemma, survives under certain additional assumptions. The new versions of the compensated compactness principle proved in the paper can be used in homogenization and in the theory of G-convergence of monotone operators with non-standard coercivity and growth properties, for instance, some degenerate operators. Bibliography: 20 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

An adelic construction of Chern classes

We give a formula expressing the second Chern class c{sub 2}(E) in terms of trivializations of a rank two vector bundle E at scheme points of a surface X over a field. To do this, starting with these trivializations, we construct a cocycle in the adelic complex associated with the sheaf K{sub 2}(O{sub X}). Furthermore we prove that the Severi formula for the second Chern class is obtained as a special case of the formula constructed in this work. Bibliography: 10 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Equations of G-minimal conic bundles

We develop a method for obtaining equations for G-minimal conic bundles with an arbitrary number of singular fibres. When the number of singular fibres is equal to 4, 6, or 7, a detailed classification is given, which includes obtaining the equations for minimal conic bundles (S,G) and an explicit indication of the action of the group G on the Picard group Pic(S) and on the surface S itself. Bibliography: 19 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia integrable system

The paper is devoted to a topological analysis of the Kovalevskaya-Yehia integrable case in rigid body dynamics. It is proved that the integral has the Bott property on isoenergy surfaces of the system; the topology of the Liouville foliation in a neighbourhood of degenerate 1-dimensional orbits and equilibria (points of rank 0) is also described. In particular, marked loop molecules are constructed for degenerate 1-dimensional orbits, and a representation in the form of an almost direct product is found for nondegenerate singularities of rank 0. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Approximation of periodic functions in the classes H{sub q}{sup {Omega}} by linear methods

The following result is proved: if approximations in the norm of L{sub {infinity}} (of H{sub 1}) of functions in the classes H{sub {infinity}}{sup {Omega}} (in H{sub 1}{sup {Omega}}, respectively) by some linear operators have the same order of magnitude as the best approximations, then the set of norms of these operators is unbounded. Also Bernstein's and the Jackson-Nikol'skii inequalities are proved for trigonometric polynomials with spectra in the sets Q(N) (in {Gamma}(N,{Omega})). Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Representations of S{sub {infinity}} admissible with respect to Young subgroups

Let N be the set of positive integers and S{sub {infinity}} the set of finite permutations of N. For a partition {Pi} of the set N into infinite parts A{sub 1},A{sub 2},... we denote by S{sub {Pi}} the subgroup of S{sub {infinity}} whose elements leave invariant each of the sets A{sub j}. We set S{sub {infinity}}{sup (N)}={l_brace}s element of S{sub {infinity}:} s(i)=i for any i=1,2,...,N{r_brace}. A factor representation T of the group S{sub {infinity}} is said to be {Pi}-admissible if for some N it contains a nontrivial identity subrepresentation of the subgroup S{sub {Pi}} intersection S{sub {infinity}}{sup (N)}. In the paper, we obtain a classification of the {Pi}-admissible factor representations of S{sub {infinity}}. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Bifurcation sets in the Kovalevskaya-Yehia problem

The two-parameter family of bifurcation diagrams {Sigma} of the moment map is investigated in the integrable Kovalevskaya-Yehia case for the motion of a rigid body. A method is developed which is useful for calculating the bifurcation set {Theta} in the parameter space which corresponds to bifurcations of diagrams in {Sigma} and for classifying these bifurcations. The properties of the sets {Sigma} and {Theta} are thoroughly investigated, and details of the modifications the bifurcation diagrams undergo as the value of the parameter crosses {Theta} are described. Illustrations which explain the structure of the different types of diagram and their interrelations are given. Bibliography: 22 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

The Cauchy problem for a quasilinear parabolic equation with gradient absorption

The qualitative properties of solutions to the Cauchy problem for a degenerate parabolic equation containing a nonlinear operator of Baouendi-Grushin type and with gradient absorption whose density depends on time, as well as the space variables, are investigated. Bounds for the diameter of the support of the solution which are sharp with respect to time are obtained, together with its maximum. A condition which determines whether or not the phenomenon of decay to zero of the total mass of the solution occurs is discovered. Bibliography: 35 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Radon transform on a space over a residue class ring

The functions on a space of dimension N over the residue class ring Z{sub n} modulo n that are invariant with respect to the group GL(N,Z{sub n}) form a commutative convolution algebra. We describe the structure of this algebra and find the eigenvectors and eigenvalues of the operators of multiplication by elements of this algebra. The results thus obtained are applied to solve the inverse problem for the hyperplane Radon transform on Z{sup N}{sub n}. Bibliography: 2 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary

The problem of stabilizing a solution of the 2D Navier-Stokes system defined in the exterior of a bounded domain with smooth boundary is investigated. For a given initial velocity field a control on the boundary of the domain must be constructed such that the solution stabilizes to a prescribed vortex solution or trivial solution at the rate of 1/t{sup k}. On the way, related questions are investigated, concerning the behaviour of the spectrum of an operator under a relatively compact perturbation and the existence of attracting invariant manifolds. Bibliography: 21 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

C*-algebras associated with reversible extensions of logistic maps

The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle. Bibliography: 34 titles.

97 MATHEMATICS AND COMPUTING↗

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