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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 1,171 records · Page 65
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DOE OSTI2018

Stochastic differential equation in a random environment

Solutions of the Itô stochastic differential equation in a random environment are considered. The random environment is formed by the generalized telegraph process. It is proved that the initial problem is equivalent to a system of two stochastic differential equations with nonrandom coefficients. The first equation is the Itô equation, and the initial process is its solution. The second equation is an equation with Poisson process, and its solution is a generalized telegraph process. The theorems of existence and uniqueness of strong and weak solutions are proved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Problem of Axisymmetric Torsion of a Multilayer Plate with Elastic Links between the Layers

By using the method of compliance functions and the Hankel transformation of the first order, we propose a procedure for the solution of the problem of torsion of a multilayer plate with elastic links between the layers. Two auxiliary functions connected with the transforms of stresses and displacements at the points of the top boundary of the layer are introduced for each layer. The recurrence relations for the auxiliary functions and the compliance functions of neighboring layers of the plate are constructed. For a two-layer plate, we analyze the influence of the coefficients of elastic links and the geometric and mechanical parameters of layers on the distribution of stresses at points of the common boundary of the layers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Regularity of Maximum Distance Minimizers

We study properties of sets having the minimum length (one-dimensional Hausdorff measure) in the class of closed connected sets Σ ⊂ ℝ{sup 2} satisfying the inequality max{sub yϵM} dist (y, Σ) ≤ r for a given compact set M ⊂ ℝ{sup 2} and given r > 0. Such sets play the role of the shortest possible pipelines arriving at a distance at most r to every point of M where M is the set of customers of the pipeline.In this paper, it is announced that every maximum distance minimizer is a union of finitely many curves having one-sided tangent lines at every point. This shows that a maximum distance minimizer is isotopic to a finite Steiner tree even for a “bad” compact set M, which distinguishes it from a solution of the Steiner problem (an example of a Steiner tree with infinitely many branching points can be found in a paper by Paolini, Stepanov, and Teplitskaya). Moreover, the angle between these lines at each point of a maximum distance minimizer is at least 2π/3. Also, we classify the behavior of a minimizer Σ in a neighborhood of any point of Σ. In fact, all the results are proved for a more general class of local minimizers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Extraction of Pairs of Harmonics from Trigonometric Polynomials by Phase-Amplitude Operators

We propose a method for extracting the sums of two harmonics from trigonometric polynomials T{sub n}(t) by the method of amplitude-phase transformations. Such transformations send polynomials T{sub n}(t) to similar polynomials by two simplest operations: multiplication by a real constant X and shift by a real phase λ, i.e., T{sub n}(t) → X ・ T{sub n}(t − λ). The harmonics are extracted by adding similar polynomials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Partial Orders Based on Inverses Along Elements

The paper introduces and investigates partial orders that are finer than the minus partial order and are based on inverses along an element and other specific outer inverses. It turns out that in this way a number of classical partial orders can be equivalently defined.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines

The purpose of this paper is to construct new types of wavelets for minimal splines on an irregular grid. The approach applied to construct spline-wavelet decompositions uses approximation relations as an initial structure for constructing the spaces of minimal splines. The advantages of this approach are the possibilities of using irregular grids and sufficiently arbitrary nonpolynomial spline-wavelets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Elliptic G-Operators on Manifolds with Isolated Singularities

In the present work we study elliptic operators on manifolds with singularities in the situation where the manifold is endowed with an action of a discrete group G. As usual in elliptic theory, the Fredholm property of an operator is governed by the properties of its principal symbol. We show that the principal symbol in our situation is a pair consisting of the symbol on the main stratum (interior symbol) and the symbol at the conical point (conormal symbol). The Fredholm property of elliptic elements is obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Factorization of generalized γ-generating matrices

The class of γ-generating matrices and its subclasses of regular and singular γ-generating matrices were introduced by D. Z. Arov in [8], where it was shown that every γ-generating matrix admits an essentially unique regular–singular factorization. The class of generalized γ-generating matrices was introduced in [14, 20]. In the present paper, subclasses of singular and regular generalized –generating matrices are introduced and studied. As the main result, a theorem of existence of the regular–singular factorization for a rational generalized γ-generating matrix is proved.

97 MATHEMATICS AND COMPUTING↗