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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 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Explicitly Solvable Models of Redistribution of the Conflict Space

We analyze a class of explicitly solvable models for the problems of redistribution of the conflict space between two alternative opponents. The existence of equilibrium state is proved for a complex nonlinear system whose time evolution is generated by the conflict interaction between its components. Explicit formulas are obtained for the limit compromise distributions in terms of the densities of probability measures. We consider a number of specific model examples of the dynamics of redistribution of the conflict territory and formation of an equilibrium (compromise) distribution of the space. We propose an interpretation of the results for the case of social and territorial conflicts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Notes on the Codimension One Conjecture in the Operator Corona Theorem

Answering a question of S. R. Treil (2004), for every δ, 0 < δ < 1, we construct examples of contractions whose characteristic function F ∈ H{sup ∞}(ε →ε{sub ∗}) satisfies the conditions ‖F(z)x‖ ≥ δ‖x‖ and dim ε{sub ∗} ⊝ F(z)ε = 1 for every z ∈ 𝔻, x ∈ ε, but is not left invertible. In addition, we show that the condition where is the trace class of operators, which is sufficient for the left invertibility of an operatorvalued function F satisfying the estimate ‖F(z)x‖ ≥ δ‖x‖ for every z ∈ 𝔻, x ∈ ε, with some δ > 0 (Treil, 2004), is necessary for the left invertibility of an inner function F such that dim ε{sub ∗} ⊝ F(z)ε < ∞ for some z ∈ 𝔻.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative

We consider a class of quasielliptic operators in R{sup n} and establish the isomorphism property in special weighted Sobolev spaces. In more general weighted spaces, we obtain the unique solvability conditions for quasielliptic equations and prove estimates for solutions. Based on the obtained results, we study the solvability of the initial problem for equations that are not solvable with respect to the higher order derivative.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Priori Tame Estimates in Sobolev Spaces for the Plasma–Vacuum Interface Problem

We study the free boundary problem for the plasma–vacuum interface in the case where the plasma density is strictly positive up to the boundary. For the linearized problem we derive the so-called tame estimates which can be used for proving the existence of solutions to the nonlinear problem by the Nash-Moser method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

A Nonlocal Inverse Problem for the Two-Dimensional Heat-Conduction Equation

We consider an inverse problem of determination of the time-dependent leading coefficient of a two-dimensional heat-conduction equation with nonlocal overdetermination condition. The existence and uniqueness conditions are established for the classical solution of the analyzed problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Discrete Morse Theory for the Barycentric Subdivision

Let F be a discrete Morse function on a simplicial complex L. We construct a discrete Morse function Δ(F) on the barycentric subdivision Δ(L). The constructed function Δ(F) “behaves the same way” as F, i.e., has the same number of critical simplices and the same gradient path structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Operator-Norm Convergence Estimates for Elliptic Homogenization Problems on Periodic Singular Structures

For an arbitrary periodic Borel measure μ we prove order O(ε) operator-norm resolvent estimates for the solutions to scalar elliptic problems in L{sup 2}(ℝ{sup d}, dμ{sup ε}) with ε-periodic coefficients, ε > 0. Here, μ{sup ε} is the measure obtained by ε-scaling of μ. Our analysis includes the case of a measure absolutely continuous with respect to the standard Lebesgue measure, as well as the case of “singular” periodic structures (or “multistructures”), when μ is supported by lower-dimensional manifolds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Vector Bundles on P{sup 1}{sub ℤ} with Simple Jumps

Vector bundles of rank 2 on the projective line over ℤ are considered. It is assumed that such a bundle E is trivial on a generic fiber, and its restriction to any special fiber is isomorphic either to O{sup 2} or to O(−1)⊕O(1). Under these assumptions it is proved that an exact sequence of the form 0→O(−2) → E →O(2) → 0 exists.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Kräuter–Seifter Theorem on Permanent Divisibility

The paper investigates the divisibility of the permanent function of (1,−1)-matrices by different powers of 2. It is shown that the Kräuter–Seifter bound is the best possible one for generic(1,−1)-matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Generalization of the Theorem on Forming a Matroid from Parts

The following generalization of the theorem on forming a matroid from parts is proved: If a finite set is subdivided into some blocks, each of which is supplied with a matroid structure, and the ranks of every union of certain blocks are prescribed and satisfy the conditions on the rank function of a matroid, then the rank function can be extended to all the subsets of the original set in such a way that the latter becomes a matroid.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Semirings of Continuous (0,∞]-Valued Functions

The semiring C{sup ∞}(X) of all continuous functions on an arbitrary topological space X with values in the topological semiring (0,∞] is studied. General properties of semirings C{sup ∞}(X) are considered. Properties of lattices of ideals and congruences of semirings C{sup ∞}(X) over the P-spaces X, the F-spaces X, and the finite discrete spaces are proved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Application of the p-Adic Topology on ℤ to the Problem of Finding Solutions in Integers of an Implicit Linear Difference Equation

We study solutions in integers of an implicit linear inhomogeneous first order difference equation bx{sub n+1} = ax{sub n} + f{sub n}. Based on the p-adic topology on the ring of integers, we obtain a criterion for the existence of solutions and show that for a = 1 a typical (in the natural topological sense) equation has no integer solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time

We study the problem for a homogeneous partial differential equation of the second order with respect to time with given homogeneous two-point conditions in this variable and, in general, of the infinite order in the other (space) variable. It is proved that the analyzed problem possesses solely the trivial solution if the characteristic determinant is not identically equal to zero. In the case where the set of zeros of the characteristic determinant of this problem is nonempty, we propose a method for the construction of nontrivial solutions of the problem.

97 MATHEMATICS AND COMPUTING↗