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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 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Optimal Control of the Rigid Inclusion Size in the Problem of Equilibrium of Inhomogeneous Timoshenko Type Plates Containing Cracks

We consider the equilibrium problem for plates with cracks located along rigid inclusions and analyze the dependence of the solution and the derivative of the energy functional on variations of the inclusion size. We establish the solvability of the optimal control problem, where the quality functional is given by the derivative of the energy functional, whereas the control parameter correspond to the inclusion size. A similar analysis is performed for the equilibrium problems for inhomogeneous plates with rigid delaminated inclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems

We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ{sup 2}) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ{sup 2}; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method of mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Filtration of stationary Gaussian statistical experiments

The filtration of stationary Gaussian statistical experiments is determined by a solution of the equation of optimum filtration, which is characterized by the two-dimensional matrix of covariances. The parameters of a filtered signal are set by empiric covariances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Estimates in the Problem of Ideals in the Algebra H{sup ∞}

By using the fixed-point approach due to D. Rutsky, the problem of ideals in H{sup ∞} is solved for “data sequences” in H{sup ∞}(l{sup 1}) (instead of H{sup ∞}(l{sup 2}) in the traditional setting). Bibliography: 7 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A{sub 1}-Regularity and Boundedness of Riesz Transforms in Banach Lattices of Measurable Functions

Let X be a Banach lattice of measurable functions on ℝ{sup n} × Ω having the Fatou property. We show that the boundedness of all Riesz transforms R{sub j} in X is equivalent to the boundedness of the Hardy–Littlewood maximal operator M in both X and X′, and thus to the boundedness of all Calderón–Zygmund operators in X. We also prove a result for the case of operators between lattices: If Y ⊃ X is a Banach lattice with the Fatou property such that the maximal operator is bounded in Y ′, then the boundedness of all Riesz transforms from X to Y is equivalent to the boundedness of the maximal operator from X to Y , and thus to the boundedness of all Calderón–Zygmund operators from X to Y .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Sufficient Condition for Consistency of Infinite Systems

Based on the theory of double series, we obtain a sufficient condition for the existence of strictly partial solutions to infinite systems of linear algebraic equations. We prove series expansion theorems for infinite determinants of Gaussian infinite matrices. Examples of application of the proposed condition are given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Groups with Almost Regular and Almost Perfect Involutions

We establish the solubility of a group with Sylow 2-subgroup of the least order in the centralizer of an almost regular involution. We also study the structure of a group G with an almost perfect and almost regular involution a.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Prym Differentials on Variable Tori

We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays

We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These conditions have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Cliffed Cape Does Not Trap Water Waves in the Sea of Constant Depth

The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater than π, whereas the water layer lying under the free surface is of constant depth. Under these assumptions it is shown that there are no trapped mode solutions of the problem for all values of a non-dimensional spectral parameter; in other words, no point eigenvalues are embedded in the continuous spectrum of the problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components

A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Systems with Parameters, or Efficiently Solving Systems of Polynomial Equations: 33 Years Later. I

Consider a system of polynomial equations with parametric coefficients over an arbitrary ground field. We show that the variety of parameters can be represented as a union of strata. For values of parameters from each stratum, the solutions of the system are given by algebraic formulas depending only on this stratum. Each stratum is a quasiprojective algebraic variety with degree bounded from above by a subexponential function in the size of the input data. Also, the number of strata is subexponential in the size of the input data. Thus, here we avoid double exponential upper bounds on the degrees and solve a long-standing problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Regularity of a Boundary Point for the p(x)-Laplacian

We study the behavior of solutions to the Dirichlet problem for the p(x)-Laplacian with a continuous boundary function. We prove the existence of a weak solution under the assumption that p is separated from 1 and ∞. We present a necessary and sufficient Wiener type condition for regularity of a boundary point provided that the exponent p has the logarithmic modulus of continuity at this point.

97 MATHEMATICS AND COMPUTING↗