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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 1,657 records · Page 92
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DOE OSTI2018

Double Cosets of Stabilizers of Totally Isotropic Subspaces in a Special Unitary Group. I

Let D be a division algebra with a fixed involution, and let V be the corresponding unitary space over D with T -condition (see N. Bourbaki, Algèbre). For a pair of totally isotropic subspaces u, v ≤ V, the double cosets P{sub u}γP{sub v} of their stabilizers P{sub u}, P{sub v} in Γ = SU(V ) are considered. A description of the cosets P{sub u}γP{sub v} in terms of the intersection distance d{sub in}(u, γ(v)) and the Witt index of u + γ(v) is given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Ultrasolvability of p-Extensions of an Abelian Group by a Cyclic Kernel

The paper contains a solution of A. V. Yakovlev’s problem in the embedding theory for p-extensions of odd order with a cyclic normal subgroup and an Abelian quotient group: for such nonsplit extensions there exists a realization for the quotient group as a Galois group over number fields such that the corresponding embedding problem is ultrasolvable (i.e., this embedding problem is solvable and has only fields as solutions). A solution for embedding problems of p-extensions of odd order with kernel of order p and with a quotient group that is represented by a direct product of its proper subgroups is also given – this is a generalization for p > 2 of an analogous result for p = 2 due to A. Ledet.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Ultrasolvability of Some Classes of Minimal Nonsplit p-Extensions with Cyclic Kernel for p > 2

For any nonsplit p > 2-extension of finite groups with a cyclic kernel and a quotient group with two generators all the accompanying extensions of which split, there exists a realization of the quotient group as a Galois group of number fields such that the corresponding embedding problem is ultrasolvable (i.e., this embedding problem is solvable and has only fields as solutions).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Depth of k-Valued Logic Functions Over Arbitrary Bases

The behavior of the Shannon function of the depth of k-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all k, k ≥ 3, for an arbitrary basis of k-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all k, k ≥ 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Nonclassical Birational Models for Spec ℚ

Generalized subrings of the ring of integers that give birational models for the field of rationals are studied. A homogeneous strengthening of Evdokimov’s theorem is proved. An approach to calculation of homotopy groups with the help of generalized rings is proposed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On an Equivalent Norm on the Space BMO

We extend the inequality proved by S. V. Bochkarev to a larger class of convolution operators assuming that the Fourier transforms of the kernels of these operators satisfy certain conditions in the spirit of the Hörmander–Mikhlin multiplier theorem. Therefore, we give a new characterization of BMO.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Interaction of Elastic and Scalar Fields

In this work, we consider the problem of interaction of elastic body with scalar field. The general solution of a uniform system of equations (of elasticity theory) for the static case is solved by using the Papkovich representation method. The contact problem is solved by using a special boundary-contact condition, in the case where the contact surface is a stretched spheroid. The uniqueness theorem for the solution is also proved. Solutions are obtained in the form of absolutely and uniformly convergent series.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Games with Ordered Outcomes

We present a brief review of the most important concepts and results concerning games in which the goal structure is formalized by binary relations called preference relations. The main part of the work is devoted to games with ordered outcomes, i.e., game-theoretic models in which preference relations of players are given by partial orders on the set of outcomes. We discuss both antagonistic games and n-person games with ordered outcomes. Optimal solutions in games with ordered outcomes are strategies of players, situations, or outcomes of the game. In the paper, we consider noncooperative and certain cooperative solutions. Special attention is paid to an extension of the order on the set of probabilistic measures since this question is substantial for constructing the mixed extension of the game with ordered outcomes. The review covers works published from 1953 until now.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Physical Interpretation of Strict Solutions of Diffraction Problems by Heuristic Relations

We propose a new approach to construct heuristic relations describing solutions of diffraction problems. Those relations are based on physical principles and allow one to interpret mathematically strict solutions. Since the heuristic relations possess high performance and accuracy, they can also be used along with any strict approach or experimental results for a significant improvement of efficiency of solutions of practical problems related to applications of the diffraction theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Higher-Order Bessel Equations Integrable in Elementary Functions

The eigenfunction problem for a scalar Euler operator leads to an ordinary differential equation, which is an analog of higher-order Bessel equations. Its solutions are expressed through elementary functions in the case where the corresponding Euler operator can be factorized in a certain appropriate way. We obtain a formula describing such solutions. We consider the problem on common eigenfunctions of two Euler operators and present commuting Euler operators of orders 4, 6, and 10 and a formula for their common eigenfunction and also commuting operators of orders 6 and 9.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions

We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are C{sup 1}. Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP(f, g) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Smoothing by cubic spline modified applied to solve inverse thermal problem

This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A new bi-objective periodic vehicle routing problem with maximization market share in an uncertain competitive environment

This paper presents a new variant of periodic vehicle routing problem in which the reaching time to the customers affects market share. Thus, there is a competition between distributors to achieve more market share by reaching the customers earlier than others; moreover, travel time between each two pairs of customers is uncertain. This situation is called an uncertain competitive environment. For the given problem, a new bi-objective mathematical model including minimization of total traveled time and maximization of the market share is presented. In order to solve this model, a multi-objective particle swarm (MOPSO) and local MOPSO algorithms are applied; and to evaluate the algorithm performance, some samples are generated; and the results of algorithms are compared based on some comparison metrics. The results demonstrate that the proposed LMOPSO algorithm leads to a better performance compared to the MOPSO in most comparison metrics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Dynamics of an epidemic model with delays and stage structure

In this paper, dynamics of a stage-structured epidemic model with delays and nonlinear incidence rate is analyzed. Local stability and existence of Hopf bifurcation is discussed by choosing possible combination of the delays as the bifurcation parameter. It is proved that the unique endemic equilibrium is locally asymptotically stable when the delay is suitably small and a bifurcating periodic solution will be caused once the delay passes through the corresponding critical value of the delay. We make use of the normal form theory and center manifold theorem to obtain the explicit formulas for determining the properties of the Hopf bifurcation. Numerical simulations supporting our obtained findings are carried out in the end.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A family of second-order fully explicit time integration schemes

A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Hilfer–Katugampola fractional derivatives

We propose a new fractional derivative, the Hilfer–Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer–Hadamard, Riemann–Liouville, Hadamard, Caputo, Caputo–Hadamard, Liouville, Weyl, generalized and Caputo-type. As an application, we consider a nonlinear fractional differential equation with an initial condition using this new formulation. We show that this equation is equivalent to a Volterra integral equation and demonstrate the existence and uniqueness of solution to the nonlinear initial value problem.

97 MATHEMATICS AND COMPUTING↗