Differential-Invariant Solutions
We construct differential-invariant solutions to automorphic systems and propose a method for classifying differential-invariant submodels.
97 MATHEMATICS AND COMPUTING↗
SEARCH · Engineering Papers
Results for “Mathematical Computing”
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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On the Problem on Slow Entrance of a Flat Piston in Compressed Liquid
In this paper, slow movement of a flat piston in compressed liquid is considered. The solution of the problem is constructed with two different methods: the first is based on the theory of Riemann’s simple waves, and the second on the small parameter method. Then we compare the results obtained by the two methods.
42 ENGINEERING↗
Uniform Global Attainability and Global Lyapunov Reducibility of Linear Control Systems in the Hessenberg Form
For a linear control system in the Hessenberg form, we obtain new sufficient conditions for Lyapunov reducibility to a system in the Frobenius canonical form, for uniform global attainability, and for global Lyapunov reducibility.
97 MATHEMATICS AND COMPUTING↗
The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect
We consider an abstract hybrid system of functional-differential equations. Both equations are functional-differential with respect to one part of variables and difference with respect to to the other part of variables. To the system of two equations with two unknowns appeared, we apply the W-method of N. V. Azbelev. We examine two models: a system of functional-differential equations and a system of difference equations. We study the spaces of their solutions and obtain the Bohl–Perron-type theorems on the exponential stability.
97 MATHEMATICS AND COMPUTING↗
On the global behavior of homeomorphisms of metric spaces
For the metric spaces, the homeomorphisms more general than conformal mappings are studied. It is proved that the families of ine indicated mappings are equicontinuous in their closure under definite conditions imposed on the boundaries of the corresponding domains.
97 MATHEMATICS AND COMPUTING↗
Stationary Electrohydrodynamic Flows of Incompressible Polymeric Media with Strong Discontinuity
We study the motion of an incompressible polymeric fluid with volume charge and construct stationary solutions of the electrohydrodynamical equations.
97 MATHEMATICS AND COMPUTING↗
Initial-Boundary Value Problem for the Non-Stationary Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions
We consider the initial-boundary value problems for the nonstationary radiative transfer equation in a system of semitransparent bodies with boundary and initial data in the complete scale of Lebesgue spaces. We establish the unique solvability of the first initial-boundary value problem, the problem with “shooting conditions,” and the problem with Fresnel reflection and refraction conditions on the body boundaries.
97 MATHEMATICS AND COMPUTING↗
On the Classical Fundamental Solutions of the Cauchy Problem for Ultraparabolic Kolmogorov-Type Equations with Two Groups of Spatial Variables
For a Kolmogorov-type ultraparabolic equation with two groups of spatial variables, we establish estimates for the increments of the classical fundamental solution of the Cauchy problem and its derivatives in the spatial variables.
97 MATHEMATICS AND COMPUTING↗
Abstract Interpolating Fraction of the Thiele Type
We construct an abstract continued fraction of the Thiele type as an interpolating fraction for a nonlinear operator acting from a linear topological space X to an algebra Y with identity. In some special cases, this fraction transforms either into a classical Thiele fraction or into a matrix-valued fraction of the Thiele type depending on many variables.
97 MATHEMATICS AND COMPUTING↗
Generalized Bessel–Struve Operator and Its Properties
We define the generalized Bessel–Struve operator in the space of functions analytic in an arbitrary domain. The conditions of equivalence of the generalized Bessel–Struve operator to the operator of second derivative are investigated. We also describe the commutant of the generalized Bessel–Struve operator and establish its hypercyclicity and chaotic nature.
97 MATHEMATICS AND COMPUTING↗
Singular Ibragimov–Mamontov Type Equations
We study an Ibragimov–Mamontov type equation with singular Bessel operators playing the role of second order derivatives. We obtain a representation of the solution by using a special Bessel transform.
97 MATHEMATICS AND COMPUTING↗
Local-Global Principle for the General Quadratic and General Hermitian Groups and the Nilpotency of KH{sub 1}
In this article, an analog of the Quillen–Suslin’s local-global principle was established for the elementary subgroup of the general quadratic group and the general Hermitian group. It is shown that unstable K{sub 1}-groups of the general Hermitian groups over module finite rings are nilpotent-by-Abelian. This generalizes earlier results by A. Bak, R. Hazrat, and N. Vavilov.
97 MATHEMATICS AND COMPUTING↗
On the A. V. Mikhalev Problem for Weakly Artinian Lie Algebras
The A. V. Mikhalev problem for weakly Artinian Lie algebras is solved. The theorem about solvability of prime radical of weakly Artinian Lie algebras is proved. An analogous result was generalized for Ω-groups.
97 MATHEMATICS AND COMPUTING↗
Nonstationary Problem of Complex Heat Transfer in a System of Semitransparent Bodies with Boundary-Value Conditions of Diffuse Reflection and Refraction of Radiation
We consider a nonstationary initial boundary-value problem describing complex (radiative-conductive) heat transfer in a system of semitransparent bodies. To describe radiation propagation, we use the radiation transfer equation with boundary-value conditions of diffuse reflection and refraction of radiation. We take into account that the radiation intensity and optical properties of bodies depend on the radiation frequency. The unique solvability of a weak solution is established. The comparison theorem is proved. A priori estimates of a weak solution as well as its regularity are obtained.
97 MATHEMATICS AND COMPUTING↗
On Construction of Anticliques for Noncommutative Operator Graphs
In this paper, we construct anticliques for noncommutative operator graphs generated by generalized Pauli matrices. It is shown that application of entangled states for the construction of the code space K allows one to substantially increase the dimension of a noncommutative operator graph for which the projection on K is an anticlique.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Lyapunov Characteristics of Oscillation, Rotation, and Wandering of Solutions of Differential Systems
A number of Lyapunov exponents are defined for solutions of linear systems on the half-line. These exponents are responsible for such properties of the solutions as oscillation, rotation, and wandering and are defined in terms of certain functionals applied to the solutions on finite intervals as a result of two operations: upper or lower averaging in time and minimization over all bases in the phase space. We consider important special cases of systems: those of a low order, autonomous systems, those associated with equations of an arbitrary order. We obtain a set of relations (equalities and inequalities) between the said exponents, together with their refined values in special cases. It is shown that this set is complete in the sense that it cannot be extended or strengthened by any other meaningful relation.
97 MATHEMATICS AND COMPUTING↗
Approximative characteristics of functions from the classes S{sub p,θ}{sup Ω}B(ℝ{sup d}) with a given majorant of mixed moduli of continuity
We obtain the exact-by-order estimates of the approximation of functions from the classes S Ω p,θ Sp,θΩ B(ℝd) in the space Lq(ℝd), 1 < p < q < ∞, by entire functions of the exponential type with supports of their Fourier transforms in sets generated by the level surfaces of a function Ω.
97 MATHEMATICS AND COMPUTING↗
Nonlinear Integral Equations with Potential-Type Kernels on a Segment
We study various classes of nonlinear equations containing operators of potential type (Riesz potential). By the method of monotone operators in the Lebesgue spaces of real-valued functions L{sub p}(a, b) we prove global theorems on the existence, uniqueness, estimates, and methods of construction of their solutions. We present applications that illustrate the results obtained.
97 MATHEMATICS AND COMPUTING↗