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卷 215, 编号 4 (2016)
- 年: 2016
- 文章: 11
- URL: https://journals.rcsi.science/1072-3374/issue/view/14741
Article
Further Generalizations of Results on Structures of Continuous Functions
摘要
We consider new applications of the generalized interpretation method for studying the decidability of theories of some structures in analysis. We study the algebraic structure of continuous functions over a perfectly normal space and prove the decidability of the theory of this structure. Bibliography: 20 titles.
421-435
Differential Identities for Nonlinear Partial Differential Equations
摘要
We obtain new algebraic analytic presentations for solutions and coefficients of nonlinear second order differential equations and systems of such equations. Bibliography: 18 titles.
436-443
Algebraic-Analytic Methods for Constructing Solutions to Differential Equations and Inverse Problems
摘要
We present new algebraic-analytic methods for constructing solutions to differential equations and inverse problems. In particular, we develop a new approach based on the ray method for inverse problems in mathematical physics. Bibliography: 23 titles.
444-459
Boolean Algebras with Distinguished Endomorphisms and Generating Trees
摘要
We characterize computable Boolean algebras with distinguished endomorphisms in terms of generating trees and mappings of these trees. We show that every degree spectrum of a countable family of subsets of ω is the degree spectrum of some natural enrichment of a Boolean algebra. Bibliography: 20 titles.
460-474
Structure of Phase Portraits of Nonlinear Dynamical Systems
摘要
We consider phase portraits of some piecewise linear dynamical systems of chemical kinetics. We construct an invariant piecewise linear surface that consists of eight planar polygons and is formed by the trajectories which do not enter the attraction basin of a stable cycle. We prove that the dynamical system does not have cycles on this surface. Bibliography: 26 titles. Illustrations: 1 figure.
475-483
Predictor-Corrector Difference Scheme for Numerical Solution of the Euler and Navier–Stokes Equations
摘要
We generalize optimal splitting schemes for numerical solving the Euler and Navier–Stokes equations in the curvilinear coordinates. We introduce a splitting of the equations, common in both divergence and nondivergence forms, that makes it possible to construct a class of economic difference schemes. The schemes are realized at fractional steps by scalar sweeps and have a large steady margin. The proposed algorithm is tested for stationary and nonstationary problems.
484-498
Perturbation Propagation in a Thin Layer of a Viscosity-Stratified Fluid
摘要
We consider a nonlinear system of equations governing the motion of a viscosity-layered fluid with a free surface in long-wave approximation. Using the semi-Lagrangian coordinates, we rewrite the governing equations in the integro-differential form and obtain necessary and sufficient hyperbolicity conditions. We approximate the integro-differential model by a finite-dimensional system of differential conservation laws and propose a model of propagation of nonlinear perturbations in a viscosity-stratified fluid.
499-509
Conjugate Problem for a Third Order Equation with Multiple Characteristics and a Positive Function at the Higher Order Derivative
摘要
We establish the existence and uniqueness of a regular solution to the conjugate (generalized diffraction) problem for the equation ut − h(x)uxxx + c(x, t)u = f(x, t), where h(x) is positive and can have discontinuity of the first kind at the point x = 0.
510-516
Generators of Groups and Lie Algebras of the Form F/[N,N]
摘要
Let F be a free product of nontrivial groups Ai, i ∈ I, and a free group G, and let N be a normal subgroup of F such that N ∩ Ai = 1, i ∈ I. We establish necessary and sufficient conditions for a given element of the group F/[N,N] to belong to the subgroup generated by a given set of elements of F/[N,N] and necessary and sufficient conditions for a given finite set of elements of F/[N,N] to be a set of generators of F/[N,N]. Similar results are obtained for Lie algebras. Bibliography: 10 titles.
517-528
Computable Families of Sets in the Ershov Hierarchy Without Principal Numberings
摘要
We construct an example of a computable family of sets that does not possess \( {\displaystyle {\sum}_{{}_a}^{-1}} \) -computable principal numberings for any a ϵ . Bibliography: 19 titles.
529-536
Optimal System of Subalgebras of the Direct Sum of Two Ideals
摘要
We find an optimal system of subalgebras of the direct sum Aff(ℝ)⊕SL(2,ℝ). We find invariant solutions to some nonlinear partial differential equation.
537-542