卷 218, 编号 6 (2016)
- 年: 2016
- 文章: 27
- URL: https://journals.rcsi.science/1072-3374/issue/view/14777
Article
Elasticity and Plasticity Problem for a Square Plate Weakened by a Hole with Partially Unknown Boundary
摘要
We consider an elasticity and plasticity problem for a square plate weakened by a square hole with rounded vertices. The plasticity region contains only the unknown rounded part of the hole contour and is not spread inside the plate. We contract the solutions and obtain the equation of the unknown part of the hole contour when the normal displacement is constant on the linear parts of the boundary and there is no normal stress on the unknown part of the hole contour.
Analysis of Spatial Economic Processes for Defining Investment Policy
摘要
In this paper, we consider principles of construction of mathematical models of spatial economic systems. By a spatial economic system we mean a region (system) whose constituent districts (subsystems) exchange goods, products, and investments.
Some Results of the Theory of Exponential R-Groups
摘要
This paper is devoted to the study of groups from the category M of R-power groups. We examine problems on the commutation of the tensor completion with basic group operations and on the exactness of the tensor completion. Moreover, we introduce the notion of a variety and obtain a description of abelian varieties and some results on nilpotent varieties of A-groups. We prove the hypothesis on irreducible coordinate groups of algebraic sets for the nilpotent R-groups of nilpotency class 2, where R is a Euclidean ring. We state that the analog to the Lyndon result for the free groups (see [10]) holds in this case, whereas the analog to the Myasnikov–Kharlampovich result fails.The paper is dedicated to partial R-power groups which are embeddable to their A-tensor completions. The free R-groups and free R-products are described with usual group-theoretical free constructions.
Derivations of the (n, 2, 1)-nilpotent Lie Algebra
摘要
In the present paper, we study derivations of a (n, 2, 1)-nilpotent Lie algebra.
Limiting Theorems on Some Complete Groups
摘要
The notion of a W-exponential Hall group is introduced and the limiting theorems on w-complete groups are proved.
Properties of the Riemannian Curvature of (α, β)-Metrics
摘要
In this paper, we discuss some important properties of the Riemannian curvature of (α, β)-metrics. When the dimension of the manifold is greater than 2, we classify Randers metrics of weakly isotropic flag curvature (that is, Randers metrics of scalar flag curvature with isotropic S-curvature). Further, we characterize (α, β)-metrics of scalar flag curvature with isotropic S-curvature. We also characterize Einstein (α, β)-metrics and determine completely the local structure of Ricci-flat Douglas (α, β)-metrics when the dimension dim M ≥ 3.
Optimality Conditions and Solution Algorithms of Optimal Control Problems for Nonlocal Boundary-Value Problems
摘要
In the present paper, the Bitsadze–Samarski boundary-value problem is considered for a quasi-linear differential equation of first order on the plane and the existence and uniqueness theorem for a generalized solution is proved; the necessary (in the linear case) and sufficient optimality conditions for optimal control problems are found. The optimal control problem is posed, where the behavior of control functions is described by elliptic-type equations with Bitsadze–Samarski nonlocal boundary conditions. The necessary and sufficient optimality conditions are obtained in the form of the Pontryagin maximum principle and the solution existence and uniqueness theorem is proved for the conjugate problem. Nonlocal boundary-value problems and conjugate problems are solved by the algorithm, which reduces nonlocal boundary value problems to a sequence of Dirichlet problems. The numerical method of solution of an optimal control problem by the Mathcad package is presented.
Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation
摘要
We consider an abstract hyperbolic equation with a Lipschitz continuous operator, where the main operator is self-adjoint and positive definite and represents a sum of two similar operators. For this equation, we construct a decomposition scheme of high order of accuracy. This scheme is based on rational splitting of cosine-operator function.
Lie Groups as Multiplication Groups of Topological Loops
摘要
In this paper, we present some new results on the question whether a Lie group can be represented as the multiplication group of a three-dimensional topological loop. We deal with the classes of quasi-simple Lie groups and nilpotent Lie groups.
A Weighted Inequality for a Potential-Type Integral
摘要
A sufficient condition is found for a pair of weights (v, w), which ensures the boundedness of a potential type operator from one weighed Lebesgue space to another.
New Invariants for the Graph Isomorphism Problem
摘要
In this paper, we introduce a novel polynomial-time algorithm to compute graph invariants based on the idea of a modified random walk on graphs. Though not proved to be a full graph invariant yet, our method gives the right answer for the graph instances other well-known methods could not compute (such as special Fürer gadgets and point-line incidence graphs of finite projective planes of higher degrees).
On Weighted Degree for Polynomial Rings
摘要
We take up a systematic study of all steps to derive a proof of [5, Lemma 2] from that of [1, Lemma 6.8.3].
On The Stability of the Disturbance Algorithm for a Semi-Discrete Scheme of Solution of an Evolutionary Equation in the Banach Space
摘要
A purely implicit three-layer semi-discrete scheme of second-order approximation is considered in the Banach space. The three-layer semi-discrete scheme is reduced by means of the disturbance algorithm to two two-layer schemes. Using the solutions of these schemes, we construct an approximate solution of the initial problem. The stability of the constructed scheme is proved.
B∞-Algebra Structure in Homology of a Homotopy Gerstenhaber Algebra
摘要
The minimality theorem states, in particular, that on cohomology H(A) of a dg algebra there exists sequence of operations mi : H(A)⊗i→ H(A), i = 2, 3, . . . , which form a minimal A∞-algebra (H(A), {mi}). This structure defines on the bar construction BH(A) a correct differential dm so that the bar constructions (BH(A), dm) and BA have isomorphic homology modules. It is known that if A is equipped additionally with a structure of homotopy Gerstenhaber algebra, then on BA there is a multiplication which turns it into a dg bialgebra. In this paper, we construct algebraic operations Ep,q : H(A) ⊗p ⊗H(A) ⊗q→ H(A), p, q = 0, 1, 2, . . ., which turn (H(A), {mi}, {Ep,q}) into a B∞-algebra. These operations determine on BH(A) correct multiplication, so that (BH(A), dm) and BA have isomorphic homology algebras.
Construction of a Monadic Heyting Algebra in a Logos
摘要
Connections between certain types of categories (logoses and toposes) and intuitionistic predicate logic was established in 1960–1970 by Lowvere. The possibility of extending this connection to some types of modal logics by using the internal structure of categories of particular type (logos) was also established. Category-theoretical constructs were hence used as one of the possible semantic interpretations of intuitionistic logic. This interpretation has also included intuionistic modal logics using different semantical tools such as adjoint pair of functors. In this paper, we discuss one of the possible extension of intuitionistic logic.
Projection of Rational Lie Rings
摘要
This paper is a direct continuation of [26], where we proved that every normal lattice isomorphism of supersolvable Lie ring is induced at the isomorphism. In the present paper,we generalize this theorem for rational Lie rings.
Algebraic Approach in Pseudo-Spectra Estimation
摘要
We prove that m principal singular vectors of a matrix Xd constructed on the basis of a time series, contained periodical deterministic components with additive white noise, have equal pseudospectra and their pseudo-spectral structure is identical to that of the time series. The structures of pseudo-spectra of the rest singular vectors differ from the structures of pseudo-spectra of the principal vectors and the time series. It is shown that the time series allow one to increase the resolving capacity and to improve the statistical stability of spectral estimation.
New Developments in Holonomy Theory of Differentiable Systems
摘要
We define the abstract holonomy group of a family \( \mathcal{S} \) of left loops on M such that the holonomy groups with respect to different points are isomorphic and consider new developments in holonomy theory of differentiable systems.
Lagrangian and Hamiltonian Duality
摘要
We propose a setting for De Donder–Hamilton field theory in jet bundles, generalizing the usual multisymplectic formalism. Using a reformulation of Hamilton theory for the family of local Lagrangians related to a global Euler–Lagrange form, we construct a dual Hamiltonian bundle and corresponding Legendre maps, linking a Lagrangian system on a jet bundle with a canonical Hamiltonian system on the affine dual. Our approach significantly extends the family of regular variational problems that can be treated directly within a dual Hamiltonian formalism, thus avoiding the necessity to use the Dirac constraint formalism.
On the Nonlinear Dynamical System of Amplitude Equations Corresponding to Intersections of Bifurcations in the Flow Between Permeable Cylinders with Radial and Axial Flows
摘要
In the present work, we study various modes that arise after a circular Couette flow loses its stability in the presence of an axial flow due to a constant axial pressure gradient and a radial flow through the permeable walls of the cylinders. The basic object of our investigation is a nonlinear system of amplitude equations describing multiple flow bifurcations between permeable cylinders. Different bifurcations will be investigated theoretically with application of numerical methods.
General Representation of Solutions of the Equation of Penetration and Diffusion of X-Rays in Plane Geometry
摘要
In this paper, we present a general procedure for solving of homogeneous equations that describe penetration and diffusion of X-rays in plane geometry. Starting from Van Kampen’s and Case’s observation that it suffices that “solutions” be distributions, elementary solutions of a homogeneous equation are found. We also prove that general solutions can be obtained by superposition of elementary solutions.
Weighted Cauchy Problem for Differential Equations with Deviating Arguments
摘要
For higher-order nonlinear differential equations with deviating arguments and with non-integrable singularities with respect to the time variable, we establish sharp sufficient conditions for the Cauchy problem to be solvable and well posed.
Weakly Locally Compact Topological Abelian Groups and Their Basic Properties
摘要
The notion of a weakly locally compact topological abelian group introduced in this paper generalizes the notion of a fibrous topological abelian group studied by N. Ya. Vilenkin.
Since in the class of locally compact topological abelian groups we distinguish classes of compact and discrete topological groups, in the class of weakly locally compact topological abelian groups we distinguish classes of quasicompact and quasidiscrete groups which are dual in the sense of Pontryagin’s theory of characters. We prove here that the group of characters of a weakly locally compact topological abelian group is weakly locally compact and construct universal groups for weakly locally compact groups.
On the Well-Posedness of the Cauchy Problem for a Functional Differential Equation Taking Into Account Variable Delay Perturbation
摘要
In the present paper, theorems on the continuous dependence of solution on perturbations of the initial data and the right-hand side of equation are formulated. Under initial data we imply the collection of initial moment, variable delay, initial vector and initial function.
Idempotent Elements of the Semigroup BX(D) Defined by Semilattices of the Class Σ3(X, 8) when Z7 = Ø
摘要
The paper presents a full description of idempotent elements of the semigroup of binary relations BX(D), which are defined by semilattices of the class Σ3(X, 8). For the case where X is a finite set and Z7 = Ø, we derive formulas for calculating the number of idempotent elements of the respective semigroup.
On the Regular Elements of the Semigroup of Binary Relations
摘要
In this paper we give a full description of regular elements of the semigroup that are defined by semilattices of the class, when Z7 ∩ Z6 ≠ ∅. Formulas are derived by means of which the number of regular elements of the semigroup is calculated when it is a finite set.
Idempotent Elements of the Semigroup BX(D) Defined by Semilattices of the Class Σ2(X, 8)
摘要
A complete semigroup of binary relations is defined by semilattices of the class Σ2(X, 8). A description of idempotent elements of this semigroup is given. For the case where X is a finite set and Z7 ∩ Z6 ≠ ∅, formulas are derived by calculating the number of idempotent elements of the semigroup.