On stresses in a strip with a crack

The solution of the problem of a loaded crack in an infinite strip is given using the method of superposition of three problems (a loaded crack in the infinite plane; an infinite homogeneous strip with normal and tangent stresses that are given on nonhomogeneous boundaries; an infinite strip with longitudinal generators which are free from load and an arbitrary load at the end), which makes it possible to satisfy the boundary conditions exactly.Translated from Dinamicheskie Sistemy, No. 9, pp. 65–71, 1990.     

Stable graphs for a family of endomorphisms

We prove several fixed subgraph properties. In particular it is shown that if is a commuting family of contractions of a connected graph G without infinite path and infinite interval, then there exists a nonempty finite subgraph F which is invariant under any element of . In particular this subgraph F is a simplex if G is moreover a strongly dismantlable graph or a ball-Helly graph without infinite block, or if it is chordal. This implies that for any commuting family of contractions of a tree without infinite path, there is a common fixed vertex or a common fixed edge.     

除环上无限方阵的分解

对除环上无限方阵的逆方阵作了简单讨论,证明了除环上无限方阵的分解定理.     

除环上无限方阵的分解

对除环上无限方阵的逆方阵作了简单讨论,证明了除环上无限方阵的分解定理．     

域上无限方阵的分解

讨论了域上无限上三角方阵存在单侧逆方阵的充分条件 ,证明了域上无限方阵的分解定理     

The geometry at infinity of a hyperbolic Riemann surface of infinite type

We study geodesics on planar Riemann surfaces of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these geodesics and relate them to the structure of the boundary of a Dirichlet polygon for a Fuchsian group representing the surface.      

蠕动流中圆球阻力系数的入口效应

本文研究了圆球在半无穷长圆管入口处的蠕动流。得到了速度分布,压力分布和流函数的无穷级数形式的分析解.采用配置法将无穷级数截断并确定出级数中各项系数.求出了均匀入口流绕静止圆球以及圆球以瞬时速度在管内静止流体中运动这两种情形下圆球的阻力系数以及圆球表面上的应力分布.结果表明,当圆球在入口处运动时会遭受到较无穷圆管内为大的阻力.本文还对配置法的收敛性进行了数值实验.试验证明,该法具有好的收敛性.     

一类无穷维Hamilton算子的半群生成定理

研究了无穷维H am ilton算子生成C0半群的问题,得到了类无穷维H am ilton算子生成C0半群的一个充分条件.把结果应用在一类双曲型混合问题生成的无穷维H am ilton算子上,证明此类算子生成C0半群,并利用H ille-Y osida定理进一步说明了结果的正确性和有效性.另外,还给出了波动方程相应的无穷维H am ilton算子所生成的C0半群的具体表达式.     

There Exists a Linear Problem with Infinite Combinatory Complexity

We present a linear problem whose information complexity is finite but whose combinatory complexity is infinite. Thus, this linear problem has infinite complexity due to infinite combinatory complexity and not due to information complexity. This holds in a real number model in which we only allow arithmetic operations, comparisons of real numbers as well as precomputation of finitely many arbitrary elements. The result is not true if we can also evaluate logarithms, exponentials, and ceilings.     

Stability of a von Karman equation with infinite memory

In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.     

Transonic shock wave in an infinite nozzle asymptotically converging to a cylinder

We construct a single transonic shock wave pattern in an infinite nozzle asymptotically converging to a cylinder, which is close to a uniform transonic shock wave. In other words, suppose there is a uniform transonic shock wave in an infinite cylinder nozzle which can be constructed easily, if we perturbed the supersonic incoming flow and the infinite nozzle a little bit, we can obtain a transonic wave near the uniform one. As a consequence, we can show that the uniform transonic wave is stable with respect to the perturbation of the incoming flow and nozzle wall. Based on the theory of [G.Q. Chen, M. Feldman, Existence and stability of multi-dimensional transonic flows through an infinite nozzle of arbitrary cross-sections, Arch. Ration. Mech. Anal. 184 (2007) 185-242], the crucial parts of this paper are to derive the uniform Schauder estimates of the linear elliptic equation for the infinite nozzle asymptotically converging to a cylinder.     

The thermoelastic problem for a halfspace with a semiinfinite elastic thermal insulator

Numerical conditions are given in an infinite and semiinfinite plate (heat insulator), which is connected by a vertical two-sided connection only with an elastic halfspace, in the interior of which is a concentrated source of heat, which generates a stationary heat field. The problem is reduced to the solution of an integral-differential equation of the Wiener-Hopf type with respect to the Fourier transform of the contact stress. Its exact solution is constructed using the factorization method, and the final solution is represented by a series with respect to Chebyshev-Laguerre polynomials. Calculations of bending moments and transverse forces are given in an infinite plate, semiinfinite, and infinite beam-rolling plates.Translated from Dinamicheskie Sistemy, No. 7, pp. 114–123, 1988.     

Method of infinite systems of equations for solving an elliptic problem in a semistrip

Many problems of mechanics and physics are posed in unbounded (or infinite) domains. For solving these problems one typically limits them to bounded domains and finds ways to set appropriate conditions on artificial boundaries or use quasi-uniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite systems of equations. In this paper we develop this approach for an elliptic problem in an infinite semistrip. Using the idea of Polozhii in the method of summary representations we transform the infinite system of three-point vector equations to infinite systems of three-point scalar equations and obtain the approximate solution with a given accuracy. Numerical experiments for several examples show the effectiveness of the proposed method.     

关于一类无穷级数无穷和的一个递推公式

在本文中，我们利用周期函数的付立叶展开式，建立一类无穷级数无穷和的一个递推公式：其中     

Hille-Yosida定理在一类无穷维Hamiltion系统中的应用

应用Hille-Yosida定理研究了无穷维Hamilton算子,得到了一个无穷维Hamilton系统初值问题解的存在性定理,并把结果应用在由一类双曲型偏微分方程导出的无穷维Hamilton系统中,给出了此类无穷维Hamilton系统解的存在性定理.     

The first fundamental problem of the theory of elasticity for a rectangular parallelepiped

In 1852 Lame [1] formulated the first fundamental problem of the theory of elasticity for a rectangular parallelepiped. An approximate solution to this problem was given by Filonenko-Borodich [2 and 3] who used Castigliano's variational principle. Later Mishonov [4] obtained an approximate solution to Lamé's problem in the form of divergent triple Fourier series. These series contain constants which are found from infinite systems of linear equations. Teodorescu [5] has considered a particular case of Lame's problem. Using his own method the author solves the problem in the form of double series analogous to those used in [6 to 8] and by Baida in [9 and 10] in solving problems on the equilibrium of a rectangular parallelepiped. The solution of the problem reduces to three infinite system of linear equations and the author asserts that these infinite systems are regular. It is shown in Section 5 that the infinite systems obtained by Teodorescu, on the other hand, will not be regular.

In the references mentioned above which investigate Lamé's problem the authors confine their attention either to obtaining a solution by an approximate method, or to reducing the solution process to one of obtaining infinite systems, leaving these uninvestigated. It must be emphasized that the main difficulty in solving this problem lies in investigating the infinite systems obtained which are significantly different from the infinite systems of the corresponding plane problem.

In this paper a solution is given to the first fundamental problem of the theory of elasticity for a rectangular parallelepiped with prescribed external stresses on the surface (Sections 2, 3 and 4). For the solution of this problem the author has used a form of the general solution of the homogeneous Lamé equations which contains five arbitrary harmonic functions and which constitutes a generalization of the familiar Papkovich-Neuber solution (Section 1). The solution is expressed in the form of double series containing four series of unknown constants which can be found from four infinite systems of linear algebraic equations. The infinite systems of linear equations obtained is studied for values of Poisson's ratio within the range 0 < σ ≤ 0.18. It is shown that for these values of Poisson's ratio the infinite systems are quasi-fully regular.     

Diffraction of a plane wave by an infinite elastic plate stiffened by a doubly periodic set of rigid ribs

The diffraction of a plane wave by an infinite elastic plate stiffened by a doubly periodic set of rigid ribs of moderate wave dimensions is studied. The problem is reduced to an infinite quasiregular system of linear algebraic equations, and their solution describes the amplitudes of the waves propagating from the plate into the fluid.     

The existence off-local subgroups in a group

An infinite subgroup with nontrivial finite radical is called f-local. We study the structure of subgroups of an infinite fan (set), which contain an element of prime order not embeddable in an f-local subgroup. It is proved that f-local and infinite Abelian subgroups exist in groups under certain finiteness conditions. Supported by a grant of the Russian Federation State Committee on Higher Schools of Learning. Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 573–598, September–October, 1997.     

一类余维3的鞍-焦点异宿环分支

对余维3系统X_μ(x)具有包含一个双曲鞍-焦点O_1和一个非双曲鞍-焦点O_2的异宿环f进行了研究.证明了在f的邻域内有可数无穷条周期轨线和异宿轨线,当非粗糙异宿轨线Γ~0破裂时X_μ(x)会产生同宿轨分支,并给出了相应的分支曲线和两种同宿环共存的参数值.在3参数扰动下Γ~0破裂和O_2点产生Hopf分支的情况下,在f的邻域内有一条含O_1点同宿环,可数无效多条的轨线同宿于O_2点分支出的闭轨H_0,一条或无穷多条(可数或连续统的)异宿轨线等.     

The breaking of a non-homogeneous fiber embedded in an infinite non-homogeneous medium

The torsion of an infinite non-homogeneous elastic cylindrical fiber, containing a penny-shaped crack embedded in an infinite non-homogeneous elastic material is considered. The cylinder and elastic medium have different shear moduli. Using integral transformation techniques the solution of the problem is reduced to the solution of dual integral equations. Later on the solution of the dual integral equations is transformed into the solution of a Fredholm integral equation of the second kind, which is solved numerically. Closed form expressions are obtained for the stress intensity factor and numerical values for the stress intensity factors are graphed to demonstrate the effect of non-homogeneity of the fiber and infinite medium. In the end the stress singularity is obtained when the crack touches the infinite non-homogeneous medium (matrix).