On pointwise convergence of Fourier series of radial functions in several variables

We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.

     

C-wellposedness of the complete second order abstract cauchy problem and applications

In this paper, we first give a sufficient and necessary condition for to generate an exponentially bounded -semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem ((ACP₂) for short) in some sense. Then we use these results and those in [1] to discuss the C-(exponential) wellposedness of a kind of (ACP₂) with application backgrounds, and develop the results in [2]. This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province, China     

恒定电场边值问题中点源的处理

讨论了不同情况下恒定电场中点源函数的表达式;用两种方法对点源作不同的处理;通过一个实的求解验证和说明了本文的方法。     

Elastoplastic stress analysis for cylindrical shell with flat strip imperfection

Based on unequidistant B-spline function, generalized spline subdomain displacement mode of rotational shell is obtained by taking double-direction interpolation of spline. The elastoplastic constitutive equation of shells is established by using the endochronic theory.According to the initial deflection theory of shells, the elastoplastic stress analysis of cylindrical shells with flat strip geometrical imperfection is studied. Numerical results show that the geometrical imperfection has a great effect on the stress distribution of shells.     

A preconditioned conjugate gradient Uzawa-type method for the solution of the stokes problem by mixed Q1–P0 stabilized finite elements

We study the behaviour of a conjugate gradient Uzawa-type method for a stabilized finite element approximation of the Stokes problem. Many variants of the Uzawa algorithm have been described for different finite elements satisfying the well-known Inf-Sup condition of Babu?ka and Brezzi, but it is surprising that developments for unstable ‘low-order’ discretizations with stabilization procedures are still missing. Our paper is presented in this context for the popular (so-called) Q1–P0 element. First we show that a simple stabilization technique for this element permits us to retain the property of a convergence factor bounded independently of the discretization mesh size. The second contribution of this work deals with the construction of a less costly preconditioner taking full advantages of the block diagonal structure of the stabilization matrix. Its efficiency is supported by 2D and. 3D numerical results.     

四元数矩阵方程AX-YB=C的最佳逼近解

本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．     

带Poisson跳随机微分方程终值与边值问题的适应解

Poisson跳的拟线性倒向随机微分方程x(t) ∫tf(s,x(s),,x(s)) y(s)]dMs =ξ,t∈[0,1],这里M = (W,Q)T,其中W为Wiener过程,Q为补偿Poisson过程.利用区间延拓和 Bihari 不等式证明了在某种弱于Lipschitz条件下方程存在唯一适应解,并给出了解的估计,从而将文章[1]的结论推广到带 Poission 跳的情形.另外,本文还讨论了以下形式的边值问题:dx(t) = f(t,x(t),y(t))dt y(t)dMt,Ax(0) Bx(1) =ξ*,t∈[0,1],并证明了在Lipschitz条件下适应解的存在唯一性.     

Waiting time problems for a sequence of discrete random variables

Let X ₁, X ₂,... be a sequence of nonnegative integer valued random variables.For each nonnegative integer i, we are given a positive integer k _i . For every i = 0, 1, 2,..., E _i denotes the event that a run of i of length k _i occurs in the sequence X ₁, X ₂,.... For the sequence X ₁, X ₂,..., the generalized pgf's of the distributions of the waiting times until the r-th occurrence among the events % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaiWabeaacaWGfbWaaSbaaSqaaiaadMgaaeqaaaGccaGL7bGaayzF% aaWaa0baaSqaaiaadMgacqGH9aqpcaaIWaaabaGaeyOhIukaaaaa!43D8!\[\left\{ {E_i } \right\}_{i = 0}^\infty\]are obtained. Though our situations are general, the results are very simple. For the special cases that X's are i.i.d. and {0, 1}-valued, the corresponding results are consistent with previously published results.This research was partially supported by the ISM Cooperative Research Program (90-ISM-CRP-11) of the Institute of Statistical Mathematics.     

Analogy solutions of axisymmetrical twist problems by axisymmetrical finite element program

It used to be considered that an axisymmetrical problem and a twist problem of an axisymmetrical body cannot be simulated by each other, because the number of unknown variables in an axisymmetrical problem is greater than that in a twist problem, and the governing equations are not the same. This paper proposes a degenerated analogy method, by which the twist problems of axisymmetrical bodies can be simulated by axisymmetrical problems with finite element programs.An ordinary structural analysis method can be used to analyze an axisymmetrical problem, but a twist problem of axisymmetrical bodies is treated as a 3-dimensional problem usually. According to the method proposed in this paper, the analysis of a twist problem can be simulated by the analysis of an axisymmetrical body with a structural analysis problem. The example of analysis computation is also given. Thecomputed result is in agreement with the theoretical result.In this paper, the constitutive relation of the degenerated analogy problem is given.The authors suggest that a twist problem of a body made of any materials is simulated by an axisymmetrical problem of a body made of orthotropic material. If you have to use some program for the axisymmetrical problem to be limited to isotropic materials the penalty coefficient method can be used to solve the problem.