具有超抛物型极限方程的非线性奇摄动反应扩散问题

讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.     

一类具有跳跃层的非线性反应扩散系统的渐近行为

讨论了一类具有跳跃层的反应扩散系统.首先,求出了问题的外部解.其次,引入伸长变量,构造了跳跃层校正项.最后,利用微分不等式理论,得到了原问题解的一致有效的渐近展开式.从而研究了相应问题的解的渐近性态.     

群的融合自由积的几种广义Fratttini子群

M.K.Azarian将C.Y.Tang的一个引理推广到了下拟Frattini子群的情况,并且还提出了两个公开问题.为了回答这两个问题,进一步研究了群的融合自由积的一些广义Frattini子群,并且得到了一些结果.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

关于z.Ditzian定理

1987年Z.Ditzian提出了反映Bernstein算子收敛阶与所逼近函数光滑模之间关系的一个定理,并在α+β≤2情形下给出了这个定理的证明.对于α+β》2情形,Z.Ditzian给出了猜想.1992年周定轩证明了Z.Ditzian的猜想,完成了Z.Ditzian定理的证明.本文对于Z.Ditzian定理给出了一个新的直接证明,这个证明不需要讨论α,β的情况,而且还将Z.Ditzian定理拓广到Bernstein算子线性组合上.     

一类非对称结构线性方程组的子结构预处理子(英文)

针对一类具结构的非对称线性方程组提出了一类子结构预处理子,该预处理子只保留了约束条件的一半项.研究表明,预处理矩阵只有三个离散的特征值.为了避免计算Schur补的逆,还给出了正则化的子结构预处理子,同样对预处理矩阵进行了谱分析.这些结果将Zhou和Niu(Zhou J T,Niu Q.Substructure preconditioners for a class of structuredlinear systems of equations.Math.Comput.Model.,2010,52:1547-1553)的结果推广到非对称结构线性方程组.数值算例验证了提出的子结构预处理子的有效性.     

粗糙子群和粗糙子环

文[1]研究了半群中的理想,首次提出了粗半群和粗理想的概念.本文继续研究了群中的粗糙子群和粗正规子群.同时,在环中引入了粗子环的概念.最后,研究了粗糙集的同态问题.     

多维布朗运动的几个极限定理

本文研究了d(≥3)维布朗运动离开起点a.s.趋向无穷远的速度问题,获得了精密的结果.作为推论,给出了一个有趣的重对数律.同时,我们也给出了布朗运动靠近起点的相应性质.     

具有无界变差的连续函数研究进展

讨论了具有无界变差的连续函数的结构.首先按照局部结构和分形维数对连续函数进行了分类,给出了相应的例子.对这些具有无界变差的函数的性质进行了初步的讨论.对于新定义的奇异连续函数,给出了一个等价判别定理.基于奇异连续函数,又给出了局部分形函数和分形函数的定义.同时,分形函数又由奇异分形函数、非正则分形函数和正则分形函数组成.相应于不连续函数的情形也进行了简单的讨论.     

不对称柔性壁管道内幂律流体蠕动传输的精确解

在不对称管道内,研究了壁面柔曲性对非Newton流体蠕动流的影响.流变学性质由幂律流体本构方程表征.在数学表达中,采用了长波和低Reynolds数近似.得到了流函数和速度的精确解.给出了流线图及其俘获现象.对所讨论的流动,陈列了关键参数的显著特征,并最后给出了主要结论.     

Semi-parametric estimation for heavy tailed distributions

In this paper, we generalize several studies in the area of extreme value theory for the estimation of the extreme value index and the second order parameter. Weak consistency and asymptotic normality are proven under classical assumptions. Some numerical simulations and computations are also performed to illustrate the finite-sample and the limiting behavior of the estimators.     

Estimation of return values for significant wave height from satellite data

Estimation of extreme wave height across the oceans is important for marine safety and design, but is hampered by lack of data. Buoy and platform data are geographically limited, and though satellite observations offer global coverage, they suffer from temporal sparsity and intermittency, making application of standard methods of extreme value estimation problematical. A possible strategy in the face of such difficulty is to use extra model assumptions to compensate for lack of data. In this spirit we report initial exploration of an approach to estimation of extreme wave heights using crossings methods based on a log-Gaussian model. The suggested procedure can utilize either intermittent satellite data or regular time series data such as obtained from a buoy, and it is adapted to seasonal variation in the wave height climate. The paper outlines derivation of the method and illustrates its application to data from the Atlantic and Pacific oceans. A numerical comparison is made with the results of an annual maximum analysis for sites at which both satellite and buoy data are available. The paper concludes with a discussion of the applicability of the new approach, its relationship to other extreme value methods and desirable directions for further development.     

A Spatial Markov Model for Climate Extremes

Spatial climate data are often presented as summaries of areal regions such as grid cells, either because they are the output of numerical climate models or to facilitate comparison with numerical climate model output. Extreme value analysis can benefit greatly from spatial methods that borrow information across regions. For Gaussian outcomes, a host of methods that respect the areal nature of the data are available, including conditional and simultaneous autoregressive models. However, to our knowledge, there is no such method in the spatial extreme value analysis literature. In this article, we propose a new method for areal extremes that accounts for spatial dependence using latent clustering of neighboring regions. We show that the proposed model has desirable asymptotic dependence properties and leads to relatively simple computation. Applying the proposed method to North American climate data reveals several local and continental-scale changes in the distribution of precipitation and temperature extremes over time. Supplementary material for this article is available online.     

一类块隐式混合单步并行计算方法

本文讨论了一类解常微分方程初值问题的块隐式混合单步并行算法，这种算法的块数为K，精度阶为2d＋2，可在S台处理机上进行并行计算，其中K＝S·d．本文讨论了方法的一般性质，给出了方法的稳定性定理，最后给出了一个数值例子．     

Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping

In this paper, based on some mesh-dependent estimates on the extreme eigenvalues of a general finite element system defined on a simplicial mesh, novel and sharp bounds on the permissible time step size are derived for the mass lumping finite element approximations of parabolic equations. The bounds are dependent not only on the mesh size but also on the mesh shape. These results provide guidance to the stability of numerical solutions of parabolic problems in relation to the unstructured geometric meshing. Numerical experiments on both uniform meshes and adaptive meshes are presented to validate the theoretical analysis.     

Extreme eigenvalues of real symmetric Toeplitz matrices

We exploit the even and odd spectrum of real symmetric Toeplitz matrices for the computation of their extreme eigenvalues, which are obtained as the solutions of spectral, or secular, equations. We also present a concise convergence analysis for a method to solve these spectral equations, along with an efficient stopping rule, an error analysis, and extensive numerical results.

     

调和方程自然边界元Shannon 小波方法

1 引言 调和方程无论是在数学上还是在物理学中都占有重要地位,它有很多不同的物理背景,在力学和物理学中研究的许多问题都可归结为调和方程的边值问题,所以对调和方程进行深入研究有重要意义.余德浩教授在[3]中主要对调和方程在典型域(即单位圆,上半平面)上的情形进行了考虑.特别地,对单位圆的情形给出了刚度矩阵系数的计算公式和调和方程解的存在唯一性.本文采用由冯康教授[1]开创的自然边界元方法和Galerkin小波方法相耦合,对上半平面的调和方程Neumann问题进行了研究,得到十分有效的计算结果.     

多目标规划在条件微分方程组中的应用

从工程实际出发,借助最佳逼近论和总体极值的思想,运用常微分方程组的求解理论,最优化理论与数值方法,为在最优控制中的一类条件微分方程组的求解,开辟了一条新的求解途径,并用多个计算实例,证明了算法的有效性和可行性。     

Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition

We consider the numerical solution for the Helmholtz equation in R~2 with mixed boundary conditions.The solvability of this mixed boundary value problem is estab- lished by the boundary integral equation method.Based on the Green formula,we express the solution in terms of the boundary data.The key to the numerical real- ization of this method is the computation of weakly singular integrals.Numerical performances show the validity and feasibility of our method.The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.     

Numerical solution of first‐order hyperbolic partial differential‐difference equation with shift

In this article, we continue the numerical study of hyperbolic partial differential‐difference equation that was initiated in (Sharma and Singh, Appl Math Comput 9 ). In Sharma and Singh, the authors consider the problem with sufficiently small shift arguments. The term negative shift and positive shift are used for delay and advance arguments, respectively. Here, we propose a numerical scheme that works nicely irrespective of the size of shift arguments. In this article, we consider hyperbolic partial differential‐difference equation with negative or positive shift and present a numerical scheme based on the finite difference method for solving such type of initial and boundary value problems. The proposed numerical scheme is analyzed for stability and convergence in L^∞ norm. Finally, some test examples are given to validate convergence, the computational efficiency of the numerical scheme and the effect of shift arguments on the solution.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010