非线性υ-循环系统的SOR迭代法

0引言 1971年Rheinboldt~[16]根据Ortega的一篇未发表的短文，将M-矩阵的概念推广到非线性函数。其后，由More,Rheinboldt进步将Fiedler和Ptek~[4]定义过的P-矩阵，S-矩阵等矩阵类推广到非线性函数。同时，他们还研究了M-函数的非线性Gauss-Seidel迭代法和非线性SOR迭代法的收敛性问题~([11][17])。1986年，Alefeld和Volkmann研究了M-函数的SSOR迭代法~[1]。1991年Frommer将广义对角矩阵推广到非线性函数，并讨论了M-函数的异步非线性JOR，SOR和SSOR迭代法的收敛性~[6]。     

非线性波方程准确孤立波解的符号计算

该文将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性发展方程孤立波解的一种统一算法，并在计算机数学系统上加以实现，推导出了一批非线性发展方程的精确孤立波解．算法的基本原理是利用非线性发展方程孤立波解的局部性特点，将孤立波表示为双曲正切函数的多项式．从而将非线性发展方程（组）的求解问题转化为非线性代数方程组的求解问题．利用吴文俊消元法在计算机代数系统上求解非线性代数方程组，最终获得非线性发展方程（组）的准确孤立波解.     

变量分离法与变系数非线性薛定谔方程的求解探索

把变量分离法应用于(1+1) 维非线性物理模型，构建了色散缓变光纤变系数非线性薛定谔方程的一类新的孤子解.作为特例，也得到了常系数非线性薛定谔方程的包络型孤子解，只是解的形式有点变化.     

有序拓扑向量空间中的共鸣定理

本文研究有序拓扑向量空间中非线性映照的共鸣定理．对于取值于有序拓扑向量空间中的映照，利用序关系，引入了一类广泛的非线性映照．对于这类非线性映照，应用纲理论，并给出了关于点态序有界蕴涵一致序有界的共鸣定理．     

求解2—D波动方程系数反问题的迭代方法及收敛性

本文针对地震勘探中提出一类重要的２－Ｄ波动方程反演问题，通过定义一个新的非线性算子将２－Ｄ波动方程的反演问题归结为一个新的非线性算子方程，详细讨论了非线性算子的性质，给出了求解反问题的迭代方法，并证明了这种迭代方法的收敛性。     

非线性广义系统平衡点的定性分析

本文研究非线性广义系统平衡点的定性行为．利用系统的正则性，证明了可以通过其线性系统的定性行为研究非线性系统的定性性态，为定性研究非线性系统提供了一种方法．     

E2类二阶椭圆组一般形式的非线性边值问题

研究了E2类二阶椭圆型方程组相当广泛的一类非线性边值问题，通过引进一种代换把它化为一类非线性广义Riemann-Hilbert边值问题，再引进奇异积分算子，建立与该问题等价的非线性奇异积分方程。应用奇异积分算子性质和泛函分析与函数论方法，在一定的假设条件下，证得了该问题的可解性。     

Banach空间中一类周期非线性受控系统最优控制的存在性

研究一类强非线性发展方程的周期解及相应的最优控制问题的存在性，首先，证明了Banach空间中一类包含非线性单调算子和非线性非单调扰动的强非线性发展方程周期解的存在性；其次，给出了保证相应的Lagrange最优控制的充分条件；最后，举例说明理论结果在拟线笥抛物方程周期问题及相应的最优控制问题中的应用。     

多项式形的静态非线性投入产出模型解的存在性研究

经济系统时常表现明显的非线性特征，研究非线性投入产出具有重要的现实意义。在假定直接消耗系数是关于部门总产品的多项式函数的条件下，利用不动点理论求得在一定条件下，静态非线性投入产出模型的解的范围。由于多项式函数具有分段区间单词性的特点，使得多项式型的非线性投入产出模型突破了以往的研究中要求直接消耗系数仅仅是关于部门总产品的单调递减或单调递增的函数的限制，使建立非线性投入产出模型的条件更为宽松，更能描述现实的经济系统。     

一类边值问题的有限差分牛顿型方法

本文利用微分方程的非线性差分格式的特殊结构，提出了一种新的牛顿型方法求解非线性差分方程，若新方法每步不队加计算非线性方程组的函数值，那么新自满收敛速度可在室Ｒ－１＋√４／２阶；若新方法每步附加计算一个非线性方程组的向量函数值，那么新算法收敛速度可达到Ｑ－平方阶。     

Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.     

On the Geometry of Liouville Equation: Symmetries, Conservation Laws, and Bäcklund Transformations

Various geometrical structures related to the Liouville equation are considered. Properties of the symmetry algebra are discussed and local conserved currents are constructed. Bäcklund transformations for the Liouville equation are integrated and nontrivial generalizations of the latter are studied as well as the structures on them.     

Stability of random impulsive coupled systems on networks with Markovian switching

Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof.Lu Jinake

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子

本文研究了两个材半限弹性的接合面附近存在与接合面平行的双裂纹，并承受剪切冲击时的瞬态应力，运用付里叶（Ｆｏｕｒｉｅｒ）和拉普拉斯（Ｌａｐｌａｃｅ）变换，将问题归结为求解二元积分方程，求解时将裂纹所在面上，下的位移差展成级数，并让其自动满足裂纹面外的位移差为零的条件，利用裂纹面上的边界条件和施密特（Ｓｃｈｍｉｄｔ）方法求解级数中的待定系数，在拉普拉斯像空间中，求得动应力强度因子，并将其数值地逆变换至     

Magnetically created instability in a collisionless plasma

In the Vlasov–Maxwell theory we prove that there are homogeneous equilibria that are monotone decreasing in every direction and are arbitrarily close to a Maxwellian. They are unstable under certain electromagnetic perturbations, but are stable under purely electric perturbations as well as under electromagnetic perturbations of sufficiently short period. These statements are valid both in the linear and nonlinear senses.     

Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.