线性方程组的正解

讨论了线性方程组正解的若干性质,给出了线性方程组有正解的一个充要条件,以及由此得到的求正解的一般方法,还介绍了正解问题的若干应用.     

算子方程AX-XA*=B的正解与实正解

利用算子矩阵分块技巧和算子的广义逆,在A是幂等算子的情况下,给出了算子方程AX-XA＊=B有正解和有实正解的充要条件,并给出了正解和实正解的通式。     

一类边界条件中带有扰动参数的积分边值问题正解的存在性

本文研究边界条件中带有扰动参数的积分边值问题正解的存在性与不存在性及扰动参数对正解存在性的影响.利用不动点指数理论,得出边值问题至少有一个正解、两个正解以及无解的充分条件.     

一类中立型时滞差分方程的正解

研究一类中立型时滞差分方程面　　　　的正解,获得了方程存在最终正解以及非增正解的充要条件,建立了比较定理．     

一类奇异次线性边值问题正解存在的充分必要条件

本文研究一类奇异次线性边值问题正解的存在性，得到Ｃ［０，１］正解和Ｃ１［０，１］正解存在的充分必要条件，也得到正解的唯一性．     

一类四阶两点边值问题正解的存在性

本文应用锥上的不动点指数理论,研究四阶两点边值问题—个正解及多个正解的存在性,给出了此类问题有一个正解及多个正解存在的与其相应线性问题的第一个特征值有关的充分条件,该条件中所涉及的值是最优的.     

非齐次线性方程组的半正解

线性方程组的不带负分量的非零解向量称为半正解.本文给出非齐次线性方程组AX= b (b≠0)的半正解结构,进而得到该类线性方程组有半正解的充分条件和必要条件以及唯一半正解的充要条件.     

二阶常微分方程组积分边值问题的正解

在借助于非负矩阵获得正解的先验估计的基础上,用不动点指数理论研究二阶非线性常微分方程组积分边值问题正解和多重正解的存在性.     

半线性椭圆方程正解的存在性和唯一性

本文致力于研究半线性椭圆方程正解的存在性,唯一性和非退化性;给出了保证我们所考虑的问题存在正解的一个充要条件;证明了如果某类半线性椭圆问题的正解是唯一的和非退化的,则对问题中的微分算子做小扰动后其正解也是唯一的和非退化的．作为推论,证明了正解的唯一性在区域的小扰动下是不变的．     

二阶非线性中立型时滞差分方程的正解

本文研究了一类二阶非线性中立型时滞差分方程的正解,得到了最终正解的存在性判据及存在正解的必要条件,建立了一些正解不存在性定理,所得结论推广并改进了已知的一些结果。     

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.     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

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.     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

近程空中目标航路研究

本文在等加速俯冲飞行假定下,分析了近程空中目标航路的特点,并据此提出了目标航路模型.经过投影变换,把目标航路模型转化为二次函数,从而使目标航路的滤波及预报问题得到简化,采用弟推最小二乘(RLS)原理,给出了目标航路的滤波器及预报器,最后,对本文方法进行了仿真,并对仿真结果进行了分析.     

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.     

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.     

On spectra of algebras over ultranormed fields

Algebras over ultranormed fields are studied. Conditions under which spectra of such algebras are non-void are investigated. For this purpose extensions of fields are considered.     

关于(余)反射的等价性和可扩张性及其应用

该文研究了（余）反射的等价性和可扩张性及应用，得到的主要结果如下：(1) 余反射余代数范畴和反射代数范畴是等价的．(2) 反射和余反射都具有可扩张性．使用这些结果可以用来推广和化简［1-4］中部分结论     

Morse decompositions of nonautonomous dynamical systems

The global asymptotic behavior of dynamical systems on compact metric spaces can be described via Morse decompositions. Their components, the so-called Morse sets, are obtained as intersections of attractors and repellers of the system. In this paper, new notions of attractor and repeller for nonautonomous dynamical systems are introduced which are designed to establish nonautonomous generalizations of the Morse decomposition. The dynamical properties of these decompositions are discussed, and nonautonomous Lyapunov functions which are constant on the Morse sets are constructed explicitly. Moreover, Morse decompositions of one-dimensional and linear systems are studied.