L（IR）中卷积函数类在L_2（IR）中的平均σ－K宽度

本文研究了Ｌ（ＩＲ）中的卷积函数类在Ｌ＿２（ＩＲ）中的平均σ－Ｋ宽度且得到一些精确结果．同时，对非卷积情形，得到一些渐近结果．     

L（IR）中卷积函数类在L2（IR）中的平均σ－K宽度

本文研究了Ｌ（ＩＲ）中的卷积函数类在Ｌ₂（ＩＲ）中的平均σ－Ｋ宽度且得到一些精确结果．同时，对非卷积情形，得到一些渐近结果．     

偏序集的零调性与可缩性

本文将给出偏序集零调与可缩的几个充分条件，它们包含和深化了文［１］和［２］中的一些结果，把［２］中的一些结果推广到无限偏序集的情形．     

高阶泛函微分方程解的振动定理

证明了一类高阶非线性泛函微分方程的若干振动准则，推广了文献中的一些振动结果．     

一个投资问题的信息结构

本文研究一个投资问题中的信息价值，其中信息可以是不完美的，信息价值依赖于其结构．信息结构由状态变量与信息变量联合概率(或条件概率)矩阵来描述．我们定义了矩阵的一些偏序，通过这些偏序给出了信息价值的比较关系．由这些结果，我们导出了信息价值的一些基本性质．     

具有连续变量的变系数差分方程的振动性

本文建立了具有连续交量的变系数差分方程振动的充分条件，改进了最近文献中的一些结果．     

拓扑空间中的一个非空交定理及其应用

在FC-空间中证明了一新的非空交定理．作为应用，一不动点定理，一极大元定理，一重合点定理和一些极小极大不等式被证明．这些定理推广了近期文献中的结果．     

局部凸H-空间中的Fan—Ha型截口定理及应用

首先在局部凸H-空间中，建立了新Fan—Ha型截口定理及一些相应的等价形式．作为应用，我们在H-空间中研究极大极小定理，本文中的定理把已有文献中的相应结果改进和推广到H-空间．     

整函数和亚纯函数多项式的导数

本文考虑整函数和亚纯函数多项式的导数的值分布问题，得到了类似Ｔｕｍｒａ－Ｃｌｕｎｉｅ定理的一些结果，它们包含了文［１，４，５］中的结果作为特殊情况．     

多指标随机变量Marcinkiewicz大数定律完全收敛性和收敛速度

本文考虑指标在，ｄ≥１中的独立同分布随机变量序列，得到了有关大数定律的完全收敛性和收敛速度等一些结果．     

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.     

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.     

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     

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.     

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.     

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.     

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.

     

On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

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.     

Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems

A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given.