一类三参数超越方程稳定区域的界面位置

本文讨论一类三参数超越方程根的分布．Ｂｅｌｌｍａｎ和 Ｃｏｏｋｅ在文［３］中对部分情况ａ＞０，ｂ≥０给出了结果．但这个结果是分析的，不便于应用． 本文对这类方程在整个参数空间（ａ，ｂ，ｃ）中给出根在左半平面的条件，并给出稳定区域的大致形状及边界曲面的大致位置的图形．应用上较为方便，特别是在分支理论中．     

相似于线规划中单纯形解法的Lemke-Howson 方法的改进

参考文献中对Lemke—Howson算法给出了相似于线性规划中的单纯形解法．我们在参考文献中给出一个反例．本文对文献中给出的相似于线性规划中的单纯形解法的Lemke—Howson算法作出改进，     

奇异值分解中两个酉矩阵的配置

给出求解矩阵奇异值分解的明确步骤．说明了分解中两个酉矩阵的相互关系．并利用两个酉矩阵之间的关系，针对第二个酉矩阵无法单独通过标准正交特征向量来确定的问题，给出了解决的方法．     

粘弹性薄板动力响应的边界元方法（Ⅰ）

本文中我们给出了粘弹性薄板动力响应的边界元方法．在Laplace变换区域中，给出了基本解的两种近似方法，运用这些近似基本解建立了边界元方法，再利用改进的Bellman反交换技术，求得问题的解，计算表明该方法具有较高精度和较快收敛性．     

p耗散算子的扩张

该文研究Ｂａｎａｃｈ空间中ｐ耗散算子的极大耗散扩张．通过建立自然边界空间，将ｐ耗散算子的极大耗散扩张与自然边界空间中极大负子空间—一对应，并给出表达式．利用这一工作本文给出一类Ｓｃｈｒｏｄｉｎｇｅｒ算子的扩张应用．     

也谈一类竞赛不等式的创新证法

在国内外的数学竞赛中，常出现一些分式不等式的证明问题．这些不等式形式优美、内涵丰富，命题者给出的证法异彩纷呈．文给出了分式不等式的一种创新证法——向量内积法，笔者深受启发．本文通过构造离散型随机变量的概率分布列，利用数学期望的一个性质给出这类不等式的另一种新证法，先给出数学期望的一个性质。     

Sn中Moebius形式为零的曲面

本文证明了S^n中Moebius形式为零且法丛平坦的曲面的余维数约化定理，并且给出了这类曲面的分类．在此基础上，进一步给出了S^n中Moebius形式为零的曲面的分类．     

最大公因式的一个性质

给出了最大公因式的两个性质，应用此性质推广了文[1]中相应的结论，并给出了两个推论．     

集团抽样不等概方法的均值估计及其性质

在集团抽样调查中，［１］和［２］给出了一般抽样方法及均值估计和它性质的论述，但未考虑各集团在总体中的地位对估计结果的影响．本文给出了集团抽样的不等概方法和均值的无偏估计，同时也给出了这种估计的方差及方差的无偏估计．     

判别分析中变量的选择－附加信息检验法

本文借用Ｓｈａｎｎｏｎ熵的概念给出了判别模型中附加信息检验原假设的解析形式．在母体眼从等方差正态分布的情形，导出了检验的似然比统汁量．在母体具有离散指标．服从多项分布的情形．导出了检验的似然比统汁量，并给出其极限分布．     

Matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions

We study matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions. Meanwhile, given any matrix eigenvalue problem with coupled eigenparameter‐dependent boundary conditions and transmission conditions, we construct a class of Sturm‐Liouville problems with given boundary conditions and transmission conditions such that they have the same eigenvalues.     

两邻接B样条曲面的G1连续条件

本文得到了非均匀重内节点邻接B样条曲面间G1连续的充要条件 ,给出了一类G1连续的充分条件 ;基于对B样条曲线参数连续性的分析 ,本文着重给出了这类充分条件成立的内在约束 ,即对公共边界控制顶点的约束条件 .     

Generalized boundary conditions on representative volume elements and their use in determining the effective material properties

We discuss generalized boundary conditions for representative volume elements (RVE), which include the classical boundary conditions as special cases. From the generalization, stochastic boundary conditions are derived. These allows to adjust the the stiffness of the boundary conditions smoothly between the extremal cases of homogeneous strain and homogeneous stress boundary conditions. We found that it needs to be distinguished between the resistance of the boundary conditions against homogeneous and inhomogeneous RVE deformation. The stochastic BC can combine the moderate stiffness of the well known periodic boundary conditions with the high resistance against localization of the homogeneous strain boundary conditions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非全局Lipschitz条件下随机延迟微分方程Euler方法的收敛性

大多数随机延迟微分方程数值解的结果是在全局Lipschitz条件下获得的.许多延迟方程不满足全局Lipschitz条件,研究非全局Lipschitz条件下的数值解的性质,具有重要的意义.本文证明了漂移系数满足单边Lipschitz条件和多项式增长条件,扩散系数满足全局Lipschitz条件的一类随机延迟微分方程的Eul...     

集值优化问题的高阶最优性条件(借助Studniarski导数)(英文)

本文研究的是约束集值优化问题的高价最优性条件.首先通过借助集值映射的Stud-niarski导数和严格局部有效性,讨论了集值优化问题的高阶必要条件和充分条件.对于充分条件,初始空间必须是有限维的.其次在初始空间和目标空间是有限维的以及集值映射是m阶稳定的条件下,也得到了此约束集值优化问题的高阶最优性条件.     

Integrability conditions for multiple trigonometric series

Sufficient conditions (the Boas-Telyakovskii conditions) on the coefficients of multiple trigonometric series are found that guarantee integrability of the sums of these series. Under these conditions, estimates are obtained for integrals of the moduli of the functions defined by multiple trigonometric series. In addition, the Boas-Telyakovskii conditions are compared with previously known conditions. It is shown that the Boas-Telyakovskii conditions are the most general ones.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 340–365, March, 1992.     

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

<正>In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.     

Degenerate boundary conditions for the diffusion operator

We describe all degenerate two-point boundary conditions possible in a homogeneous spectral problem for the diffusion operator. We show that the case in which the characteristic determinant is identically zero is impossible for the nonsymmetric diffusion operator and that the only possible degenerate boundary conditions are the Cauchy conditions. For the symmetric diffusion operator, the characteristic determinant is zero if and only if the boundary conditions are falsely periodic boundary conditions; the characteristic determinant is identically a nonzero constant if and only if the boundary conditions are generalized Cauchy conditions.     

Constraint Qualifications in Nonsmooth Multiobjective Optimization

For an inequality constrained nonsmooth multiobjective optimization problem involving locally Lipschitz functions, stronger KT-type necessary conditions and KT necessary conditions (which in the continuously differentiable case reduce respectively to the stronger KT conditions studied recently by Maeda and the usual KT conditions) are derived for efficiency and weak efficiency under several constraint qualifications. Stimulated by the stronger KT-type conditions, the notion of core of the convex hull of the union of finitely many convex sets is introduced. As main tool in the derivation of the necessary conditions, a theorem of the alternatives and a core separation theorem are also developed which are respectively extensions of the Motzkin transposition theorem and the Tucker theorem.     

Eine abstrakte Theorie der Kegel- und Segmentbedingungen

We develop an abstract theory of geometric regularity conditions for subsets of normed linear spaces, of the type which occurs in the theory of Sobolev spaces (cone conditions, …). The theory is to systematize the diversity of existing conditions, to replace complicated conditions by simpler ones, and to clarify the interplay between different conditions. Our main result is a very general decomposition theorem.