广义投影型的超线性收敛算法

该文利用矩阵分解与广义投影等技巧，给出了求解线性约束的非线性规划的一个广义投影型的超线性收敛算法，不需要δ－主动约束与每一步反复计算投影矩阵，避免了计算的数值不稳定性，利用矩阵求逆的递推公式，计算简便，由于采用了非精确搜索，算法实用可行，文中证明了算法具有收敛性及超线性的收敛速度．     

块阵广义逆的块独立性的一些等价条件

基于[1]中关于块阵广义逆的块独立性的讨论,给出了两个同阶矩阵关于{1,2}-逆具有块独立性的一些等价条件.     

投影对的广义投影束的性质

设T∈B(H)是Hilbert空间H上的有界线性算子,本文研究了算子投影对(P,Q)和复数对(α,β)的广义投影束T=P+αQ+βPQ的性质.用投影算子的Halmos分解定理,得到了算子T为广义投影束的一些等价条件,给出了广义投影束T的谱性质,证明了广义投影束T在一定条件下与对角算子相似的性质,建立起广义投影束T的谱跟投影P和Q的谱之间的关系.最后,讨论了广义投影束T为特殊算子类,例如Fredholm算子、紧算子、自伴算子的充要条件,并给出了算子T关于幂等对的广义投影束的几个性质.     

计算广义逆A^（1,2）T,S和A^（2）T,S的投影法及共应用

本文讨论的投影法计算广义逆Ａ＾（１，２）Ｔ，Ｓ和Ａ＾（２）Ｔ，Ｓ同时利用该方法解线性方程组得到了一些常用的迭代公式。     

矩阵核心逆在0点特征投影的刻画

研究了矩阵核心逆在0点特征投影的刻画,并利用特征投影的性质给出了核心逆的扰动界.     

广义超特殊p-群的自同构群(Ⅱ)

重新确定了广义超特殊p-群G的自同构群的结构.设|G|=p~(2n+m),|ζG|=p~m,其中n≥1,m≥2,Aut_cG是AutG中平凡地作用在ζG上的元素形成的正规子群,则(i)若p是奇素数,则AutG=〈θ〉×Aut_cG,其中θ的阶是(p-1)p~(m-1);若p=2,则AutG=〈θ_1,θ_2〉×Aut_cG,其中〈θ_1,θ_2〉=〈θ_1〉×〈θ_2〉≌Z_(2m-2)×Z_2.(ii)如果G的幂指数是p~m,那么Aut_cG/InnG≌Sp(2n,p).(iii)如果G的幂指数是p~(m+1),那么Aut_cG/InnG≌K×Sp(2n-2,p),其中K是p~(2n-1)阶超特殊p-群(若p是奇素数)或者初等Abel 2-群.特别地,当n=1时,Aut_cG/InnG≌Z_p.     

关于广义逆矩阵AT，S^（1,2）的刻画推广

本文通过一类秩等方程给出了AT,S^(1,2)、AT,S^(2)的一种刻画及一类秩等方程有解的充分必要条件，推广了文献[1]、[4]的结论，并改进了[4]关于矩阵A的Drazin逆Af的一类刻画的证明。     

广义非线性互补问题的投影收缩法

广义非线性互补问题的投影收缩法孙德锋（中国科学院应用数学研究所）ＡＰＲＯＪＥＣＴＩＯＮＡＮＤＣＯＮＴＲＡＣＴＩＯＮＭＥＴＨＯＤＦＯＲＴＨＥＮＯＮＬＩＮＥＡＲＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＡＮＤＩＴＳＥＸＴＥＮＳＩＯＮＳ￥ＳｕｎＤｅ－ｆｅ...     

极大极小问题的广义投影算法

研究了无约束极大极小问题.通过引入一个可微的辅助函数,利用广义投影技术产生下降搜索方向,结合Armjio非精确线搜索建立了一个广义梯度投影算法.在初始点任意的条件下,证明了算法的全局收敛性.     

A note on generalized and hypergeneralized projectors

Groß and Trenkler [Generalized and hypergeneralized projectors, Linear Algebra Appl. 264 (1997) 463–474] have introduced two generalizations of orthogonal projectors called generalized projectors and hypergeneralized projectors. In this note we characterize these generalizations by their spectral decompositions.     

The invertibility of the difference and the sum of commuting generalized and hypergeneralized projectors

In this article, we study necessary and sufficient conditions for the invertibility of a linear combination c ₁ A ^k ?+?c ₂ B ^l , in the case when A and B are both commuting generalized or hypergeneralized projectors. We present some results relating different matrix partial orderings and the invertibility of a linear combination c ₁ A ^k ?+?c ₂ B ^l when A and B are hypergeneralized projectors.     

Some properties and characterizations for generalized multivariate Pareto distributions

In this paper, several distributional properties and characterization theorems of the generalized multivariate Pareto distributions are studied. It is found that the multivariate Pareto distributions have many mixture properties. They are mixed either by geometric, Weibull, or exponential variables. The multivariate Pareto, MP^(k)(I), MP^(k)(II), and MP^(k)(IV) families have closure property under finite sample minima. The MP^(k)(III) family is closed under both geometric minima and geometric maxima. Through the geometric minima procedure, one characterization theorem for MP^(k)(III) distribution is developed. Moreover, the MP^(k)(III) distribution is proved as the limit multivariate distribution under repeated geometric minimization. Also, a characterization theorem for the homogeneous MP^(k)(IV) distribution via the weighted minima among the ordered coordinates is developed. Finally, the MP^(k)(II) family is shown to have the truncation invariant property.     

一类广义正则半环上同余的特征

在半环中引入了一类理想的概念,讨论了这类理想的性质,并研究了一类广义正则半环上的同余,给出了这类半环上一种半环同余的特征．     

On the product of projectors and generalized inverses

We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. This problem is equivalent to the question when the product of two projectors is again a projector, and we discuss necessary and sufficient conditions in terms of their kernels and images alone. We give a new representation of the product of generalized inverses that does not require explicit knowledge of the factors. Our approach is based on implicit representations of subspaces via their orthogonals in the dual space. For Fredholm operators, the corresponding computations reduce to finite-dimensional problems. We illustrate our results with examples for matrices and linear ordinary boundary problems.     

Some equivalent definitions of Besov spaces of generalized smoothness

In this paper, we present some alternative definitions of Besov spaces of generalized smoothness, defined via Littlewood–Paley‐type decomposition, involving weak derivatives, polynomials, convolutions and generalized interpolation spaces.     

Some combinatorial and geometric characterizations of the finite dual classical generalized hexagons

We characterize the dual of the generalized hexagons naturally associated to the groupsG ₂(q) and³ D ₄(q) by looking at certain configurations, and also by considering intersections of traces. For instance, the dual of a generalized hexagon of finite order (s, t) is associated to the Chevalley groups mentioned above if and only if the intersection of any two tracesx ^y andx ^z, with some additional condition, contains at mostt/s + 1 elements.     

Axiomatic characterizations of generalized values

In the framework of cooperative game theory, the concept of generalized value, which is an extension of that of value, has been recently proposed to measure the overall influence of coalitions in games. Axiomatizations of two classes of generalized values, namely probabilistic generalized values and generalized semivalues, which extend probabilistic values and semivalues, respectively, are first proposed. The axioms we utilize are based on natural extensions of axioms involved in the axiomatizations of values. In the second half of the paper, special instances of generalized semivalues are also axiomatized.