Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.     

Minimax multivariate empirical Bayes estimators under multicollinearity

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions, that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.     

On some geometric parameters in Banach spaces

Let X be a normed linear space and be the unit sphere of X. Let , , and J(X)=sup{‖x+y‖∧‖x−y‖}, x and y∈S(X) be the modulus of convexity, the modulus of smoothness, and the modulus of squareness of X, respectively. Let . In this paper we proved some sufficient conditions on δ(?), ρX(?), J(X), E(X), and , where the supremum is taken over all the weakly null sequence xn in X and all the elements x of X for the uniform normal structure.     

基于指数分布的进化策略

典型的进化策略受自然进化过程的启发而成为求解全局优化问题的重要方法。传统的ES变异算子作为一个主要的进化技术是建立在正态分布的随机变量基础上的，本文提出了基于指数分布的进化策略由于采用了新的变异算子有效地减少了产生探试解的成本，从而优于传统的进化策略。     

Proper actions on cohomology manifolds

Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.

     

关于正规Boole矩阵行空间的基数

称Ｂｏｏｌｅ矩阵Ａ是正规的，是指Ａ的行秩与列秩相等．本文主要得到两个结果．第一，推广了Ｊ．Ｋｏｎｉｅｃｚｎｙ在ＳｅｍｉｇｒｏｕｐＦｏｒｕｍ，ｖｏｌ．４４（１９９２）发表的论文Ｏｎｃａｒｄｉｎａ－ｌｉｔｉｅｓｏｆｒｏｗｓｐａｃｅｏｆＢｏｏｌｅａｎｍａｔｒｉｃｅｓ的主要结果．第二，若ｎ阶Ｂｏｏｌｅ矩阵的行空间基数大于２￣（ｎ－２）－２，则Ａ必是正规的．     

A Judging Method for Normal Family

ＡＪｕｄｇｉｎｇＭｅｔｈｏｄｆｏｒＮｏｒｍａｌＦａｍｉｌｙ￥ＺｈｕＺｈｅｎｘｉｎｇ（Ｄｅｐｔ．ｏｆＳｙｓｔｅｍＳｃｉｅｎｃｅａｎｄＭａｔｈ．，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｚｈｅｎｇｚｈｏｕ，４５００５２）Ａｂｓｔｒａｃｔ：Ｉｎ１９６４，Ｈ...     

关于RNP和SCS的若干等价条件

使用切片方法，讨论了Banach空间中有界闭凸子集的RNP和SCS的若干等价条件．