不等式约束下线性预测的可容许性

研究了带有不等式约束的多元线性模型中未来观察值的线性预测的可容许性，得到了齐次线性预测（非齐次线性预测）在齐次线性预测类（非齐次线性预测类）中是可容许的充要条件．     

共同均值矩阵的线性估计的泛容许性

本文给出了多元线性模型中共同均值矩阵可估函数的线性估计的泛容许性定义,并得到了共同均值矩阵可估函数的线性估计分别在齐次和非齐次线性估计类中的泛容许性特征。     

矩阵损失下一般Gauss-Markov模型线性预测的可容许性

本文研究了一般Gauss-Markov模型中线性可预测变量的线性预测的可容许性.在给出线性预测可容许性定义的基础上,通过构造一个特殊的常量矩阵D0,分别得到了齐次和非齐次线性预测类中可容许的充要条件.     

不等式约束下线性模型中线性估计的可容许性

本文研究了带有不等式约束的多指标线性模型中线性估计的可容许性.利用矩阵论的相关知识,在矩阵损失下得到了齐次线性估计在齐次线性估计类中是可容许的充要条件,以及非齐次线性估计在非齐次线性估计类中是可容许的若干条件,推广了不等式约束下可容许性的相关结果.     

一般生长曲线模型中共同均值参数线性估计的泛容许性

本文研究一般生长曲线模型中共同均值参数的估计问题,给出了共同均值参数线性估计的泛容许定义,并在较特殊的齐次与非齐次线性估计类中得到了泛容许的充要条件．     

矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性

在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件.     

平衡损失下约束线性回归模型中回归系数的可容许估计

本文在平衡损失函数下得到等式约束模型中回归系数在齐次(非齐次)估计类中存在可容许估计的充要条件,给出带有不完全椭球约束模型中回归系数的线性估计在一切估计类中为可容许估计的充要条件.     

带不等式约束的线性模型中非齐次线性预测的可容许性

本文针对带不等式约束的线性模型,在矩阵损失下研究了线性预测的可容许性,得到了条件线性可预测变量的非齐次线性预测Lys α是可容许线性预测的充要条件.     

平衡损失下不等式约束回归系数的线性容许估计

对回归系数在不等式约束和平衡损失下讨论了其线性估计的可容许性,给出了齐次和非齐次线性估计类中可容许估计的充要条件.     

平衡损失下有限总体回归系数的线性可容许预测

本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果.     

解空间结构与几何空间中线面关系的判定

讲述了如何通过分析线性方程组导出组的解空间结构去判定几何空间中的线面关系.     

The life and work of André Cholesky

Cholesky’s method for solving a system of linear equations with a symmetric positive definite matrix is well known. In this paper, I will give an account of the life of Cholesky, analyze an unknown and unpublished paper of him where he explains his method, and review his other scientific works. I dedicated this work to John (Jack) Todd with esteem and respect at the occasion of his 95th anniversary.     

On regular linear relations

For a closed linear relation in a Banach space the concept of regularity is introduced and studied. It is shown that many of the results of Mbekhta and other authors for operators remain valid in the context of multivalued linear operators. We also extend the punctured neighbourhood theorem for operators to linear relations and as an application we obtain a characterization of semiFredholm linear relations which are regular.     

线性正算子序列在空间C_m(D)的收敛性问题

本文将Коровкин关于线性正算子序列和线性连续多项式算子序列逼近一元连续函数的主要结果推广到ｍ维连续函数空间Ｃｍ（Ｄ）．     

Minimal representation of convex polyhedral sets

A system of linear inequality and equality constraints determines a convex polyhedral set of feasible solutionsS. We consider the relation of all individual constraints toS, paying special attention to redundancy and implicit equalities. The main theorem derived here states that the total number of constraints together determiningS is minimal if and only if the system contains no redundant constraints and/or implicit equalities. It is shown that the existing theory on the representation of convex polyhedral sets is a special case of the theory developed here.The author is indebted to Dr. A. C. F. Vorst (Erasmus University, Rotterdam, Holland) for stimulating discussions and comments, which led to considerable improvements in many proofs. Most of the material in this paper originally appeared in the author's dissertation (Ref. 1). The present form was prepared with partial support from a NATO Science Fellowship for the Netherlands Organization for the Advancement of Pure Research (ZWO) and a CORE Research Fellowship.     

单A直和子空间

引入单直和子空间的概念,证明了线性空间可唯一分解为单直和子空间的直和,并且给出了计算方法.     

Linear Discrepancy of the Product of Two Chains

The linear discrepancy of a partially ordered set P = (X, ≺) is the minimum integer l such that ∣f(a) − f(b)∣ ≤ l for any injective isotone and any pair of incomparable elements a, b in X. It measures the degree of difference of P from a chain. Despite of increasing demands to the applications, the discrepancies of just few simple partially ordered sets are known. In this paper, we obtain the linear discrepancy of the product of two chains. For this, we firstly give a lower bound of the linear discrepancy and then we construct injective isotones on the product of two chains, which show that the obtained lower bound is tight.     

具有2n线性复杂度的2n周期二元序列的3错线性复杂度

线性复杂度和k错线性复杂度是度量密钥流序列的密码强度的重要指标.通过研究周期为2n的二元序列线性复杂度,提出将k错线性复杂度的计算转化为求Hamming重量最小的错误序列.基于Games-Chan算法,讨论了线性复杂度为2n的2n周期二元序列的3错线性复杂度分布情况;给出了对应k错线性复杂度序列的完整计数公式, k=3,4.对于一般的线性复杂度为2n-m的2n周期二元序列,也可以使用该方法给出对应k错线性复杂度序列的计数公式.     

New lower bounds on the size of (n,r)‐arcs in PG(2,q)

An $\left(n,r\right)$‐arc in $\text{PG}\left(2,q\right)$ is a set of $n$ points such that each line contains at most $r$ of the selected points. It is well known that $\left(n,r\right)$‐arcs in $\text{PG}\left(2,q\right)$ correspond to projective linear codes. Let $m_r\left(2,q\right)$ denote the maximal number $n$ of points for which an $\left(n,r\right)$‐arc in $\text{PG}\left(2,q\right)$ exists. In this paper we obtain improved lower bounds on $m_r\left(2,q\right)$ by explicitly constructing $\left(n,r\right)$‐arcs. Some of the constructed $\left(n,r\right)$‐arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.