线性微分方程的一个反问题

讨论了线性微分方程的一个反问题.给定一个线性无关的函数组,可以得到一个高阶线性微分方程,该微分方程的基本解组恰好是此函数组.另外,对一阶线性微分方程组也进行了类似的讨论.     

V_n(R~+)中半线性生成子空间的基与维数

在交换的零和自由半环上,首先讨论了半线性空间V_n中向量组线性相关性的一些性质,并给出向量组中极大线性无关组所含向量个数相同的条件.其次通过对半环R~+,+,.,0,1上生成子空间基的讨论,给出了向量组的极大线性无关组含相同向量个数的条件.最后对R~+,+,.,0,1上生成子空间的维数进行详细讨论并给出相应的结果.     

部分线性模型中的非参数部分的线性性检验

In this paper,we propose the test statistic to check whether the nonpara- metric function in partially linear models is linear or not.We estimate the nonpara- metric function in alternative by using the local linear method,and then estimate the parameters by the two stage method.The test statistic under the null hypothesis is calculated,and it is shown to be asymptotically normal.     

二阶线性差分方程解的渐近线性

本文给出充分或必要的条件使二阶线性差分方程的解在不同程度上渐近于线性函数,并对收敛速度作出估计.所用的主要工具是第一和第二 Riccati 差分方程.     

二阶常系数线性微分方程的通解公式

讨论了求二阶常系数线性微分方程一个通解公式.     

关于Fuzzy值变量的线性回归分析

本文主要讨论了以下三方面内容:1.给出了可能性理论的框架。2.给出了可能性变量分布参数的maximin(μ/E)估计原理。3.建立了取值为Fuzzy数的两种不同的线性回归模型。     

线性变换的右拟线性内逆的存在性

引入线性空间中线性变换的拟线性内逆的概念,给出拟线性内逆存在的充要条件,同时给出拟线性内逆与拟线性可补的对应关系.     

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.     

探讨线性代数的核心

本文从关于线性代数基本结构的各种不同看法出发，探讨线性代数在整个数学学习中的基本问题，并根据线性代数基本问题讨论线性代数的结构安排.     

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.     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.     

Polynomial-time algorithms for regular set-covering and threshold synthesis

A set-covering problem is called regular if a cover always remains a cover when any column in it is replaced by an earlier column. From the input of the problem - the coefficient matrix of the set-covering inequalities - it is possible to check in polynomial time whether the problem is regular or can be made regular by permuting the columns. If it is, then all the minimal covers are generated in polynomial time, and one of them is an optimal solution. The algorithm also yields an explicit bound for the number of minimal covers. These results can be used to check in polynomial time whether a given set-covering problem is equivalent to some knapsack problem without additional variables, or equivalently to recognize positive threshold functions in polynomial time. However, the problem of recognizing when an arbitrary Boolean function is threshold is NP-complete. It is also shown that the list of maximal non-covers is essentially the most compact input possible, even if it is known in advance that the problem is regular.     

Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

Compromise solutions and estimation of the noninferior set

A general framework is presented in which the relation of the set of noninferior points and the set of compromise solutions is studied. It is shown that the set of compromise solutions is dense in the set of noninferior points and that each compromise solution is properly noninferior. Also, under convexity of the criteria space, a characterization of the properly noninferior points in terms of the compromise solutions is presented. In this characterization, the compromise solutions depend continuously on the weights. Use of the maximum norm is studied also. It is shown that a subset of these max-norm solutions, obtained by taking certain limits of compromise solutions, is dense and contained in the closure of the set of noninferior points.     

Milnor方图中的w-凝聚性

整环R称为ω-凝聚整环,是指R的每个有限型理想是有限表现型的.本文证明了ω-凝聚整环是v-凝聚整环,且若(RDTF,M)是Milnor方图,则在Ⅰ型情形,R是ω-凝聚整环当且仅当D和T都是ω-整环,且T_M是赋值环;对于Ⅱ-型情形,R是ω-凝聚整环当且仅当D是域,[F:D]<∞,M是R的有限型理想,T是ω-凝聚整环,且R_M是凝聚整环.     

递推阻尼最小二乘法的收敛性与稳定性

递推最小二乘法是参数辨识中最常用的方法,但容易产生参数爆发现象,因此对一种更稳定的辨识方法－－递推阻尼最小二乘法进行了收敛特性的分析,在使用算法之前先旭一化测量向量,结果表明,参数化距离收敛于一个零均值随机变量并且在持续激励条件下,适应增益矩阵的条件数有界。参数化距离的方差有 。     

Chaotic synchronization with filter based on wavelet transformation

A kind of chaotic synchronization method is presented in the paper. In the transmitter, part signals are transformed by wavelet and the detail information is removed. In the receiver, the component with low frequency is reconstructed and discrete feedback is used, we show that synchronization of two identical structure chaotic systems is attained. The effect of feedback on chaotic synchronization is discussed. Using the synchronous method, the transmitting signal is transported in compressible way, system resource is saved, the component with high frequency is filtered and the effect of disturbance on synchronization is reduced. The synchronization method is illustrated by numerical simulation experiment.     

Logic optimality for multi-objective optimization

Pareto dominance is one of the most basic concepts in multi-objective optimization. However, it is inefficient when the number of objectives is large because in this case it leads to an unmanageable number of Pareto solutions. In order to solve this problem, a new concept of logic dominance is defined by considering the number of improved objectives and the quantity of improvement simultaneously, where probabilistic logic is applied to measure the quantity of improvement. Based on logic dominance, the corresponding logic nondominated solution is defined as a feasible solution which is not dominated by other ones based on this new relationship, and it is proved that each logic nondominated solution is also a Pareto solution. Essentially, logic dominance is an extension of Pareto dominance. Since there are already several extensions for Pareto dominance, some comparisons are given in terms of numerical examples, which indicates that logic dominance is more efficient. As an application of logic dominance, a house choice problem with five objectives is considered.     

An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem

In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method.