仿酉对称矩阵的构造及对称正交多小波滤波带的参数化

仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带.     

D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

名人名著谈统计学

W.E.Denting(1940),Discussion of Professor Hottelling's Paper "The Teaching of Statistics"(Ann.Math.Stat.Vol.11,457-470): Above all,a statistician must be a scientist. 最重要的是,统计学家应该是科学家.     

柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解

在З.Л.Аксельрад(E.L.Axelrad)非轴对称载荷下柔性旋转壳线性方程的基础上,导出了圆环壳在子午面内整体弯曲的复变量方程和相应的细环壳方程.该方程可与钱伟长给出了一般解的В.В.Новожилов(V.V.Novozhilov)轴对称环壳方程相类比.通过类比,给出了细环壳在子午面内整体弯曲的一般解.所给出的解可以用来计算波纹管整弯曲的应力和端面位移.     

β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.     

单节点图的弱最大亏格

单节点图即只有一个点的图.本文讨论了该图类的三种嵌入.并得到了对应的最大亏格.对于这类图的弱嵌入.插值定理是成立的.     

(伪)单调集值映射拟均衡问题

主要讨论G-凸上的广义向量拟均衡问题,推广W.O ettli,D.Sch l ger,Q.H.A nsari,I.V.K onnov,和J.C.Y ao的一些主要结果.     

TWO-DIMENSIONAL RIEMANN PROBLEMS： FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的一个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱于J.-P.Aubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.-P.Aubin与H.Frankowska的结果给出一个新的简单证明,最后用反例说明本文给出的条件与J.-P.Aubin与H.Frankowska条件都是充分而不必要的.     

Interpretation of redundancy analysis: Rotated vs. unrotated solutions

Some properties of redundancy analysis are summarized and suggestions for normalization are given. The relations between redundancy analysis and principal component analysis and, to a lesser extent, canonical analysis, are reasons for considering rotation techniques on the primary solution. An example from practice is given in which redundancy analysis is a useful technique, but where rotation of its results is desired in order to simplify the interpretation.     

Interpreting multiple correspondence analysis

The practical aspects of interpreting multiple correspondence analysis are reviewed. The geometric concepts associated with simple correspondence analysis are shown to be inadequate for multiple correspondence analysis. An alternative approach, called joint correspondence analysis, is shown to be a more natural generalization of the simple case. The practical interpretation of homogeneity analysis is also discussed and a compromise is proposed between classical multiple correspondence analysis and joint correspondence analysis, preserving the optimal scaling properties of homogeneity analysis. A simple example is used throughout the discussion to illustrate the issues involved.     

多元统计分析在大学生综合素质评价中的应用

德育和智育是衡量大学生综合素质的重要因素,本文根据天津工业大学某年度某班级学生的各科成绩和影响学生综合素质的相关因素的实际数据,应用因子分析对影响学生综合素质的各因素进行主成份分析,计算各个学生的因子综合得分并按得分高低进行排序,把它和常见的的两种评价方法进行比较,结果发现该方法能够弥补仅仅依靠平均积点分和按综合测评总分排序的不足。最后,以因子综合得分和平均积点分和综合测评总分为指标采用聚类分析对所有学生进行分类,得出了令人满意的结果。实证分析结果表明因子分析和聚类分析是衡量学生综合素质行之有效的方法。     

Decision analysis as a replacement for cost/benefit analysis

Decision analysis has recently been employed to analyse public policy issues, and in contexts where cost/benefit analysis might equally well have been applied. In this paper we examine whether these two techniques are in competition, and if so, which is most fitted for public policy analysis. The intellectual origins of the two techniques are outlined, and different modes of interpretation are identified. The two techniques are compared on several different issues, including their handling of uncertainty, equity and conflicting objectives. It is argued that as an aid to decision-making the approach of decision analysis has advantages over cost/benefit analysis.     

数值分析双语教学的探讨

首先指出了数值分析双语教学的目的和意义.其次,分析了数值分析双语教学中存在的问题.最后,给出了数值分析双语教学的一些措施.     

基于扩展事件图的因果分析方法及在仿真中的应用

通过因果分析对仿真结果作出因果解释是仿真非常重要的一个环节.为了能够支持因果分析,首先提出扩展事件图,以重构仿真中发生的事件以及事件之间的因果关系;然后根据扩展事件图提出若干分析算法,通过对图模型的概率参数的可能性和主要性分析,获取因果知识;最后以一个攻防对抗仿真为例,对以上方法进行了必要的验证.     

Numerical simulation based on fuzzy stochastic analysis

In this paper mathematical methods for fuzzy stochastic analysis in engineering applications are presented. Fuzzy stochastic analysis maps uncertain input data in the form of fuzzy random variables onto fuzzy random result variables. The operator of the mapping can be any desired deterministic algorithm, e.g. the dynamic analysis of structures. Two different approaches for processing the fuzzy random input data are discussed. For these purposes two types of fuzzy probability distribution functions for describing fuzzy random variables are introduced. On the basis of these two types of fuzzy probability distribution functions two appropriate algorithms for fuzzy stochastic analysis are developed. Both algorithms are demonstrated and compared by way of an example.     

Matlab软件在多元统计分析中的应用

许多实际问题往往需要对数据进行统计分析,建立合适的统计模型.过去一般采用SAS、SPSS软件分析,本文给出Matlab软件在多元统计分析上的应用,主要介绍Matlab在主成份分析、聚类分析、判别分析上的应用。文中均给以实例,结果令人满意。     

Wide sense regenerative processes with applications to multi-channel queues and networks

A general method for the analysis of queueing networks called regenerative decomposition is discussed. It includes global ergodic analysis of the whole network and a following detailed analysis of each separate node.In the first stage, ergodic conditions are deduced under which the processes describing the network and each node are regenerative (in a wide sense). In the paper, we concentrate mainly on the following stage of analysis (local analysis) which includes obtaining some rate conservation laws for the limiting distributions of the continuous time and (embedded) discrete time processes describing a separate nodes under ergodic conditions.Some useful properties of regenerative wide sense processes are considered in detail.     

Status quo analysis in the graph model for conflict resolution

The graph model for conflict resolution, an analysis paradigm for strategic conflicts, has mainly relied on stability analysis for its conclusions. This paper proposes algorithms to apply another analysis technique, status quo analysis, to a graph model. Status quo analysis is dynamic and forward-looking, in contrast to Stability Analysis, which is static and contingent. Status quo analysis is carried out by means of a directed graph that tracks moves and countermoves from a status quo state, and a table that records the reachability status of states from the status quo. Different algorithms are proposed to produce status quo diagrams with and without restrictions on moves; more efficient versions of the algorithm for the case of transitive graphs are also put forward. Properties of diagrams generated by different algorithms are investigated. A case study illustrates how status quo analysis can be applied, and how it interacts with other analysis methodologies.