小波分析简介

近年来，小波的研究已成为数学家，理论物理学家和工程学家们密切关注的热点之一，在数学家眼中，它被认为是调和分析即现代Ｆｏｕｒｉｅｒ分析这一重要学科发展新阶段的标志；在其它科技领域，特别是信号分析、图象分析、量子物理和非线性科学等部门，它被当作是近年来工具和方法上的重大突破。《ＩＲＥＥ Ｔｒａｎｓａｃｔｉｏｎ ｏｎ Ｉｎｆｏｒｍａｔｉｏｎ Ｔｈｅｒｏｙ》１９９２年３月号专门出了一期小波分析及其应用的专     

能源问题

我们常常使用煤气和电来做饭，许多人都很关心用电和用煤气哪个更合算，为分析此问题，我用烧水来做对比分析．     

模糊模式识别在房地产预警信息系统中的应用

本文利用模糊模式识别和主成分分析等方法，进行房地产预警实证分析。以南京房地产市场为例说明。在面对若干繁冗驳杂的一系列指标时，如何进行指标归类，建立一套指标体系，以及如何分析这些指标反映的房地产市场所处的警情的层面。从而适时的得出一些分析结果，以供管理者做出及时的政策调整，避免房地产业危机的产生。     

数量经济学中的统计分析与预测方法

本文介绍了数量经济学中的一些基本概念，以及主成分分析在经济波动研究中的应用，并结合例子介绍了经济波动的频率域分析，详细介绍了一种区间控制计量经济模型．     

产品开发决策的灵敏性分析

文章着重研究了市场需求服从正态分布时参数估计误差变化对产品开发决策正确性的影响。通过实例分析，得到了处理这类问题的方法。文章进而给出了需求为有限方差与数学期望的一般随机量的处理方法，还给出了对Poisson变量的分析公式。     

用PLS回归方法对中国沿海与内陆城市经济的比较分析

本文采用ＰＬＳ回归方法，对中国部分沿海及内陆城市的经济发展进行比较分析，观察两类城市经济变量间的相互关系，并建立了多因变量对多自变量的ＰＬＳ回归模型     

典型相关分析在大学生体育达标因素分析中的应用

为了贯彻德，智，体全面发展的教育方针，国家教委1990年向全国各高校颁发了《大学生体育合格标准》．影响大学生体育达标等级的因素有很多，主要分成身体形态指标，机能指标和运动素质指标三大类．对这些指标中的因素进行分析，找出各指标之间的关系，确定相对重要的因素，这对高校体育教师与学生在教学与平日锻炼中具有一定的指导作用．本文运用典型相关分析方法，分析了大学生身体形态指标与运动素质指标之间的相关关系．我们从华东地质学院95级625名学生的体育达标成绩中，随机抽取男，女各302人，每人七项指标，运用典型相关分析方法，…     

数学建模中的数据挖掘方法

结合我校数模培训和参赛的经验，介绍了数据挖掘中的多元回归分析，主成分分析、人工神经网络等方法在建模中的一些成功应用。     

典型相关分析在考评教师业务素质中的应用

教学工作量，教学质量，科研能力，专业书籍阅读量是学校考评教师业务素质的基本指标，而这些指标间又存在着一定的关系。本文运用典型相关分析的方法，分析了这些指标间的相关关系，并由分析结果，提出了笔者对考评方法的一点参考意见。     

基于多尺度再生核质点法的h型自适应分析

基于多尺度再生核质点法(RKPM)的多分辨分析特性，给出了适于求解二维问题的h型自适应分析方法，讨论了不同高梯度指标对检测高梯度区的影响，同时还提出了基于邻节点搜索(SNN)及局部Delaunay三角分解(LDT)技术的适于任意节点分布的无网格自适应分析节点加密技术．通过对二维线弹性平面应力及平板弯曲问题的h型自适应分析，说明了不合适的高梯度指标将对自适应分析的收敛造成不良影响，且LDT节点加密技术较SNN技术的效率更高．数值算例的结果说明自适应分析的有效性、稳定性及良好的收敛特性．     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².