不同序下Groebner基分离子插值函数模型分析

不同序下Groebner基分离子是不相同的,因此不同序下Groebner基分离子插值函数模型也有所差别.字典序下Groebner基分离子含有多个变量且变量次数低,相应插值函数模型则为多变元多项式;分次字典序下Groebner基分离子变量少且变量次数较高,插值函数模型次数也较高.通过实例分析说明,在实际应用中,应根据实际需要恰当选择所需的单项式序下函数模型.     

广义字典序积的自同态幺半群

讨论了图的广义字典序积的自同态幺半群的性质,给出了广义字典序积图X[Yz|x∈V（X）]的自同态幺半群与X,Yx(x∈V(X))的自同态幺半群的圈积相等的充要条件。     

图的P-正则自同态幺半群

刻划了具有Ｐ－正则自同态幺半群的二分图,讨论了字典序积图的自同态幺半群的Ｐ－正则性。     

树依谱矩的排序

首先给出了图的四种变换,得到其对任意图的谱矩的影响规律,并且利用图的这四种变换给出了树依谱矩序列s4的字典序排在前三位和后三位的图及其特征。     

树,单圈图,双圈图依谱矩的排序

设G=(V(G),E(G))是一个n阶简单图,V(G),E(G)分别为图G的顶点集和边集.G的k阶谱矩sk(G)为G的所有特征值λ1,λ2,···,λn的k次幂之和,即sk(G)=n i=1λi k.该文首先列出图的五种变换,然后得到了其对任意图的零到四阶谱矩的变化规律,最后依次给出了树和单圈图依谱矩序列S4的字典序分别排在前4-6位和后4-6的图及其特征以及双圈图依谱矩序列S4的字典序排在前6位和后6位的图及其特征.     

双权最小树形图

本文在朱－刘算法的基础上，讨论了网络双权最小树形图问题．采用字典序方法得到了该问题的一个复杂性为Ｏ（ｍｎ）的多项式算法．     

线性规划问题的一种新的摄动法

在用单纯形方法解线性规划的问题时，不可避免会出现退化情况，而某些退化情况会导致循环。目前采用的避免循环的方法一共有两类：传统的摄动法（字典序）和Bland方法。本分析了传统摄动法的一些不足，给出了一种新的摄动法。     

图的字典序积和自同态幺半群

Ｆ．Ｈａｒａｒｙ￣［１］和Ｇ．Ｓａｂｉｄｕｓｓｉ￣［２］考虑过图Ｘ和ｙ的字典序积Ｘ［Ｙ］的自同构群ＡｕｔＸ［Ｙ］与它们各自的自同构群的圈积ＡｕｔＸ［ＡｕｔＹ］的关系，并给出了两者相等的一种刻划．在本文，我们考虑更广意义上的问题，即Ｘ［Ｙ］的自同态幺半群ＥｎｄＸ［Ｙ］与各自的自同态幺半群的圈积ＥｎｄＸ［ＥｎｄＹ］的关系，也给出了两者相等的一种刻划，同时得到了下面结果：如果Ｘ和Ｙ都是不含Ｋ＿３导出子图的连通图，且其中之一图有奇数围长，那么ＥｎｄＸ［Ｙ］＝ＥｎｄＸ［ＥｎｄＹ］．     

离散时间折扣多目标马氏决策模型：加权与字典序准则

定义了离散时间折扣多目标马氏决策模型,在加权准则下,证明了存在（ｎ,∞）最优马氏策略;在字典序准则下,利用最优策略的结构性质,将其最优问题转化为一系列单目标模型的最优问题。     

阿基米德序半群的链的若干刻画

本文首先引入了一个序半群$S$的准素模糊理想的概念,通过序半群$S$上的一些二元关系以及它的理想的模糊根给出了该序半群是阿基米德序子半群的半格的一些刻画.进一步地借助于序半群$S$的模糊子集对该序半群是阿基米德序子半群的半格进行了刻画.尤其是通过序半群的模糊素根定理证明了序半群$S$是阿基米德序子半群的链当且仅当$S$是阿基米德序子半群的半格且$S$的所有弱完全素模糊理想关于模糊集的包含关系构成链.     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

A linear time algorithm to list the minimal separators of chordal graphs

Kumar and Madhavan [Minimal vertex separators of chordal graphs, Discrete Appl. Math. 89 (1998) 155-168] gave a linear time algorithm to list all the minimal separators of a chordal graph. In this paper we give another linear time algorithm for the same purpose. While the algorithm of Kumar and Madhavan requires that a specific type of PEO, namely the MCS PEO is computed first, our algorithm works with any PEO. This is interesting when we consider the fact that there are other popular methods such as Lex BFS to compute a PEO for a given chordal graph.     

Modifying estimators of ordered positive parameters under the Stein loss

This paper treats the problem of estimating positive parameters restricted to a polyhedral convex cone which includes typical order restrictions, such as simple order, tree order and umbrella order restrictions. In this paper, two methods are used to show the improvement of order-preserving estimators over crude non-order-preserving estimators without any assumption on underlying distributions. One is to use Fenchel’s duality theorem, and then the superiority of the isotonic regression estimator is established under the general restriction to polyhedral convex cones. The use of the Abel identity is the other method, and we can derive a class of improved estimators which includes order-statistics-based estimators in the typical order restrictions. When the underlying distributions are scale families, the unbiased estimators and their order-restricted estimators are shown to be minimax. The minimaxity of the restrictedly generalized Bayes estimator against the prior over the restricted space is also demonstrated in the two dimensional case. Finally, some examples and multivariate extensions are given.     

Multivariate dispersive ordering of spacings of generalized order statistics

The purpose of this paper is to investigate conditions on the underlying distributions and the parameters, on which generalized order statistics are based, to establish the Shaked–Shanthikumar multivariate dispersive ordering of normalized and unnormalized spacings of generalized order statistics from one sample and two samples. Several probability inequalities concerning spacings of generalized order statistics are also given.     

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.     

Preserving multivariate dispersion: An application to the Wishart distribution

Univariate dispersive ordering has been extensively characterized by many authors over the last two decades. However, the multivariate version lacks extensive analysis. In this paper, sufficient and necessary conditions are given to preserve the strong multivariate dispersion order through properties of the corresponding transformation. Finally, these results are applied to the Wishart distribution which can be viewed as “the spread of the dispersion”.     

Towards a Tighter Coupling of Bottom-Up and Top-Down Sparse Matrix Ordering Methods

Most state-of-the-art ordering schemes for sparse matrices are a hybrid of a bottom-up method such as minimum degree and a top-down scheme such as George's nested dissection. In this paper we present an ordering algorithm that achieves a tighter coupling of bottom-up and top-down methods. In our methodology vertex separators are interpreted as the boundaries of the remaining elements in an unfinished bottom-up ordering. As a consequence, we are using bottom-up techniques such as quotient graphs and special node selection strategies for the construction of vertex separators. Once all separators have been found, we are using them as a skeleton for the computation of several bottom-up orderings. Experimental results show that the orderings obtained by our scheme are in general better than those obtained by other ordering codes.This revised version was published online in October 2005 with corrections to the Cover Date.     

Domain separation by means of sign changing eigenfunctions of p-laplacians

We are interested in algorithms for constructing surfaces Γ of possibly small measure that separate a given domain ω into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the p-Laplacians,p→1 under humogeneous Neumann houndary conditions. These eigenfunctions are proven to be limtes of a steepest descent method applied to suitable norm quotients. Finally we use these ideas for the construction of separators on simplex grids.     

Multivariate distributions of order κ

Three multivariate distributions of order κ are introduced and studied. A multivariate negative binomial distribution of order κ is derived first, by means of an urn scheme, and two limiting cases of it are obtained next. They are, respectively, a multivariate Poisson distribution of order κ and a multivariate logarithmic series distribution of the same order. The probability generating functions, means variances and covariances of these distributions are obtained, and some further genesis schemes of them and interrelationships among them are also established. The present paper extends to the multivariate case the work of Philippou (1987) on multiparameter distributions of order κ. At the same time, several results of Aki (1985) on extended distributions of order κ are also generalized to the multivariate case.     

Construction of multivariate compactly supported tight wavelet frames

Two simple constructive methods are presented to compute compactly supported tight wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF conditions in the multivariate setting. We use one of our constructive methods in order to find tight wavelet frames associated with multivariate box splines, e.g., bivariate box splines on a three or four directional mesh. Moreover, a construction of tight wavelet frames with maximum vanishing moments is given, based on rational masks for the generators. For compactly supported bi-frame pairs, another simple constructive method is presented.