实轮换对称型及其半正定性判定的可读证明

可读证明是不等式机器证明领域中的热点问题.针对具有对称零点的实轮换对称型,文章提出了其线性空间的一组基以及分拆算法和两种分拆形式用于对不等式进行可读证明研究.讨论了该线性空间的维数,以及轮换对称型半正定性的判别方法.给出了一类具有对称零点的轮换对称型的半正定性判定条件.大量实例表明此分拆方式在轮换对称型半正定性的判定及可读证明上具有很好的实用性.     

用Schur分拆证明一类含参数的不等式

利用对称多项式的Schur分拆方法,以及单变元多项式实根隔离算法,证明了一个不等式猜想.并将这一方法用于处理一类含有参数的有理对称不等式.     

中心条件推导的间接方法

对于一类多项式系统,给出两类对称条件的推导算法,具体讨论了一类三次系统的中心条件;对于Poincare型系统,给出一类等时中心的充分条件．     

对称阵的最小多项式及其应用

本文研究了对称阵的最小多项式的存在唯一性,利用对称阵的正交分解的基本思想,获得了对称阵的最小多项式的具体表示形式,改进了Hamilton-Caylay定理.并且给出了对称阵最小多项式的几个应用.     

自然数的等差分拆公式

自然数的等差分拆公式陕西华阴市黄河工程机械厂中学李建章文［１］给出了至少含有两个奇约数的自然数的等差分拆的一个定理，本文利用对称思想，给出所有大于８的合数的等差分拆的简易方法──真因数中项对称法．为方便，本方约定ｍ、ｎ均为自然数Ｎ的真因数（即非１和Ｎ...     

一类迭代方程C~1类解的讨论

本文讨论一类非多项式形式的函数迭代方程，作者给出了这类方程Ｃ１类解的存在性．唯一性和稳定性条件．     

齐次对称多项式的半正定性

给出了某些齐次对称多项式半正定的充分必要条件,并举例说明其应用.     

微积分中值定理间点的关系

根据微分中值定理和积分中值定理定义微分点与积分点．证明严格单调函数与凸（凹）函数中微分点与积分点间的一些关系式,指出在函数对称的情况下微分点与积分点之间也存在着对称关系,并给出一类向量函数以及多项式函数中微分点与积分点间的关系式．     

三奇次散乱点多项式自然样条插值

为解决较为复杂的三变量散乱数据插值问题,提出了一种三元多项式自然样条插值方法.在使得对一种带自然边界条件的目标泛函极小的情况下,用Hilbert空间样条函数方法,构造出了插值问题的解,并可表为一个分块三元三奇次多项式.其表示形式简单,且系数可由系数矩阵对称的线性代数方程组确定.     

Tarski模型外的一类机器可判定问题

利用对称多项式的降维方法和证明代数不等式的胞腔分解方法,给出了一个实用的算法, 用于判定一类变元个数也是变量的多项式正性命题.这是一类在Tarski模型外的机器可判定问题.在Maple平台上,根据该算法设计的程序nprove,可以快速实现判定目标.     

图的k-单圈划分中的优化问题

图的划分问题曾引起图论界的广泛关注，在文献[4]中讨论了k-单圈划分，本文进一步研究基于k-单圈划分的优化问题，即在一个赋权图中求一个最小权可k-单圈划分的支撑子图，以及对一个不存在k-单圈划分支撑子图的图，如何添最少的边使得它有k-单圈划分的支撑子图。     

Performance of two-disk partition data allocations

In this paper, we present a method, called the partition data allocation method, to allocate a set of data into a multi-disk system. Using the partition data allocation method, we shall show that, in a two-disk system, the performance is influenced by how we disperse similar data onto different disks.     

Feasible partition problem in reverse convex and convex mixed-integer programming

In this paper we consider the consistent partition problem in reverse convex and convex mixed-integer programming. In particular we will show that for the considered classes of convex functions, both integer and relaxed systems can be partitioned into two disjoint subsystems, each of which is consistent and defines an unbounded region. The polynomial time algorithm to generate the partition will be proposed and the algorithm for a maximal partition will also be provided.     

Rook placements and cellular decomposition of partition varieties

In this paper, we study the geometric implication of rook length polynomials introduced in the author's thesis. We introduce the idea of partition varieties. These are certain algebraic varieties which have CW-complex structures. We prove that the cell structure of a partition variety is in one-to-one correspondence with rook placements on a Ferrers board defined by a corresponding partition. This correspondence enables one to characterize the geometric attachment between a cell and the closure of another cell combinatorially. The main result of this paper is that the Poincaré polynomial of cohomology for a partition variety is given by the corresponding rook length polynomial.

This paper serves as a transition of our studies from combinatorial aspects to the geometric aspects. To make the transition accessible, we give three appendices on the known results on Grassmann manifolds and flag manifolds which are used frequently. One appendix is on a technical lemma on embeddings of manifolds.     

Convex decompositions of fuzzy partitions

In this paper we investigate some algebraic and geometric properties of fuzzy partition spaces (convex hulls of hard or conventional partition spaces). In particular, we obtain their dimensions, and describe a number of algorithms for effecting convex decompositions. Two of these are easily programmable, and each affords a different insight about data structures suggested by the fuzzy partition decomposed. We also show how the sequence of partitions in any convex decomposition leads to a matrix for which the norm of the corresponding coefficient vector equals a scalar measure of partition fuzziness used with certain fuzzy clustering algorithms.     

On the Brownian-directed polymer in a Gaussian random environment

In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment. Some further developments, concerning some concentration inequalities for the partition function, are given for the weak disorder regime.     

Sortability of Multi-partitions

Recently, the theory of sortability of partition property has been shown to be an effective tool to prove the existence of an optimal partition with that property. In this paper, we extend the theory to multi-partition where the partition is on t types of components. We apply our results to settle an optimal assignment problem whose proof was incomplete as given in the literature.     

On the inverse problem of minimum spanning tree with partition constraints

In this paper we first discuss the properties of minimum spanning tree and minimum spanning tree with partition constraints. We then concentrate on the inverse problem of minimum spanning tree with partition constraints in which we need to adjust the weights of the edges in a network as less as possible so that a given spanning tree becomes the minimum one among all spanning trees that satisfy the partition restriction. Based on the calculation of maximum cost flow in networks, we propose a strongly polynomial algorithm for solving the problem.The author gratefully acknowledges the partial support of Croucher Foundation.     

强度m的对称正交表的递归构造

本文证明了Q~n空间的正交分划的存在性,对2水平正交表的递归构造方法进行了改进,通过对正交分划的构造提出了任意强度的高水平对称正交表的递归构造方法.     

n圈中辐图的团覆盖数和团划分数

本文主要讨论 Petersen图的一类推广图—— n圈中辐图的团覆盖数和团划分数 ,由此得出该图的团覆盖数和团划分数相等的结论 ,同时给出了其在不同情况下的计算公式 .