Some Results on the Oberwolfach Problem

The well-known Oberwolfach problem is to show that it is possibleto 2-factorize K_n (n odd) or K_n less a 1-factor (n even) intopredetermined 2-factors, all isomorphic to each other; a fewexceptional cases where it is not possible are known. A completelynew technique is introduced that enables it to be shown thatthere is a solution when each 2-factor consists of k r-cyclesand one (n–kr)-cycle for all n 6kr–1. Solutionsare also given (with three exceptions) for all possible valuesof n when there is one r-cycle, 3 r 9, and one (n–r)-cycle,or when there are two r-cycles, 3 r 4, and one (n–2r)-cycle.     

格点形心问题的若干结果

设n(k)为满足如下条件的最小整数，给定平面上任意n个格点，其中必存在k个点的形心也是格点，文献[4]提出关于确定n(4)的未解问题，本文给出解答n(4)=13，并进一步给出相关的一些问题的结果。     

Some Fixed-Point Results for the Dynamic Assignment Problem

In previous work the authors consider the dynamic assignment problem, which involves solving sequences of assignment problems over time in the presence of uncertain information about the future. The algorithm proposed by the authors provides generally high-quality but non-optimal solutions. In this work, though, the authors prove that if the optimal solution to a dynamic assignment problem in one of two problem classes is unique, then the optimal solution is a fixed point under the algorithm.     

关于带宽极值问题的一些结果

本文研究的问题是确定f(p,B）的值，也就是给定顶点数p和带宽B，求满足最大度不超过B的连通图的最小边数，本文给出了一些f(p,B）的值及相应极图。     

广义Richards-Gilpin-Ayala模型的捕获优化问题

在Richards-Gilpin-Ayala模型的基础上,提出了一类更广泛的数学模型—广义Richards-Gilpin-Ayala模型.进而讨论该模型单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质.在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式.这些结果推广了相关文献中关于Schaefer模型、广义Logistic模型的相应结果.     

有关流水作业问题的若干结果

我们给出有关流水作业问题的若干结果,并讨论有待研究的一些问题．     

华林问题中的一些新结果

设Ｇ（ｋ）为所有充分大的正整数均可表示为不超过ｓ个正整数ｋ次方幂之和的最小ｓ．本文对Ｇ（１２），Ｇ（１３），Ｇ（１９）给出了新的估计．     

The Inverse Resonance Problem for Jacobi Operators

It is proved in this paper that super-exponentially decaying,possibly non-selfadjoint perturbations of the free Jacobi operatorare uniquely determined by the location of all their eigenvaluesand resonances. 2000 Mathematics Subject Classification 39A70,34K29.     

Some New Results on Optimal Codes Over F5

We present some results on almost maximum distance separable (AMDS) codes and Griesmer codes of dimension 4 over over the field of order 5. We prove that no AMDS code of length 13 and minimum distance 5 exists, and we give a classification of some AMDS codes. Moreover, we classify the projective strongly optimal Griesmer codes over F₅ of dimension 4 for some values of the minimum distance.     

Jacobi Polynomials,Weighted Sobolev Spaces and Approximation Results of Some Singularities

In this paper, we give some polynomial approximation results in a class of weighted Sobolev spaces, which are related to the Jacobi operator. We further give some embeddings of those weighted Sobolev spaces into usual ones and into spaces of continuous functions, in order to use the above approximation results in the p‐version (or the spectral method) of some finite or boundary element methods. Finally, two typical examples of the polynomial approximation of some singularities of boundary value problems in polygonal or polyhedral domains are presented.     

Stability of the Inverse Resonance Problem for Jacobi Operators

When the coefficients of a Jacobi operator are finitely supported perturbations of the 1 and 0 sequences, respectively, the left reflection coefficient is a rational function whose poles inside, respectively outside, the unit disk correspond to eigenvalues and resonances. By including the zeros of the reflection coefficient, we have a set of data that determines the Jacobi coefficients up to a translation as long as there is at most one half-bound state. We prove that the coefficients of two Jacobi operators are pointwise close assuming that the zeros and poles of their left reflection coefficients are ??-close in some disk centered at the origin.     

具非线性控制变量的非自治松驰系统时间最优追踪控制问题中的若干结果

本文讨论了一类广义非自治离散松驰系统的时间最优控制问题，将R^n中点曲线的目标约束推广为凸集值函数的超曲线约束．在证明了松驰系统与原系统可达集相等的基础上，得到了最优控制的存在性．由凸集分离定理及终端时间闺值函数方程，我们获得了最大值原理及最优控制时间的确定方法．较之Hamilton方法，本文的条件更一般．离散松驰系统的相关结论可以用于分散控制．     

关于两个伪硬币问题的一些新结果

下面的问题被称为n个外观不可区分硬币的分组测试问题,每个硬币可以是伪硬币或是标准硬币.本文所涉及的问题是:已知一个由n个硬币组成的集合中有两个伪(较重的)硬币,用一台天平以最小的称重次数,从这n个硬币组成的集合中探测出两个伪(较重的)硬币. 我们构造了找出两个伪(较重的)硬币的两个算法,并且这两个算法是最优的.     

The Optimal Scheme of Defective Coin Problem for Model P

ＴｈｅＯｐｔｉｍａｌＳｃｈｅｍｅｏｆＤｅｆｅｃｔｉｖｅＣｏｉｎＰｒｏｂｌｅｍｆｏｒＭｏｄｅｌＰ￥ＬｉｕＷｅｎａｎ；ＤｉｎｇＣｈｅｎｇｊｉｅ（Ｘｉｎｘｉａｎｇ，ＨｅｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｒｅｃｅｎｔｌｙｔｈｅｐｒｏｂ...     

最优炒股问题的动态规划模型

本文运用 Bellman的动态规划方法 ,给出了最优炒股问题的数学模型 ,并对其解进行了分析 .     

概率论中的若干典型问题

总结了概率论中几个典型问题,并列举相关的例题加以佐证.     

紧急疏散中最优抗出错路径选择模型与算法

疏散路径选择是紧急疏散中的重要问题,为了减小疏散人在紧急疏散过程中由于路径选择错误带来的损失,提出一对起讫点间最优抗出错路径选择模型。给出路径出错系数的定义,用以度量疏散人路径选择错误带来的疏散效率损失,并且设计了求解最优抗出错路径的DAE算法,证明该算法的时间复杂度为O（ mn2）。结果表明,选择最优抗出错路径作为疏散路径,能够有效地抵抗由于疏散人路径选择错误带来的损失,对提高突发事件下的疏散效率具有实际意义。