n阶4、5度循环图的计数

将所有ｎ阶４度连通循环图所构成的集合记为Ｇ＿ｎ，Ｇ＿ｎ的元素个数记为｜Ｇ＿ｎ｜。文中首先导出了｜Ｇ＿ｎ｜的计算公式。然后将Ｇ＿ｎ中的图按图的同构关系分为一些等价类，进一步再将所有等价类按一定规则划分为Ⅰ型和Ⅱ型。记Ⅰ型等价类的个数为Ｔ，文中证明了ｎ阶４度不同构的连通循环图的个数有Ｔ个（当ｍ为偶时Ｔ为０），其中ｍ为小于ｎ且与ｎ互素的正整数个数的一半。同时文中也给出了ｎ阶５度不同构的连通循环图的类似的计算公式。     

关于隐数法解(BIP)时的分枝与定界

讨论了隐数法解0-1规划(BIP)时的分枝与定界准则.运用这些准则可提高求解(BIP)的效率.     

一类循环图的计数(英文)

讨论了 ４度循环图的结构。所有ｎ阶４度非同构的连通循环图被分为两类： Ⅰ类和Ⅱ类。给出了计算Ⅰ类循环图的计算公式,改进了关于ｎ阶４度非同构的循环图的计数公式。     

Optimal selection and ordering of columns in supersaturated designs

Two methods to select columns for assigning factors to work on supersaturated designs are proposed. The focus of interest is the degree of non-orthogonality between the selected columns. One method is the exhaustive enumeration of selections of p columns from all k columns to find the exact optimality, while the other is intended to find an approximate solution by applying techniques used in the corresponding analysis, aiming for ease of use as well as a reduction in the large computing time required for large k with the first method. Numerical illustrations for several typical design matrices reveal that the resulting “approximately” optimal assignments of factors to their columns are exactly optimal for any p. Ordering the columns in E(s²)-optimal designs results in promising new findings including a large number of E(s²)-optimal designs.     

A Probability theory of hierarchic clustering using random dendrograms

It is widely recognized that a major, current problem in cluster analysis is that of validating results. This paper looks at one possible approach to the validation of results. It considers the structure of (unlabelled) dendrograms and proposes a model of random dendrograms. Algorithms for calculating the probability distribution of a coefficient of structure of a dendrogram are discussed, —both by enumeration of distinct dendrograms, and by Monte Carlo generation of dendrograms     

A Note on Independent and Exhaustive Events

In this article, we show that a finite collection of independent events cannot be exhaustive except in the trivial case in which one of the events occurs with probability one. For an infinite collection of events, however, exhaustiveness need not preclude independence. Illustrative examples are provided.     

A Two‐Queue Polling Model with Regularly Varying Service and/or Switchover Times

Abstract

We consider the cyclic polling system with two queues. One queue is severed according to the exhaustive discipline, and the other queue is served according to the 1‐limited discipline. At least one of the service and/or switchover times has a regularly varying tail. We obtain the tail behavior of the waiting time distributions. When one of the service and/or switchover times has an infinite second moment, we derive the heavy‐traffic behavior of the waiting time distribution at the 1‐limited queue.     

Skew Dyck paths,area, and superdiagonal bargraphs

Skew Dyck paths are a generalization of ordinary Dyck paths, defined as paths using up steps  U=(1,1)$U=(1,1)$, down steps  D=(1,-1)$D=(1,-1)$, and left steps  L=(−1,-1)$L=(-1,-1)$, starting and ending on the x-axis, never going below it, and so that up and left steps never overlap. In this paper we study the class of these paths according to their area, extending several results holding for Dyck paths. Then we study the class of superdiagonal bargraphs, which can be naturally defined starting from skew Dyck paths.     

Characterizing the reconstruction and enumerating the patterns of DNA sequences with repeats

A repeat in a DNA sequence is a substring that appears more than once. In DNA sequencing, the occurrence of repeats may hinder the unique reconstruction. In addition, the number of possible reconstructions depends on the pattern of repeats in a DNA sequence. Arratia et al. studied the patterns of DNA sequences with twofold repeats that result in k-way reconstructions. In this paper, multiple-fold repeats, including twofold repeats, are considered. For each pattern of DNA repeats, the possible reconstructions of the DNA sequence are enumerated by its reduced digraph. Then the reconstructions of DNA sequences with repeats are characterized using the pattern graphs. Finally, for DNA sequences with n repeats, the patterns of DNA repeats resulting in k-way reconstruction are enumerated. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.