Linear Balanceable and Subcubic Balanceable Graphs*

In Math Program 55(1992), 129–168, Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs that do not contain a cycle of length 4 (also known as linear balanced bipartite graphs), and for balanced bipartite graphs whose maximum degree is at most 3. We in fact obtain results for more general classes, namely linear balanceable and subcubic balanceable graphs. Additionally, we prove that cubic balanced graphs contain a pair of twins, a result that was conjectured by Morris, Spiga, and Webb in ( Discrete Math 310(2010), 3228–3235).     

平衡指数损失函数下的信度保费

在经典的信度保费模型中,得到的信度保费估计均是考虑的是纯保费,然而在保险实务中,保险公司收取的保费不可能是纯保费,必须具有正的安全负荷.在平衡指数损失函数下,研究了多合同的信度保费模型.利用正交投影方法,得到了未来保费的信度估计.最后对估计进行了数值模拟.     

关于两两NQD随机变量部分和强大数律的注记

In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et al. （2013）, and Qiu and Yang （2006） under some weaker conditions.     

关于判断矩阵一致性检验与调整的一个注记

首先分析了判断矩阵不一致形成的原因,认为一个判断矩阵中的不一致是由强矛盾判断,弱矛盾判断,标度离散性,标度有限性共同作用的结果,并通过两个例子指出现有一致性检验与调整方法中存在的问题,最后在已有研究基础上给出了判断矩阵一致性调整的新步骤.     

A bound for Wilson''''s general theorem

Given any set K of positive integers and positive integer λ, let c(K,λ) denote the smallest integer such that v∈B(K,λ) for every integer v≥c(K,λ) that satisfies the congruences λv(v-1)≡0 (mod β(K) and λ(v-1)≡0 (mod α(K)). Let K0 be an equivalent set of K, k and k* be the smallest and the largest integers in K0. We prove that c(K,λ)≤exp exp{Q0}Qo=max{2(2p(ko)2-k2kk)p(ko)4,(Kk242y-k-2)(y2)}, whereand y=k*+k(k-1)+1.     

On a Family of Covering Extended Building Sets

Recently Davis and Jedwab introduced the notion of covering extended building sets to construct abelian difference sets. In this paper we consider a family of covering extended building sets similar to the ones corresponding to Hadamard difference sets and Spence difference sets and derive some numerical restrictions on the parameters.     

Constructions for rotational near resolvable block designs

A (ν, k, k?1) near resolvable block design (NRBD) is r‐rotational over a group G if it admits G as an automorphism group of order (ν?1)/r fixing exactly one point and acting semiregularly on the others. We give direct and recursive constructions for rotational NRBDs with particular attention to 1‐rotational ones. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 157–181, 2001     

Block plan for a fractional 2 m factorial design derived from a 2 r factorial design

Summary For a given fractional 2 ^m factorial (2 ^m -FF) designT, the constitution of a block plan to divideT intok (2 ^r−1<k≦2 ^r ) blocks withr block factors each at two levels is proposed and investigated. The well-known three norms of the confounding matrix are used as measures for determining a “good” block plan. Some theorems concerning the constitution of a block plan are derived for a 2 ^m -FF design of odd or even resolution. Two norms which may be preferred over the other norm are slightly modified. For each value ofN assemblies with 11≦N≦26, optimum block plans fork=2 blocks with block sizes [N/2] andN−[N/2] minimizing the two norms are presented forA-optimal balanced 2⁴-FF designs of resolutionV given by Srivastava and Chopra (Technometrics,13, 257–269).