Solution of the least squares method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima. This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA K 60480.     

两两NQD列加权和的安全收敛性

本文研究两两NQD系加权和的完全收敛性，证明了一般双下标加权系数的加权部分和的完全收敛性，改进了吴群英（2002）的结果。     

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.     

EXISTENCE OF OPTIMAL STRONG PARTIALLY BALANCED DESIGNS

A strong partially balanced design SPBD（v, b, k; λ,0） whose b is the maximum number of blocks in all SPBD（v, b, k; λ, 0）, as an optimal strong partially balanced design, briefly OSPBD（v, k, λ） is studied. In investigation of authentication codes it has been found that the strong partially balanced design can be used to construct authentication codes. This note investigates the existence of optimal strong partially balanced design OSPBD（v, k, 1） for k = 3 and 4, and shows that there exists an OSPBD（v, k, 1） for any v ≥ k.     

Comparison of structural,thermodynamic, kinetic and mass transport properties of Mg2+ ion models commonly used in biomolecular simulations

The prevalence of Mg²⁺ ions in biology and their essential role in nucleic acid structure and function has motivated the development of various Mg²⁺ ion models for use in molecular simulations. Currently, the most widely used models in biomolecular simulations represent a nonbonded metal ion as an ion‐centered point charge surrounded by a nonelectrostatic pairwise potential that takes into account dispersion interactions and exchange effects that give rise to the ion's excluded volume. One strategy toward developing improved models for biomolecular simulations is to first identify a Mg²⁺ model that is consistent with the simulation force fields that closely reproduces a range of properties in aqueous solution, and then, in a second step, balance the ion–water and ion–solute interactions by tuning parameters in a pairwise fashion where necessary. The present work addresses the first step in which we compare 17 different nonbonded single‐site Mg²⁺ ion models with respect to their ability to simultaneously reproduce structural, thermodynamic, kinetic and mass transport properties in aqueous solution. None of the models based on a 12‐6 nonelectrostatic nonbonded potential was able to reproduce the experimental radial distribution function, solvation free energy, exchange barrier and diffusion constant. The models based on a 12‐6‐4 potential offered improvement, and one model in particular, in conjunction with the SPC/E water model, performed exceptionally well for all properties. The results reported here establish useful benchmark calculations for Mg²⁺ ion models that provide insight into the origin of the behavior in aqueous solution, and may aid in the development of next‐generation models that target specific binding sites in biomolecules. © 2015 Wiley Periodicals, Inc.     

Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data

Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations.     

{Cu3}单分子磁体在磁场中的热纠缠

本文研究单分子磁体Na₉[Cu₃Na₃(H₂O)₉ (α-AsW₉O₃₃)₂]·26H₂O中三角自旋 环在磁场作用下的热纠缠性质, 利用数值计算求出任意两个Cu²⁺离子量子比特之间的配对纠缠度, 分别记为C₁₂, C₂₃和C₁₃. 研究结果表明, 磁场的方向和大小以及温度对配对纠缠度具有重要影响, 而且参数的变化对C₁₂, C₂₃和C₁₃的影响也是各不相同. 给出外加三个不同方向的磁场时, 配对纠缠度C₁₂, C₂₃和C₁₃各自对应的临界温度T_c随磁场强度的变化图, 由此可以得到单分子磁体三角自旋环中存在纠缠态的参数范围. 通过选择适当的磁场方向和大小以及温度等实验参数, 可以有效地调节和提高单分子磁体中的配对纠缠度. 关键词： 配对纠缠 单分子磁体 三角自旋环     

两两独立同分布序列Cesàro强大数定律的收敛速度

设{X,Xn,n≥0}是两两独立同分布的随机变量序列,11．为了证明这一结论而获得到的两两负相关随机变量序列的Cesaro强大数定律收敛速度的结果本身也是有意义的．此结果对于同分布的两两NQD序列也是对的．