Proof of Toft's Conjecture: Every Graph Containing No Fully Odd K4 is 3-Colorable

A fully odd K₄ is a subdivision of K₄ such that each of the six edges of the K₄ is subdivided into a path of odd length. In 1974, Toft conjectured that every graph containing no fully odd K₄ can be vertex-colored with three colors. The purpose of this paper is to prove Toft's conjecture.     

“动＋个＋……”中“个”的句法语义分析

“个”是使用频率最高的量词,与词类的搭配相当自由。“动 个 ……”中“个”后面的成分既可能是一般的可个称的体词性词语,也可能是抽象的不可个称的体词性词语,还可能是表示动作行为和性质状态的谓词性词语。如果“个”后是一般的可个称的体词性词语,大家一致同意“个”为量词,这时的“个”与其他位置上的“个”无异。可是,如果“个”后是抽象的不可个称的体词性词语或谓词性词语,人们的观点不太一致。作者用普通话、方言和古语相结合、印证的办法,得出“动 个 ……”中“个”后无论是体词性词语还是谓词性词语,“个”都是量词,同时也指出这一位置上的“个”在表意上有别于其他位置上的“个”。     

Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

L-Fuzzy拓扑群的直积

证明了任意一族Ｌ－Ｆｕｚｚｙ拓扑群的直积仍是Ｌ－Ｆｕｚｚｙ拓扑群．研究了Ｌ－Ｆｕｚｚｙ拓扑群的直积的层次结构，揭示了它与分明拓扑群的直积之间的联系     

Estimation of the number of studies with positive trends when studies with negative trends are present

A two-point estimator is proposed for the proportion of studies with positive trends among a collection of studies, some of which may demonstrate negative trends. The proposed estimator is the y-intercept of the secant line joining the points (a, F?(a)) and (b, F?(b)), where F?(p) is the empirical distribution function of p-values from one-tailed tests for positive trend derived from the individual studies. Although this estimator is negatively biased for any choice of the points 0 ≤ a < b ≤ 1, the bias is less than that of the previously proposed one-point estimator defined by setting b = 1. The bias of the two-point estimator is smallest when a and b approach the inflection point of the true distribution function, E [F?(p)]. The utility of the two-point estimator is demonstrated by using it to estimate the number of male-mouse liver carcinogens among carcinogenicity studies conducted by the National Toxicology Program.     

模糊Borda法的缺陷分析及其改进思路

 通过对模糊Borda法的分析，笔者认为该方法在技术处理上偏离了评价的基本思想，根本无法实现将评价值和评价序相结合的初衷。为了实现将两者相结合的目的，本文提出了两个解决思路：利用被评价单位在评价值的差距计算相对位次；或计算名次转换值与评价值的交叉乘积。     

区域微电子技术发展实力综合评价研究

本文运用模糊数学方法,建立了多层次模糊综合评判模型。并根据实际情况选用不同算子,对中国区域微电子技术发展实力进行了综合评价,为有关部门制订微电子技术区域发展政策提供了参考。     

关于分圆域Q(ζ_p)类数的第一因子的行列式表示

设p是奇素数，是分圆域K＝Q（ζp）类数的第一因子。本文运用代数方法证明了：可表成p／2p-2γp与一个元素均为±1的（p-1）／2阶行列式的乘积，上述公式Carlitz和Olson的经典结果。     

局部环上欧氏空间中象对称表为对称的分解

局部环上欧氏几何中 ,正交变换表为对称问题 ,是环上欧氏几何的基本问题之一 .本文探讨的是如何将域上欧氏几何中 ,关于这一问题的结果 ,有效的转到环上来 .