Comments on the Paper: Attacking the Market Split Problem with Lattice Point Enumeration

We present a few comments on the paper Attacking the market split problem with lattice point enumeration by A. Wasserman, published in Journal of Combinatorial Optimization, vol. 6, pp. 5–16, 2002.     

On Combinatorial Approximation of Covering 0-1 Integer Programs and Partial Set Cover

The problems dealt with in this paper are generalizations of the set cover problem, min{cx | Ax b, x {0,1}ⁿ}, where c Q₊ⁿ, A {0,1}^{m × n}, b 1. The covering 0-1 integer program is the one, in this formulation, with arbitrary nonnegative entries of A and b, while the partial set cover problem requires only m–K constrains (or more) in Ax b to be satisfied when integer K is additionall specified. While many approximation algorithms have been recently developed for these problems and their special cases, using computationally rather expensive (albeit polynomial) LP-rounding (or SDP-rounding), we present a more efficient purely combinatorial algorithm and investigate its approximation capability for them. It will be shown that, when compared with the best performance known today and obtained by rounding methods, although its performance comes short in some special cases, it is at least equally good in general, extends for partial vertex cover, and improves for weighted multicover, partial set cover, and further generalizations.     

新时期大学生社团文化活动

高校社团的文化活动是大学生自我教育的第二课堂,是大学生素质拓展的重要环节,是大学生了解社会的重要桥梁.从新时期文化建设的战略意义出发,分析了高校大学生社团的文化活动有待加强的六个方面.并针对以上情况提出了大学生社团活动体现文化先进性要求的对策,即做到"四个结合". 认为,发现新时期大学生杜团文化活动存在的问题并提出相应的是开展社团活动、弘扬先进文化的重要举措之一.     

ROBUSTNESS OF PROCEDURES FOR THE BEHRENS-FISHER PROBLEMS: EXTENSION TO BIVARIATE NORMAL MIXTURES

In the applied sciences, it is often important to be able to compare the mean values of two populations. However, testing a hypothesis can be complex, if the two populations are heteroscedastic and exhibit non-normality in the data. This paper reviews currently available strategies for the multivariate Behrens-Fisher problem. It then carries out Monte Carlo comparisons of selected procedures to assess their robustness when applied to data from normal mixture distributions. The overall conclusion is that Johansen's procedure appears to work best for small sample data both in terms of empirical power and significance level. Johansen's procedure works reasonably well even with mixture data. The simulation also provides researchers with specific guidelines to follow at the early designing and planning stages of the investigation.     

非单调二元非线性算子方程组的迭代求解

利用锥与半序理论和混合单调算子理论 ,讨论 Banach空间中非单调二元非线性算子方程组解的存在性与唯一性 ,并给出收敛于方程组解的迭代序列和误差估计 ,改进和推广了混合单调算子方程和一元算子方程的某些相应结果 .     

克服制约因素 改善听力教学

听是语言学习的重要途径,是从声音信号中获取信息的主要手段。听力直接影响学习者对语言信息的接收和理解。听力的提高常受到一些主客观因素的制约。本文列举了这些不利因素并提出一些消除它们进而改善听力教学的方法。     

一阶常微分方程初值问题的上、下解与拟上下解的存在定理

利用上、下解与拟上下解方法讨论常微分方程问题时，文献均足假没上、下解与拟上下解是存在的，进而讨论方程的解．文章给出一阶常微分方程初值问题的上、下解与拟上下解的存在性定理，为利用上、下解与拟上下解方法讨论一阶常微分方程初值问题提供充分的依据．     

Sequence Independent Lifting in Mixed Integer Programming

We investigate lifting, i.e., the process of taking a valid inequality for a polyhedron and extending it to a valid inequality in a higher dimensional space. Lifting is usually applied sequentially, that is, variables in a set are lifted one after the other. This may be computationally unattractive since it involves the solution of an optimization problem to compute a lifting coefficient for each variable. To relieve this computational burden, we study sequence independent lifting, which only involves the solution of one optimization problem. We show that if a certain lifting function is superadditive, then the lifting coefficients are independent of the lifting sequence. We introduce the idea of valid superadditive lifting functions to obtain good aproximations to maximum lifting. We apply these results to strengthen Balas' lifting theorem for cover inequalities and to produce lifted flow cover inequalities for a single node flow problem.     

国有企业(上市公司)改革的症结与对策

国有企业 (上市公司 )存在的问题如上市公司不规范、法人财产权难以落实、资本功能残缺、内部人控制等是由各种原因促成的。作者认为政府的不适当干预是其症结所在 ,进而提出建立健全证券法规体系 ,推进国家股和法人股的流通 ,规范政府在经济中的行为等治理对策     

非线性波动方程的孤波解及余弦周期波解

利用假设待定法,求出了非线性波动方程的具有双曲正割函数分式形式且渐近值不为零的精确孤波解和余弦函数周期波解,并分别讨论了它们的有界性,揭示了行波波速改变对钟状孤波解与余弦函数周期波解波形变化的影响.