近于凸函数新子类的偏差定理和卷积性质

引进了近于凸函数的新子类.利用从属关系得到了偏差定理和卷积性质.所得结果推广了一些作者的相关结果,并得到有趣的新结果.     

关于广义Muirhead平均的Schur幂凸性

对广义Muirhead平均的Schur-幂凸性进行了讨论,给出了判定Muirhead平均的Schur-幂凸性的充要条件.结果改进了Chu和Xia在相关文献中的主要结果,Chu和Xia的结果是结果的特例.     

■混合序列加权和的强稳定性(英文)

本文给出了■混合序列加权和的强稳定性的一些结果,同时也给出了■混合序列的强大数定律的若干新结果,这些结果推广了独立随机变量序列的相应结果.     

提示信息特征对秘书问题决策影响的仿真实验研究

针对具有提示信息的秘书问题,首先分析了提示信息特征变化对决策结果的可能影响.然后在此基础上,提出了在最大值标杆策略下研究提示信息的变化特征对决策结果的影响,接着阐述了仿真试验的理论假设和设计,通过仿真试验考察了提示信息的不同变化对仿真结果的影响;最后给出了对仿真结果的分析和探讨,仿真结果验证了理论假设的判断.     

NOD序列加权和的强收敛速度

该文研究了NOD序列加权和的强收敛速度, 获得了一些新的完全收敛性的结果. 该文的结果推广了陈瑞林$^{[1]}$在NA情形时的结果,部分推广了Stout$^{[2]}$在独立同分布情形时的结果.     

NOD随机变量随机加权部分和的完全收敛性

本文研究了NOD随机变量双下标随机加权部分和的完全收敛性,获得了一些完全矩收敛结果和完全收敛结果,从而获得了Marcinkiewicz-Zygmund型强大数律.我们的结果推广了目前已有的一些结论.进一步,我们给出一些数据模拟工作来展示收敛性结果.     

一类奇异非线性两点边值问题的 Galerkin 解的误差估计

本文对一类奇异两点边值问题采用了对称的Galerkin方法.通过利用Green函数,对线性问题得到了拟最优的最大范数误差估计并将这一结果推广到了非线性问题.本文最后列举了一些数值试验结果,这些结果很好地验证了理论结果.     

一类具有时滞和反馈控制的非线性离散模型的持久性

研究了一类具有时滞和反馈控制的非线性单种群离散模型的持久性,获得了该系统持久的充分条件,并通过例子表明结果的可行性,所得结果推广了已有文献的相关结果.     

$\sigma$-$C^$-代数上的完全正映射\\[2mm]和 Stinespring 型扩张定理

研究了σ-C-代数上的完全正映射,获得了共变形式的Stinespring型扩张定理等 一系列结果.所得结果推广和改进了某些已有的结果.     

拓扑有限交性质及极大极小定理*

本文研究了更一般的拓扑有限交的性质。作为应用,利用本文结果给出了更一般的极大极小定理。本文结果推广了[5,6,9]中的主要结果。     

Mixtures of Global and Local Edgeworth Expansions and Their Applications

Edgeworth expansions which are local in one coordinate and global in the rest of the coordinates are obtained for sums of independent but not identically distributed random vectors. Expansions for conditional probabilities are deduced from these. Both lattice and continuous conditioning variables are considered. The results are then applied to derive Edgeworth expansions for bootstrap distributions, for Bayesian bootstrap distribution, and for the distributions of statistics based on samples from finite populations. This results in a unified theory of Edgeworth expansions for resampling procedures. The Bayesian bootstrap is shown to be second order correct for smooth positive “priors,” whenever the third cumulant of the “prior” is equal to the third power of its standard deviation. Similar results are established for weighted bootstrap when the weights are constructed from random variables with a lattice distribution.     

Advanced greedy algorithms and surrogate constraint methods for linear and quadratic knapsack and covering problems

New variants of greedy algorithms, called advanced greedy algorithms, are identified for knapsack and covering problems with linear and quadratic objective functions. Beginning with single-constraint problems, we provide extensions for multiple knapsack and covering problems, in which objects must be allocated to different knapsacks and covers, and also for multi-constraint (multi-dimensional) knapsack and covering problems, in which the constraints are exploited by means of surrogate constraint strategies. In addition, we provide a new graduated-probe strategy for improving the selection of variables to be assigned values. Going beyond the greedy and advanced greedy frameworks, we describe ways to utilize these algorithms with multi-start and strategic oscillation metaheuristics. Finally, we identify how surrogate constraints can be utilized to produce inequalities that dominate those previously proposed and tested utilizing linear programming methods for solving multi-constraint knapsack problems, which are responsible for the current best methods for these problems. While we focus on 0–1 problems, our approaches can readily be adapted to handle variables with general upper bounds.     

计算科学与工程本科及研究生教育的思考与实践

介绍一门新兴学科——计算科学与工程 (CSE) ,讨论该学科的本科与研究生教育的培养目标、课程设置、创新素质等 ,提出了计算科学与工程教育的几种培养模式 ,总结了本科、研究生教学实践的经验     

Antibandwidth and cyclic antibandwidth of meshes and hypercubes

The antibandwidth problem consists of placing the vertices of a graph on a line in consecutive integer points in such a way that the minimum difference of adjacent vertices is maximised. The problem was originally introduced in [J.Y.-T. Leung, O. Vornberger, J.D. Witthoff, On some variants of the bandwidth minimisation problem, SIAM Journal of Computing 13 (1984) 650-667] in connection with the multiprocessor scheduling problems and can also be understood as a dual problem to the well-known bandwidth problem, as a special radiocolouring problem or as a variant of obnoxious facility location problems. The antibandwidth problem is NP-hard, there are a few classes of graphs with polynomial time complexities. Exact results for nontrivial graphs are very rare. Miller and Pritikin [Z. Miller, D. Pritikin, On the separation number of a graph, Networks 19 (1989) 651-666] showed tight bounds for the two-dimensional meshes and hypercubes. We solve the antibandwidth problem precisely for two-dimensional meshes, tori and estimate the antibandwidth value for hypercubes up to the third-order term. The cyclic antibandwidth problem is to embed an n-vertex graph into the cycle C_n, such that the minimum distance (measured in the cycle) of adjacent vertices is maximised. This is a natural extension of the antibandwidth problem or a dual problem to the cyclic bandwidth problem. We start investigating this invariant for typical graphs and prove basic facts and exact results for the same product graphs as for the antibandwidth.     

Summability and estimates for polynomials and multilinear mappings

In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on ?_p spaces in fact hold true for mappings on arbitrary Banach spaces.     

Zeros of Gegenbauer and Hermite polynomials and connection coefficients

In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

     

Multivariate analysis using ‘and’ and ‘or’

The connectives ‘and’ and ‘or’ are potentially useful in multivariate analysis and theory construction. They are simple, logical ways to connect two or more variables together. However, until recently there has been no framework for operationalizing these connectives for continuous variables, and this lack has severely limited their use. Using fuzzy set theory as a basis for such a framework, this paper lays out the necessary tools and models to permit the use of ‘and’ and ‘or’ in multivariate analysis.Section 1 introduces conventional operators for ‘and’ and ‘or’, and Section 2 provides suitable extensions and generalizations of them. Section 3 sets out the required least-squares techniques for fitting these generalized operators to data, first in the context of ANOVA problems and then in regression contexts, for single-connective (three-variable) models. The theoretical developments and examples from real data-sets demonstrate the utility of ‘and’ and ‘or’ as a means to cell-specific interpretations of interaction effects which can also readily be translated into English. Section 4 extends these developments to multivariate, multiple-connective models and discusses issues of generalizability. The paper concludes (Section 5) with a brief discussion of remaining unsolved problems, future prospects for more sophisticated models, and computer programs.     

Strategic defense and attack for series and parallel reliability systems

A system of independent components is defended by a strategic defender and attacked by a strategic attacker. The reliability of each component depends on how strongly it is defended and attacked, and on the intensity of the contest. In a series system, the attacker benefits from a substitution effect since attacker benefits flow from attacking any of the components, while the defender needs to defend all components. Even for a series system, when the attacker is sufficiently disadvantaged with high attack inefficiencies, and the intensity of the contest is sufficiently high, the defender earns maximum utility and the attacker earns zero utility. The results for the defender (attacker) in a parallel system are equivalent to the results for the attacker (defender) in a series system. Hence, the defender benefits from the substitution effect in parallel systems. With budget constraints the ratio of the investments for each component, and the contest success function for each component, are the same as without budget constraints when replacing the system values for the defender and attacker with their respective budget constraints.     

Criteria for quasi-convexity and pseudo-convexity: Relationships and comparisons

A first order criterion for pseudo-convexity and second order criteria for quasi-convexity and pseudo-convexity are given for twice differentiable functions on open convex sets. The relationships between these second order criteria and other known criteria are also analysed. Finally, the numbers of operations required to verify these criteria are calculated and compared.This research was supported by the Natural Sciences and Engineering Research Council Canada, Grant no. A8312, and by NATO Research Grant no. 1934.     

Necessary and Sufficient Conditions for Mcshane’s Identity and Variations

Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γ to SL(2,C), this was further generalized by the authors to obtain sufficient conditions for a generalized McShane’s identity to hold for arbitrary (not necessarily type-preserving) non-reducible representations in Tan et al. (Submitted). Here we extend the above by giving necessary and sufficient conditions for the generalized McShane identity to hold (Akiyoshi, Miyachi and Sakuma had proved it for type-preserving representations). We also give a version of Bowditch’s variation of McShane’s identity to once-punctured torus bundles, in the case where the monodromy is generated by a reducible element, and provide necessary and sufficient conditions for the variations to hold.