调剂问题的Vague指派方法研究

调剂工作是硕士研究生招生录取过程中一项非常重要的工作.论文以硕士研究生调剂工作为例,通过分析基本特征,将其转化为指派问题进行研究.并借助于Vague集思想,运用面试投票的方法获得效益矩阵.根据评价者的不同偏好特征采用记分函数将Vague值转化为实数,得到了实数满意度矩阵.进而不仅实现了学生和录取单位的共赢,也实现了资源的优化配置.该方法一方面为此类问题的解决提供了一种有效途径,另一方面也在理论上找到了Vague指派的一般步骤,通过数据计算保证了该方法在问题解决上的有效性和可行性.     

On critical values of numerical parameters characterizing intersections of embedded sets

To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced, and the relation between the two parameters is examined. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000.     

Subadditive ergodic theorems for random sets in infinite dimensions

We prove pointwise and mean versions of the subadditive ergodic theorem for superstationary families of compact, convex random subsets of a real Banach space, extending previously known results that were obtained in finite dimensions or with additional hypotheses on the random sets. We also show how the techniques can be used to obtain the strong law of large numbers for pairwise independent random sets, as well as results in the weak topology.     

Decomposition and integral representation of Cauchy interactions associated with measures

Received May 29, 2000 / Published online June 1, 2001     

Detecting and imaging dielectric objects from real data: A shape-based approach

In this paper we investigate the performance of a shape-reconstruction technique as tested on the ‘Marseille data’. This approach, which is based on a level set technique, offers several advantages compared to other approaches, as for example well-defined boundaries and the incorporation of an intrinsic regularization in the form of a priori assumptions regarding the general structures in the medium. The level set strategy (which is an implicit representation of the shapes) frees us from topological restrictions during this reconstruction process. Our algorithm is aiming at, not only detecting the objects, but simultaneously determining their approximate locations, sizes and dielectric properties. The numerical experiments show the utility of this method.     

An analysis of the size of the minimum dominating sets in random recursive trees, using the Cockayne-Goodman-Hedetniemi algorithm

A random recursive tree on n vertices is either a single isolated vertex (for n=1) or is a vertex v_n connected to a vertex chosen uniformly at random from a random recursive tree on n−1 vertices. Such trees have been studied before [R. Smythe, H. Mahmoud, A survey of recursive trees, Theory of Probability and Mathematical Statistics 51 (1996) 1-29] as models of boolean circuits. More recently, Barabási and Albert [A. Barabási, R. Albert, Emergence of scaling in random networks, Science 286 (1999) 509-512] have used modifications of such models to model for the web and other “power-law” networks.A minimum (cardinality) dominating set in a tree can be found in linear time using the algorithm of Cockayne et al. [E. Cockayne, S. Goodman, S. Hedetniemi, A linear algorithm for the domination number of a tree, Information Processing Letters 4 (1975) 41-44]. We prove that there exists a constant d?0.3745… such that the size of a minimum dominating set in a random recursive tree on n vertices is dn+o(n) with probability approaching one as n tends to infinity. The result is obtained by analysing the algorithm of Cockayne, Goodman and Hedetniemi.     

On the sharpness of two-sided bounds for the Perron Root and of the related eigenvalue inclusion sets

The paper considers the sharpness problem for certain two-sided bounds for the Perron root of an irreducible nonnegative matrix. The results obtained are applied to prove the sharpness of the related eigenvalue inclusion sets in classes of matrices with fixed diagonal entries, bounded above deleted absolute row sums, and a partly specified irreducible sparsity pattern.     

Lot-sizing on a tree

For the problem of lot-sizing on a tree with constant capacities, or stochastic lot-sizing with a scenario tree, we present various reformulations based on mixing sets. We also show how earlier results for uncapacitated problems involving (Q,S_Q) inequalities can be simplified and extended. Finally some limited computational results are presented.     

An interdependency index for the outputs of uncertain systems

The study of mechanical systems with uncertain parameters is gaining increasing interest in the field of system analysis to provide an expedient model for the prediction of the system behavior. Making use of the Transformation Method, the uncertain parameters of the system are modeled by fuzzy numbers in contrast to random numbers used in stochastic approaches. As a result of this analysis, a quantification of the overall uncertainty of the system outputs, including a worst-case scenario, is obtained. The inputs of the resulting fuzzy-valued model are a priori uncorrelated but after the uncertainties are propagated through the model, interdependency (or interaction) between the outputs may arise. If such interdependency is neglected, a misinterpretation of the results may occur. For example, in the case of applying uncertainty analysis in the early design phase of a product to determine the relevant design-parameter space, the interdependency between the design variables may reduce significantly the available part of the design space. This paper proposes a measure of interdependency between the uncertain system outputs. The interdependency index can be derived by a postprocessing of the data gained by the analysis with the Transformation Method. Such information can be obtained by a negligible amount of extra computation time.     

模型论简介

本文将模型论介绍为“可定义集的数学”．首先给出“可定义集”的确切定义，并引入处理可定义集的主要工具——一阶公式的概念．然后给出一些例子．最后介绍一些相当于可定义集的组合性质的稳定性理论．