A new infinite family of minimally nonideal matrices

Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on the possible cores of minimally nonideal matrices. This paper disproves their conjecture by constructing a new infinite family of square minimally nonideal matrices. In particular, we show that there exists a minimally nonideal matrix with r ones in each row and column for any r?3.     

A new element for analyzing large deformation of thin Naghdi shell model. Part II: Plastic

In this paper a new element is developed that is based on Cosserat theory. In the finite element implementation of Cosserat theory shear locking can occur, especially for very thin shells. In the present investigation the director vector is constrained to remain perpendicular to the mid surface during deformation. It will be shown that this constraint yields accurate results in very large deformation of thin shells also the rate of convergency is very good. For plastic formulation, the model introduced by Simo is used and it has been reduced for constrained director vector and the consistent elasto-plastic tangent moduli is extracted for finite element solution. This model includes both kinematic and isotropic hardening. For numerical investigations an isoparametric nine node element is employed then by linearization of the principle of virtual work, material and geometric stiffness matrices are extracted. The validity and the accuracy of the proposed element is illustrated by the numerical examples and the results are compared with those available in the literature.     

The minmax regret gradual covering location problem on a network with incomplete information of demand weights

The gradual covering location problem seeks to establish facilities on a network so as to maximize the total demand covered, allowing partial coverage. We focus on the gradual covering location problem when the demand weights associated with nodes of the network are random variables whose probability distributions are unknown. Using only information on the range of these random variables, this study is aimed at finding the “minmax regret” location that minimizes the worst-case coverage loss. We show that under some conditions, the problem is equivalent to known location problems (e.g. the minmax regret median problem). Polynomial time algorithms are developed for the problem on a general network with linear coverage decay functions.     

有关拓扑学与覆盖粗糙集的一些结论

引入了拓扑覆盖的概念,并结合最小描述元对有限论域上的拓扑覆盖加于研究,得出了拓扑覆盖的最简覆盖和基与最小描述元之间的关系.介绍了在基于有限论域U上的覆盖,构造U上的一个拓扑的方法.并且在最小描述元的基础上将划分下的粗糙隶属函数推广至一般覆盖下的粗糙隶属函数,而后介绍了其相关运用.     

Simulation of beam plastic forming with variable bending moments

A versatile generic elastic/plastic moment/curvature equation is used to simulate beam deflections. Solutions are obtained numerically and used to investigate whether forming equations based on the assumption of pure bending can be extended in a rational way to more complicated loadings. It is concluded that the answer is affirmative, with only knowledge of the elastic/plastic behavior associated with pure bending and the elastic behavior associated with the actual loading being needed to make the extension.     

Hoek–Brown criterion applied to circular tunnel using elastoplasticity and in situ axial stress

Based on the nonlinear Hoek–Brown failure criterion, elastoplastic analytical solutions are developed for the elastoplastic stresses, strains and plastic zones around a circular tunnel subjected to different value of the axial in situ stress. Effects of the transverse in situ stress, the axial in situ stress and the strength parameters of rock masses on the elastoplastic stresses, strains and plastic zones in the surrounding rock masses are investigated. It is found from the numerical results that the stresses, strains, and plastic zones in the surrounding rock depend not only on the transverse in situ stress but also on the axial in situ stress as well as the mechanical parameters of rock masses.     

Generalized covering designs and clique coverings

Inspired by the “generalized t‐designs” defined by Cameron [P. J. Cameron, Discrete Math 309 (2009), 4835–4842], we define a new class of combinatorial designs which simultaneously provide a generalization of both covering designs and covering arrays. We then obtain a number of bounds on the minimum sizes of these designs, and describe some methods of constructing them, which in some cases we prove are optimal. Many of our results are obtained from an interpretation of these designs in terms of clique coverings of graphs. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:378‐406, 2011     

覆盖近似空间的连续与同胚映射

利用一般映射研究了覆盖近似空间的一些性质,并证明了一些结论.接着定义了覆盖空间的粗糙连续映射及粗糙同胚映射.最后在覆盖粗糙连续映射和覆盖粗糙同胚映射的条件下,研究了两个覆盖近似空间的有关性质,进而在某种程度上为覆盖近似空间的分类提供了理论依据.     

Circulant Double Coverings of a Circulant Graph of Valency Four

Several isomorphism classes of graph coverings of a graph G have been enumerated by many authors (see [3], [8]–[15]). A covering of G is called circulant if its covering graph is circulant. Recently, the authors [4] enumerated the isomorphism classes of circulant double coverings of a certain kind, called typical, and showed that no double covering of a circulant graph of valency 3 is circulant. In this paper, the isomorphism classes of connected circulant double coverings of a circulant graph of valency 4 are enumerated. As a consequence, it is shown that no double covering of a non-circulant graph G of valency 4 can be circulant if G is vertex-transitive or G has a prime power of vertices. The first author is supported by NSF of China (No. 60473019) and by NKBRPC (2004CB318000), and the second author is supported by Com²MaC-KOSEF (R11-1999-054) in Korea.