Linear Clique‐Width for Hereditary Classes of Cographs

The class of cographs is known to have unbounded linear clique‐width. We prove that a hereditary class of cographs has bounded linear clique‐width if and only if it does not contain all quasi‐threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes.     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Condensed Cramer rule for some restricted quaternion linear equations

In this paper, we derive an alternative more condensed Cramer rule for the unique solution of some restricted left and right systems of quaternion linear equations. The findings of this paper extend some known results in the literature.     

A hybrid model for selection of an outsourcing provider

Outsourcing is a good strategy for firms that need to reduce operating costs and improve competitiveness and it is important that firms scientifically select appropriate outsourcing providers. Some efforts have been made to find systematic ways to deal with outsourcing problems, but these efforts incorrectly assumed that the criteria used in the decision process are independent, which is not true in the real world. In this study, we propose a new hybrid multiple criteria decision-making (MCDM) model, which addresses the dependent relationships between the various criteria. The relations-structure among the criteria is built with the aid of the decision-making trial and evaluation laboratory (DEMATEL) method. Decision-makers tend to hold diverse opinions about their preferences due to incomplete information and knowledge, or inherent conflict between various departments. We further used the fuzzy preference programming and the analytic network process (ANP) to form a model for the selection of partners for outsourcing providers. The proposed model can help practitioners improve their decision making process, especially when criteria are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline.     

The rotational dimension of a graph

Given a connected graph G = (N, E) with node weights s∈? and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of G: Find v_i∈?^|N|, i∈N so that distances between adjacent nodes do not exceed prescribed edge lengths, the weighted barycenter of all points is at the origin, and is maximized. In the case of a two‐dimensional optimal solution this corresponds to the equilibrium position of a quickly rotating net consisting of weighted mass points that are linked by massless cables of given lengths. We define the rotational dimension of G to be the minimal dimension k so that for all choices of lengths and weights an optimal solution can be found in ?^k and show that this is a minor monotone graph parameter. We give forbidden minor characterizations up to rotational dimension 2 and prove that the rotational dimension is always bounded above by the tree‐width of G plus one. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:283‐302, 2011     

Trigonometric Widths and Best N-Term Approximations of the Generalized Periodic Besov Classes BΩp,θ

In this paper,we determine the estimates exact in order for the trigonometric widths and the best n-term trigonometric approximations of the generalized classes of periodic functions BΩp,θ in the space Lq for some values of parameters p,q.     

利他偏好下供应链效率和公平度动态演进研究

根据零售商利他偏好信息非对称性和动态演进特征,将零供博弈信息结构分为4个演进过程,采用逆向归纳法求解各个过程中供应链主观效率和客观效率、以"公平熵"计算供应链主观公平度和客观公平度,从主观与客观2个维度分析供应链利他偏好行为对供应链效率和公平度动态演进的影响.通过对比分析得出:信息对称下零售商利他偏好行为不改变供应链利润但会改变各个成员在供应链中的利润分配比例,起到"供应链利润分配机制"的作用;供应链主观效率总是不低于客观效率,供应链主观公平度总是不低于客观公平度;从主观评价供应链能够实现协调且供应链能够兼顾效率和公平.