具有联盟结构的position值

position值是图对策中著名的分支有效解, 该值充分体现了图的边在合作中的贡献, 因而也可作为网络中心性的一种测度方法。本文基于van den Brink等提出的具有联盟结构与图结构的合作对策, 将position值推广到具有联盟结构的图对策上, 提出了具有联盟结构的position值, 该值可以作为受优先联盟约束的网络中心性的一种测度方法。本文首先证明了具有联盟结构的position值可以由分割分支有效性和平衡边贡献性所唯一刻画。其次, 以跨国天然气管道网的收益分配为例, 对这个值与其他值做了比较分析。     

具有实谱值的四元数矩阵的谱值估计

本文给出了具有实谱值的四元数矩阵的定义，得到了一些具有实谱值的四元数矩阵的谱值不等式，这些不等式只涉及到了四元数矩阵的迹的实部和它的平方的迹的实部。     

一种具有不同形式效用值的群决策方法

研究了具有实数值、区间数和语言短语等三种形式效用值信息的群决策问题．首先给出了具有不同形式效用值的群决策问题的描述；然后给出了具有三种形式效用值的群决策方法的计算步骤．在该方法中，将不同形式的效用值均转化为区间数形式的效用值，通过加权法则得到每个方案的区间数群体综合效用值，并依据群体综合效用值进行方案的排序．最后通过给出一个算例说明了本给出的方法．     

具有图限制通信结构对策的有效Owen值

Owen图值是著名的Owen值在具有图通信结构合作对策上的推广,它具有分支有效性,但失去了有效性.有效性要求在合作对策中产生的总财富恰好分配给参与的所有成员.本文提出具有有效性的Owen图值,并给出这个有效Owen图值的3种公理化刻画.最后,通过应用算例,对该值与其他值做了比较分析.     

Banach空间中一类具阻尼的二阶微分包含的可控性

主要研究了Banach空间一类具有阻尼项的二阶微分包含的可控性,利用集值映射不动点定理,讨论了集值函数取凸值的情况,给出了微分包含可控性的充分条件.     

基于区间与模糊Shapley值的合作收益分配策略

将经典Shapley值三条公理进行拓广,提出具有模糊支付合作对策的Shapley值公理体系。研究一种特殊的模糊支付合作对策,即具有区间支付的合作对策,并且给出了该区间Shapley值形式。根据模糊数和区间数的对应关系,提出模糊支付合作对策的Shapley值,指出该模糊Shapley值是区间支付模糊合作对策的自然模糊延拓。结果表明:对于任意给定置信水平α,若α=1,则模糊Shapley值对应经典合作对策的Shapley值,否则对应具有区间支付合作对策的区间Shapley值。通过模糊数的排序,给出了最优的分配策略。由于对具有模糊支付的合作对策进行比较系统的研究,从而为如何求解局中人参与联盟程度模糊化、支付函数模糊化的合作对策,奠定了一定的基础。     

函数的介值性与连续性

本文指出一个具有介值性而处处间断的函数,给出了具有介值性的函数连续的充分条件与充要条件。     

具有图结构和联盟结构的Banzhaf值及应用

Banzhaf值是经典可转移效用合作对策中一个著名的分配规则,可以用来评估参与者在对策中的不同作用。本文将Banzhaf值推广到具有联盟结构和图结构的TU-对策中,首先提出并定义了具有联盟结构和图结构的Banzhaf值(简称PL-Banzhaf值),证明了PL-Banzhaf值满足公平性、平衡贡献性和分割分支总贡献性,并给出了该值的两种公理性刻画。其次,讨论了PL-Banzhaf值在跨国天然气管道案例中的应用,并和其他分配规则进行了比较分析。     

具有控制结构的集值强向量均衡问题的稳定性

研究了具有控制结构的集值强向量均衡问题.通过Ky Fan截口定理得到了具有控制结构的集值强向量均衡问题解的存在性定理.并在映射满足一定条件的基础上,得到了集值强向量均衡问题所构成的空间M中,大多数(在Baire分类意义下)强向量均衡问题解集是稳定的.     

具有区间联盟值n人对策的Shapley值

本文提出了一类具有区间联盟收益值n人对策的Shapley值.利用区间数运算有关理论,通过建立公理化体系,对具有区间联盟收益值n人对策的Shapley值进行深入研究,证明了这类n人对策Shapley值存在性与唯一性,并给出了此Shapley值的具体表达式及一些性质.最后通过一个算例检验了其有效性与正确性.     

An algorithm for constructing star-shaped drawings of plane graphs

A straight-line planar drawing of a plane graph is called a convex drawing if every facial cycle is drawn as a convex polygon. Convex drawings of graphs is a well-established aesthetic in graph drawing, however not all planar graphs admit a convex drawing. Tutte [W.T. Tutte, Convex representations of graphs, Proc. of London Math. Soc. 10 (3) (1960) 304–320] showed that every triconnected plane graph admits a convex drawing for any given boundary drawn as a convex polygon. Thomassen [C. Thomassen, Plane representations of graphs, in: Progress in Graph Theory, Academic Press, 1984, pp. 43–69] gave a necessary and sufficient condition for a biconnected plane graph with a prescribed convex boundary to have a convex drawing.In this paper, we initiate a new notion of star-shaped drawing of a plane graph as a straight-line planar drawing such that each inner facial cycle is drawn as a star-shaped polygon, and the outer facial cycle is drawn as a convex polygon. A star-shaped drawing is a natural extension of a convex drawing, and a new aesthetic criteria for drawing planar graphs in a convex way as much as possible. We give a sufficient condition for a given set A of corners of a plane graph to admit a star-shaped drawing whose concave corners are given by the corners in A, and present a linear time algorithm for constructing such a star-shaped drawing.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.     

On arithmetic Macaulayfication of Noetherian rings

The Rees algebra is the homogeneous coordinate ring of a blowing-up. The present paper gives a necessary and sufficient condition for a Noetherian local ring to have a Cohen-Macaulay Rees algebra: A Noetherian local ring has a Cohen-Macaulay Rees algebra if and only if it is unmixed and all the formal fibers of it are Cohen-Macaulay. As a consequence of it, we characterize a homomorphic image of a Cohen-Macaulay local ring. For non-local rings, this paper gives only a sufficient condition. By using it, however, we obtain the affirmative answer to Sharp's conjecture. That is, a Noetherian ring having a dualizing complex is a homomorphic image of a finite-dimensional Gorenstein ring.

     

Novel method of identifying time series based on network graphs

In this article, we propose a novel method for transforming a time series into a complex network graph. The proposed algorithm is based on the spatial distribution of a time series. The characteristics of geometric parameters of a network represent the dynamic characteristics of a time series. Our algorithm transforms, respectively, a constant series into a fully connected graph, periodic time series into a regular graph, linear divergent time series into a tree, and chaotic time series into an approximately power law distribution network graph. We find that when the dimension of reconstructed phase space increases, the corresponding graph for a random time series quickly turns into a completely unconnected graph, while that for a chaotic time series maintains a certain level of connectivity. The characteristics of the generated network, including the total edges, the degree distribution, and the clustering coefficient, reflect the characteristics of the time series, including diverging speed, level of certainty, and level of randomness. This observation allows a chaotic time series to be easily identified from a random time series. The method may be useful for analysis of complex nonlinear systems such as chaos and random systems, by perceiving the differences in the outcomes of the systems—the time series—in the identification of the systemic levels of certainty or randomness. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Characterizations of g-frames and g-Riesz bases in Hilbert spaces

In this paper, we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space, which will play a key role in studying g-frames and g-Riesz bases etc. Using the pre-frame operator Q, we give some necessary and sufficient conditions for a g-Bessel sequence, a g-frame, and a g-Riesz basis in a complex Hilbert space, which have properties similar to those of the Bessel sequence, frame, and Riesz basis respectively. We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis. Lastly, we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.     

覆盖数不超过3的图上渡河问题

1000多年前,英国著名学者Alcuin曾提出一个古老的渡河问题,即狼、羊和卷心菜的渡河问题。2006年,Prisner把该问题推广到任意的冲突图上,考虑了一类情况更一般的渡河运输问题。所谓冲突图是指一个图G=(V,E),这里V代表某些物品的集合,V中的两个点有边连结当且仅当这两个点是冲突的,即在无人监管的情况下不允许留在一起的点。图G=(V,E)的一个可行运输方案是指在保证不发生任何冲突的前提下,把V的点所代表的物品全部摆渡到河对岸的一个运输方案。图G的Alcuin数定义为它存在可行运输方案时所需船的最小容量。本文讨论了覆盖数不超过3的连通图的Alcuin数,给出了该类图Alcuin数的完全刻画。     

An algebraic index theorem for orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann-Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the Kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem.     

Slice theorem and orbit type stratification in infinite dimensions

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which the assumptions of this theorem are fulfilled. First, using Glöckner's inverse function theorem, we show that the linear action of a compact Lie group on a Fréchet space admits a slice. Second, using the Nash–Moser theorem, we establish a slice theorem for the tame action of a tame Fréchet Lie group on a tame Fréchet manifold. For this purpose, we develop the concept of a graded Riemannian metric, which allows the construction of a path-length metric compatible with the manifold topology and of a local addition. Finally, generalizing a classical result in finite dimensions, we prove that the existence of a slice implies that the decomposition of the manifold into orbit types of the group action is a stratification.