Stability Properties of Neighbourly Random Polytopes

We introduce a quantitative parameter measuring m-neighbourliness of symmetric convex polytopes in ℝ ^k . We discuss this parameter for random polytopes generated by subgaussian vectors and show its stability properties. Research of P. Mankiewicz was partially supported by KBN Grant no. 1 P03A 015 27. N. Tomczak-Jaegermann holds the Canada Research Chair in Geometric Analysis.     

表面粗糙度的变波矢光散射测量方法的研究

提出了表面粗糙度变波矢光散射测量方法，通过散射光强中心亮点光能量的参数ｌｎ，Ｅ随变化的线性关系来确定粗糙度ｗ，对６块粗糙度不同的硅片背面样品进行了实验测量。     

Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems

When the seats in a parliamentary body are to be allocated proportionally to some given weights, such as vote counts or population data, divisor methods form a prime class to carry out the apportionment. We present a new characterization of divisor methods, via primal and dual optimization problems. The primal goal function is a cumulative product of the discontinuity points of the rounding rule. The variables of the dual problem are the multipliers used to scale the weights before they get rounded. Our approach embraces pervious and impervious divisor methods, and vector and matrix problems.     

Circularly Symmetric Static Metric in Three Dimensions and Its Killing Symmetry

In this note we consider a general three-dimensional circularly symmetric static metric and investigate possible Killing symmetries it possesses.We then summarize the work by addressing Einstein equations and briefly discuss their implications on the energy momentum content of some of the metrics that arise in the process.     

关于2-连通图的哈密顿指数界限的改进

介绍了熊黎明等人所做的对满足h=n-△（G）的2-连通图的哈密顿指数的一个界限，并将这个界限给予改进并证明，而且还对满足条件的2-连通图做了更进一步的刻划.     

Common cyclic vectors for classes of operators having common spanning root spaces

The purpose of this paper is to show that various classes of operators having a common collection of root spaces whose closed linear span equals the entire space have dense sets of common cyclic vectors.     

关于区间数决策矩阵的专家群体判断共识性研究

针对群决策中基于区间数决策矩阵形式偏好信息的专家群体判断共识性问题,提出了一种分析方法.首先,给出了有关区间数的定义及其运算法则;然后,通过定义有关区间数决策矩阵的区间数向量,给出了各个专家与专家群体判断的共识性分析方法,同时,也给出了基于区间数决策矩阵的专家群体判断共识性的判别方法.最后,通过一个算例说明了本文提出的分析方法.     

Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem

We develop ideas to enhance the performance of the variable neighborhood search (VNS) by guiding the search in the shaking phase, and by employing the Skewed strategy. For this purpose, Second Order algorithms and Skewed functions expressing structural differences are embedded in an efficient VNS proposed in the literature for the degree constrained minimum spanning tree problem. Given an undirected graph with weights associated with its edges, the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph, subject to constraints on node degrees. Computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date. We report results showing that the VNS with the proposed strategies improved the best known solutions for all the hardest benchmark instances. Moreover, these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature.     

Local and nonlocal conserved vectors of the system of two-dimensional generalized inviscid Burgers equations

The concept of non-linear self-adjointness for the construction of conservation laws has attracted a lot of interest in recent years. The most noteworthy aspect of it is the likelihood of explicitly constructing the conservation laws for any arbitrary systems of differential equations, in particular for those for which Noether׳s theorem is not applicable. In this study, we shall use both Noether׳s theorem and the non-linear self-adjoint method to construct local and nonlocal conserved vectors of the system of two-dimensional Burgers equations under consideration. The first integrals obtained not only give more credence to obtained results due to their generality with respect to any arbitrary functions of the velocity components but are also independent, nontrivial and infinitely many.     

Conformal Killing Vectors in LRS Bianchi Type V Spacetimes

In this note, we investigate conformal Killing vectors (CKVs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Subject to some integrability conditions, CKVs up to implicit functions of (t,x) are obtained. Solving these integrability conditions in some particular cases, the CKVs are completely determined, obtaining a classification of LRS Bianchi type V spacetimes. The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.