Most balanced minimum cuts

We consider the problem of finding most balanced cuts among minimum st-edge cuts and minimum st-vertex cuts, for given vertices s and t, according to different balance criteria. For edge cuts we seek to maximize . For vertex cuts C of G we consider the objectives of (i) maximizing min{|S|,|T|}, where {S,T} is a partition of V(G)?C with s∈S, t∈T and [S,T]=0?, (ii) minimizing the order of the largest component of G−C, and (iii) maximizing the order of the smallest component of G−C.All of these problems are NP-hard. We give a PTAS for the edge cut variant and for (i). These results also hold for directed graphs. We give a 2-approximation for (ii), and show that no non-trivial approximation exists for (iii) unless P=NP.To prove these results we show that we can partition the vertices of G, and define a partial order on the subsets of this partition, such that ideals of the partial order correspond bijectively to minimum st-cuts of G. This shows that the problems are closely related to Uniform Partially Ordered Knapsack (UPOK), a variant of POK where element utilities are equal to element weights. Our algorithm is also a PTAS for special types of UPOK instances.     

MODELING THE EFFECTS OF URBAN HEAT ISLANDS GENERATED MESOSCALE WIND ON AIR POLLUTION DISPERSION IN A PATCHY ATMOSPHERE

Abstract The paper presents a steady‐state two‐dimensional mathematical model to study the dispersion of air pollutants continuously emitting from a point source in a patchy atmosphere. The first patch, which extends to some downwind distance from the source (present in first patch), is the urban center, whereas the second patch is its adjacent countryside. For simulating the effects of urban heat islands on pollutant distribution, a local mesoscale wind is introduced in the first patch along with the usual large‐scale wind. Keeping in mind the real‐life situations, the meteorological, deposition, and removal parameters are taken to be different in different patches. The concentration of pollutants in both the patches has been computed under different stability conditions of the atmosphere through finite difference scheme. The results of the model show that the urban heat island (mesoscale wind) has a tremendous impact on air pollution distribution, both over the urban center as well as its adjacent countryside (rural). The model solutions also reveal about the concentration distribution of pollutants in different parts of the atmosphere in different atmospheric conditions.     

Soft ordered semigroups

Molodtsov introduced 1999 the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to ordered semigroups. The notions of (trivial, whole) soft ordered semigroup, soft ordered subsemigroup, soft left (right) ideal, and left (right) idealistic soft ordered semigroup are introduced, and various related properties are investigated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

齐次树上三次循环树指标马氏链的强极限定理

首先给出齐次树上三次循环树指标马氏链的定义,利用构造鞅的方法,研究齐次树上三次循环树指标马氏链的强极限定理,并给出其状态及状态序偶发生频率的强大数定律.     

区间效应代数的张量积

本文主要研究了区间效应代数的张量积的结构.证明了[0,]与[0,1]的张量积不是[0,1].     

对硅片上自组装生长的Pentacene薄膜生长机制及其结晶相态的研究

采用热蒸发的方法在硅片衬底上自组装生长的Pentacene薄膜,薄膜在80℃温度下经2 h恒温真空热处理,通过原子力显微镜(AFM)对Pentacene薄膜表面形貌及其生长机制进行研究.结果得到,在硅片上生长的Pentacene薄膜足以台阶岛状结构生长,其岛状直径约为100 nm.且Pentacene分子以垂直于衬底的方向生长,台阶岛状结构中每个台阶的平均高度约为1.54 nnl·s-1,与Pentacene分子的沿长轴方向的长度相近.从Pentacene薄膜的XRD图谱中可以看出,薄膜在形成的过程中会因条件的不同而形成不同的结晶相,分别为薄膜相和三斜体相,且薄膜的结晶相将随着薄膜厚度的增加向三斜体相转变,其临界厚度为80和150 nm,当薄膜大于150 nm时,薄膜的三斜体相占主导地位,而当Pentacene薄膜的厚度小于80 nm时,Pentacene薄膜呈薄膜相存在.     

通过软X射线信号研究芯部等离子体的结构

介绍了如何从软X射线原始信号上分析等离子体芯部磁场结构的方法. 在HT-7托卡马克上,通过分析一炮典型的放电数据,直接从软X射线原始信号上分析了磁岛的位置和旋转方向. 通过软X射线图像反演的结果和Mirnov信号上观察到的m=2模的走向验证了磁岛旋转的方向和位置. 关键词： 软X射线 MHD不稳定性 磁岛     

理论预测晶体表面吸附二维原子岛的形状

提出了凝结势概念用以建立一种预测晶体表面吸附二维原子岛几何结构的理论方法.基于半经验相互作用势（SEAM势和OJ势）的计算表明,同相外延生长的二维原子岛在Cu和Ag的（111）面呈现正六边形结构, 而在Pt（111）面呈现截角三角形状;Cu和Ag的（100）面二维岛则形成正方形.这些理论预测均与实验观测结果一致.由于凝结势的计算不受原子数量的限制,该模型可普遍应用于预测各种表面二维原子岛形状. 关键词： 表面吸附 二维原子岛 量子点     

Study of the island morphology at the early stages of Fe/Mo(110) MBE growth

We present theoretical study of morphology of Fe islands grown at Mo(110) surface in submonolayer MBE mode. We utilize atomistic SOS model with bond counting, and interactions of Fe adatom up to third nearest neighbors. We performed KMC simulations for different values of adatom interactions and varying temperatures. We have found that, while for the low temperature islands are fat fractals, for the temperature 500 K islands have faceted rhombic-like shape. For the higher temperature, islands acquire a rounded shape. In order to evaluate qualitatively morphological changes, we measured average aspect ratio of islands. We calculated dependence of the average aspect ratio on the temperature, and on the strength of interactions of an adatom with neighbors.