Topologically invariant Chern numbers of projective varieties

We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three we prove that only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation-preserving. These results solve a long-standing problem of Hirzebruch's. We also determine the linear combinations of Chern numbers that can be bounded in terms of Betti numbers.     

Continuous-Time Independent Edge-Markovian Random Graph Process

In this paper, the continuous-time independent edge-Markovian random graph process model is constructed. The authors also define the interval isolated nodes of the random graph process, study the distribution sequence of the number of isolated nodes and the probability of having no isolated nodes when the initial distribution of the random graph process is stationary distribution, derive the lower limit of the probability in which two arbitrary nodes are connected and the random graph is also connected, and prove that the random graph is almost everywhere connected when the number of nodes is sufficiently large.     

基于云模型的三维土工网防护边坡侵蚀稳定性综合评价

在分析各项影响因素分级标准的基础上,建立了三维土工网护坡侵蚀稳定性的综合评价体系.针对三维土工网边坡侵蚀稳定性分析中不确定性问题,将云模型理论引入到综合评判中,实现了定性与定量的不确定性转换.通过构建前件云发生器和后件云发生器,利用不确定推理,确定各项评价指标的具体分值.借助层次分析法与敏感度分析确定各项评价指标的权重,进而得出综合评价体系的整体得分.工程实例计算结果证实了模型的实用性和有效性,为三维土工网防护边坡侵蚀稳定性的评价提供了一条新的途径.     

An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

A hybrid-Trefftz element containing an elliptic hole

Much work on special elements that simplify geometrical modelling of structures containing holes, cracks and/ or inclusions has been reported extensively in the literature. This paper presents a hybrid-Trefftz element containing elliptic hole formulated using Hellinger–Reissner principle by employing trial functions based on the mapping technique and the Cauchy integral method. The element presented in this paper could be regarded as an improved formulation over Piltner [Special finite elements with holes and internal cracks, Int. J. Numer. Methods Eng. 21 (1985) 1471–1485] element because the chosen trail functions in this paper have provided relatively more stable solutions. The use of the element with other ordinary displacement-based finite elements has also yielded very accurate solutions even when very coarse meshes relative to the size of the elliptic hole have been used.     

Generalized synchronization between two different complex networks

In this paper, generalized synchronization (GS) between two coupled complex networks is theoretically and numerically studied, where the node vectors in different networks are not the same, and the numbers of nodes of both networks are not necessarily equal. First, a sufficient criterion for GS, one kind of outer synchronizations, of two coupled networks is established based on the auxiliary system method and the Lyapunov stability theory. Numerical examples are also included which coincide with the theoretical analysis.     

Global analysis of an SIS model with an infective vector on complex networks

In this paper, a modified SIS model with an infective vector on complex networks is proposed and analyzed, which incorporates some infectious diseases that are not only transmitted by a vector, but also spread by direct contacts between human beings. We treat direct human contacts as a social network and assume spatially homogeneous mixing between vector and human populations. By mathematical analysis, we obtain the basic reproduction number R₀ and study the effects of various immunization schemes. For the network model, we prove that if R₀<1, the disease-free equilibrium is globally asymptotically stable, otherwise there exists an unique endemic equilibrium such that it is globally attractive. Our theoretical results are confirmed by numerical simulations and suggest a promising way for the control of infectious diseases.     

基于结构元的复模糊数及其序列极限

复模糊数是模糊复分析中的基本概念,在模糊复分析中,它的运算是基于扩张原理的形式给出的,是对元素遍历某个条件所对应的结果进行运算,这种遍历过程给实际操作带来了很多的不便,因此,在一定程度上也阻碍了模糊复分析理论的应用.对此,本文基于模糊结构元的理论基础,探讨了复模糊数运算的另一种新的途径,这种方法简化了复模糊数的运算,也...     

Locally connected models for Julia sets

Let P be a polynomial with a connected Julia set J. We use continuum theory to show that it admits a finest monotone map φ onto a locally connected continuumJP_∼, i.e. a monotone map φ:J→JP_∼ such that for any other monotone map ψ:J→J^′ there exists a monotone map h with ψ=h°φ. Then we extend φ onto the complex plane C (keeping the same notation) and show that φ monotonically semiconjugates PC_| to a topological polynomialg:C→C. If P does not have Siegel or Cremer periodic points this gives an alternative proof of Kiwi's fundamental results on locally connected models of dynamics on the Julia sets, but the results hold for all polynomials with connected Julia sets. We also give a characterization and a useful sufficient condition for the map φ not to collapse all of J into a point.