Global attractivity for half-linear differential systems with periodic coefficients

The system to be considered in this paper is

     

一类具阶段结构的Leslie系统正周期解的存在性

考虑一类具有阶段结构和Holling-TannerⅡ类功能反应的Leslie周期系统,利用重合度理论得到该系统正周期解存在的充分条件.     

Continuation of separately analytic functions defined on part of the domain boundary

Let D ? ? ⁿ be a domain with smooth boundary ?D, let E??D be a subset of positive Lebesgue measure mes(E) > 0, and let F ? G be a nonpluripolar compact set in a strongly pseudoconvex domain D ? ? ^m . We prove that, under an additional condition, each function separately analytic on the set X = (D × F) ∪ (E × G) has a holomorphic contination to the domain $\rlap{--} X = \{ (z,w) \in D \times G:\omega _{in}^ * (z,E,D) + \omega ^ * (w,F,D) < 1\} $ , where ω* is the P-measure and ω*_in is the interior P-measure.     

The changing of the guard: Molecular diversity and rapid evolution of β-defensins

Summary Defensins are small cationic peptides involved in innate immunity and are components of the first line of defence against invading pathogens. β-defensins are a subgroup of the defensin family that display a particular cysteine spacing and pattern of intramolecular bonding. These molecules are produced mostly by epithelia lining exposed surfaces and appear to have both antimicrobial and cell signalling functions. The unusually high degree of sequence variation in the mature peptide produced by the paralogous and in some cases orthologous genes implies extensive specialisation and species specific adaptation. Here we review recent functional data that are an important addition to our knowledge of the innate immune response and novel antibiotic design. We also consider the organisation and evolution of the genomic loci harbouring these genes where radical and rapid changes in β-defensin sequences have been shown to result from the interplay of both positive and negative selection. Consequently these genes provide some unusually clear glimpses of the processes of duplication and specialisation that have shaped the mammalian genome.     

投机、期货市场与原油价格变动

从原油的金融资产属性出发,探讨了原油期货市场中的投机行为下价格泡沫的存在性,在实证中针对美国商品交易委员会报告中的不足进行修正,考察了多种因素对价格的影响.结果表明：投机是近一轮油价波动的原因,但却无法据此质疑原油期货市场的作用,原油期货市场仍在总量上对价格起到了稳定的负反馈作用.结论在肯定投机推高油价的同时,证明石油期货市场并非是价格波动的根源,相反具有调节作用,从而强调了石油期货市场监管的重要性.     

Dirichlet零边值问题的正解存在性

由于一些本质困难,N=3被称为具Sobolev临界指数2*的Dirichlet问题-△u=λu+|u|2*-2u,x∈ΩRN;u(x)0,x∈Ω;u=0,x∈Ω的临界维数.众所周知,N=3时,上述问题存在古典(正)解的一个充分条件是Ω为R3上的小球以及14λ1λλ1.本文考虑Ω是R3中更一般的有界光滑区域,得出了一正解存在性结论,从而肯定了沈尧天在文中提及的一个未解决的问题.     

Variational construction of unbounded orbits in Lagrangian systems

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtained here are not required sufficiently large.     

Local dependence functions for some families of bivariate distributions and total positivity

The purpose of this paper is to investigate a very useful application of a certain local dependence function γ_f(x,y), which was considered recently by Holland and Wang [20]. An interesting property of γ_f(x,y) is that the underlying joint density f(x,y) is TP₂ (that is, totally positive of order 2) if and only if . This gives an elegant way to investigate the TP₂ property of any bivariate distribution. For the Saramanov family, the Ali-Mikhail-Haq family of bivariate distributions and the family of bivariate elliptical distributions, we derive the local dependence function and obtain conditions for f(x,y) to be TP₂. These families are quite rich and include many other large classes of bivariate distributions as their special cases. Similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with Pareto conditionals.     

Analysis of a prey-predator model with disease in prey

In this paper, a system of reaction-diffusion equations arising in eco-epidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the predator is treated as bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.     

RELAXATION SOLVERS FOR IDEAL MHD EQUATIONS-A REVIEW

We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH.