Pullback attractors for non-autonomous reaction-diffusion equations on ?n

We study the long time behavior of solutions of the non-autonomous reaction-diffusion equation defined on the entire space Rn when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L2(Rn) and H1(Rn), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.     

非定域正则Ward恒等式

基于相空间Green函数的生成泛函,导出了非定域变换下正则形式的Ward恒等式．用于非AbelChern－Simons（CS）理论,得到了正规项角间的一些关系式．这里给出的形式的显著优点在于匆需作出相空间生成泛函中对正则动量的路径积分．在非AbelCS理论中的非定域变换下,仅要求和不变,即可导出正规顶角间的一些关系式．     

Voter model in a random environment in ?d

We consider the voter model with flip rates determined by {μ_e, e ∈ E_d}, where E_d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ?d. Suppose that {μ_e, e ∈ E_d} are independent and identically distributed (i.i.d.) random variables satisfying μ_e≥1. We prove that when d = 2, almost surely for all random environments, the voter model has only two extremal invariant measures: δ₀ and δ₁.     

省钱妙招:货比三家

阿龙和美美要给全班同学采购40盒蜡笔.他们去了学校附近的三家文具店,发现每家文具店都有同款蜡笔,每盒售价都是9.9元,但三家的促销活动都不一样.你觉得在哪家店购买最便宜呢?     

τ-Categories I: Ladders

In this series of papers, we introduce τ-categories, which are additive categories with some kind of Auslander–Reiten sequences. We apply them to study the category of lattices over orders. In this first paper, we study minimal projective resolutions in functor categories over τ-categories. Then we give a structure theorem of completely graded τ-categories using mesh categories. Presented by K. Roggenkamp Mathematics Subject Classifications (2000) primary 16G30; secondary 16E65, 16G70, 18E05. Osamu Iyama: Current address: Department of Mathematics, University of Hyogo, Himeji, 671-2201, Japan. e-mail: iyama@sci.u-hyogo.ac.jp.     

我的目标:又快又好

快点!快点!写完了作业我们好去玩游戏! 我是一只小蜗牛,我的同学都叫我"悠悠".其实我知道他们是想叫我"慢悠悠",说我做作业慢呗!提起这作业我就头疼,唉!     

编者寄语:关于参考文献

参考文献是一篇文章的重要组成部分,认真加以标引,不仅是尊重他人和前人的表示,同时也是作者自我尊重的一种表现.引用或者评述已有的成果,必须以直接而明确的方式加以标明,这已成为尊重知识产权的一种共识,也是遵守国家“著作权法”的一项义务.作者在确定自己的创新前,应认真做好查新,以免因不慎导致侵权之误.这里有一点也要说明,那些写入基础教材,形成学科常识的内容,除非撰文的立意就在于针对某具体的问题进行比较研究,一般就不必加以标引列举了.参考文献应列对于作者本文写作来说最关键、最重要的,即文中直接引用或给予评述的那些文献.这…     

一个方程组的解及相关边值问题

该文考虑方程组 t(u_x - v_y - w_t ) + w = 0 (H) u_y = -v_x, u_t = -w_x, v_t = w_y 的解f = u + iv + jt ∈C²,找到(H)可解的一个充要条件,并讨论相关边值问题解的存在性和积分表示,推广了1992年H. Leutwiler［1］的结果.     

丹麦:童话之都

正伍丽青丹麦是北欧发达国家,气候温和宜人,一年四季都适合旅游。在丹麦,无论走到哪里,都能感受到那种激发安徒生创作美丽童话的氛围和景观。丹麦的乡村美丽宁静,众多的庄园和古城堡更为丹麦增添许多妩媚。中世纪风情的国徽丹麦国徽的历史可以追溯到12世     

质量:美国在急起直追

前些年的举足失措和犹豫不决已经成为过去,美国工业目前正发起全面反击,以求在质量方面缩短日本公司在近十年时间里拉开的距离。某些行业与日本的质量竞赛已取得显著成功,尤其是电视机和半导体行业,尽管这些成绩还没有被顾客普遍意识到。许多专家相信,如果质量运动的势头继续以     

Generalized area operators on Lp(?n)

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces ?+n+1. The characterization of the boundedness and compactness of the generalized area operator from L^p(?n) to L^q(?n) is investigated in terms of s-Carleson measures with 1<p, q<+∞. In the case of p = q = 1, the weak type estimate is also obtained.     

EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I: APPROXIMATION:

In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.     

Floer Cohomology of Lagrangian Intersection:I~*(T~n, RP~n: CP~n)

）（陈柏辉，李安民）ＦｌｏｅｒＣｏｈｏｍｏｌｏｇｙｏｆＬａｇｒａｎｇｉａｎＩｎｔｅｒｓｅｃｔｉｏｎ：Ｉ~＊（Ｔ~ｎ，ＲＰ~ｎ：ＣＰ~ｎ）ＦｌｏｅｒＣｏｈｏｍｏｌｏｇｙｏｆＬａｇｒａｎｇｉａｎＩｎｔｅｒｓｅｃｔｉｏｎ：Ｉ~＊（Ｔ~ｎ，ＲＰ~ｎ：ＣＰ~ｎ）￥）Ｃ...     

Comments on: Farkas’ Lemma: three decades of generalizations for mathematical optimization

In these comments on the excellent survey by Dinh and Jeyakumar, we briefly discuss some recently developed topics and results on applications of extended Farkas’ lemma(s) and related qualification conditions to problems of variational analysis and optimization, which are not fully reflected in the survey. They mainly concern: Lipschitzian stability of feasible solution maps for parameterized semi-infinite and infinite programs with linear and convex inequality constraints indexed by arbitrary sets; optimality conditions for nonsmooth problems involving such constraints; evaluating various subdifferentials of optimal value functions in DC and bilevel infinite programs with applications to Lipschitz continuity of value functions and optimality conditions; calculating and estimating normal cones to feasible solution sets for nonlinear smooth as well as nonsmooth semi-infinite, infinite, and conic programs with deriving necessary optimality conditions for them; calculating coderivatives of normal cone mappings for convex polyhedra in finite and infinite dimensions with applications to robust stability of parameterized variational inequalities. We also give some historical comments on the original Farkas’ papers.     

集值Superpramart的上鞅逼近

文中讨论了可积随机集条件期望的若干性质,在此基础上,给出了集值Superpramart的上鞅逼近.同时,证明了集值Superpramart在Kuratowski-Mosco意义下的收敛定理.