对称超二次二阶哈密尔顿系统的周期解

我们利用Ambrosetti-Rabinowitz对称形式的山路引理证明了给定周期T的对称超二次二阶哈密尔顿系统具有无穷多个反T/2-周期且奇的周期解.     

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.     

${\mathbb{Z}}/3{\mathbb{Z}}$-量子群的Gr\"{o}bner-Shirshov 基

通过计算合成, 我们证明了Yamane 给出的关系是 ${\mathbb{Z}}/3{\mathbb{Z}}$-量子群的一个Gr\"{o}bner-Shirshov 基.     

Convex mappings on some circular domains

In this paper,we consider some circular domains.And we give an extension theorem for some normalized biholomorphic convex mapping on some circular domains.Especially,we discover the normalized biholomorphic convex mapping on some circular domains have the form f(z) =(f1(z1),...,fn(zn)),where fj:D → C are normalized biholomorphic convex mapping.     

Hamilton ?-cycles in uniform hypergraphs

We say that a k-uniform hypergraph C is an ?-cycle if there exists a cyclic ordering of the vertices of C such that every edge of C consists of k consecutive vertices and such that every pair of consecutive edges (in the natural ordering of the edges) intersects in precisely ? vertices. We prove that if 1??<k and k−? does not divide k then any k-uniform hypergraph on n vertices with minimum degree at least contains a Hamilton ?-cycle. This confirms a conjecture of Hàn and Schacht. Together with results of Rödl, Ruciński and Szemerédi, our result asymptotically determines the minimum degree which forces an ?-cycle for any ? with 1??<k.     

非Lipschitz条件下半鞅随机微分方程解的唯一性(英文)

本文研究了非Lipschitz条件下半鞅随机微分方程.利用It(o)分析和Gronwall不等式,探讨了随机微分方程无爆炸解,并证明了随机微分方程解的唯一性.     

Quasi-Piecewise-Koszul Modules

In this article we first study an equivariant cyclic cohomology for weak H-module agebras over a weak Hopf algebra H with a bijective antipode. Then we define an equivariant K-theory for weak quantum Yetter–Drinfeld algebras over H and establish a generalized Connes' pairing between the equivariant cyclic cohomology and the equivariant K-theory. As an application we consider our theory for groupoids.     

Markov processes generated by linear stochastic evolution equations †

A class of Hilbert space-valued Markov processes which can be expressed as the mild solution of a linear abstract evolution equation is studied. Sufficient conditions for the generator of the Markov process to be well-defined are given and Kolmogorov's equation and an equation for the characteristic function of the process are derived. The theory is illustrated by examples of parabolic, hyperbolic and delay stochastic differential equations.