双参数 C-半群

引入单参数C-半群和双参数C0-半群,给出了更一般的双参数C-半群和无穷小生成元的定义,应用双参数半群与单参数半群的关系和双参数半群的性质,给出了双参数C-半群的阶全微分,偏微分,指数有界性,和双参数C-半群是由C、A1和A2唯一确定的闭稠定线性算子的一个充分条件.     

Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media

ABSTRACT

We study the homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. The “viscosity” and the spatial oscillations are assumed to be of the same order. We identify the asymptotic (effective) equation, which is a first-order deterministic Hamilton–Jacobi equation. We also provide examples that show that the associated macroscopic problem does not admit suitable solutions (correctors). Finally, we present as applications results about large deviations of diffusion processes and front propagation (asymptotics of reaction-diffusion equations) in random environments.     

主成分计算的改进自然幂迭代方法

提供快速估计与跟踪一个向量序列的主特征向量的改进自然幂迭代方法．它是自然幂迭代方法的一个延伸,不仅跟踪主子空间,而且得到了主特征向量．与一些基于幂迭代的方法(例如Oja,PAST与NIC)相比,改进自然幂迭代方法具有最快的收敛速度,且能容易地以每步迭代O(np)的计算量加以实现,这里n为所考虑向量序列的维数,p为所要跟踪的主子空间的维数(或主特征向量的个数)．与某些非幂迭代的方法(例如MALASE与OPERA)相比,改进自然幂迭代方法保证了全局指数收敛．     

单调映象方程解的遍历收敛性

通过对正则化迭代格式使用遍历性技术,建立了有界单调映象和满足线性增长条件单调映象方程解的大范围遍历收敛定理,所得结果对于伪压缩映象有直接应用。     

Maximal ergodic theorems for some group actions

We prove maximal ergodic inequalities for a sequence of operators and for their averages in the noncommutative Lp-space. We also obtain the corresponding individual ergodic theorems. Applying these results to actions of a free group on a von Neumann algebra, we get noncommutative analogues of maximal ergodic inequalities and pointwise ergodic theorems of Nevo-Stein.     

Noncommutative maximal ergodic theorems for positive contractions

Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L₂(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations.     

Uniform existence of the integrated density of states for models on $${\mathbb{Z}}^d$$

We provide an ergodic theorem for certain Banach-space valued functions on structures over , which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density of states for associated discrete finite-range operators in the sense of convergence of the distributions with respect to the supremum norm. These results apply to various examples including periodic operators, percolation models and nearest-neighbour hopping on the set of visible points. Our method gives explicit bounds on the speed of convergence in terms of the speed of convergence of the underlying frequencies. It uses neither von Neumann algebras nor a framework of random operators on a probability space.      

Fell拓扑,Choquet容量和遍历的 Choquet容量系统

本文描述了Fell 拓扑的结构与收敛条件,重新确立了关于随机集的Choquet 定理在概率论中的重要作用,并提出了不变Choquet 容量的概念。此外,利用环面上的双曲自同构和随机映射,具体构造了一个遍历的Choquet 容量系统,且进一步探讨了这种系统的动力性态。     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.