新(2+1)-维超可积系统的生成

本文利用二项式残数表示方法生成(2+1)-维超可积系统. 由这些系统得到了一个新的(2+1)-维超孤子族,它能约化为(2+1)-维超非线性Schrodinger方程. 特别地,我们得到两个具有重要物理应用的结果,一个是(2+1)-维超可积耦合方程,另一个是(2+1)-维的扩散方程. 最后借助超迹恒等式给出了新(2+1)-维超可积系统的Hamilton结构.     

Constructing super D-Kaup-Newell hierarchy and its nonlinear integrable coupling with self-consistent sources

How to construct new super integrable equation hierarchy is an important problem. In this paper, a new Lax pair is proposed and the super D-Kaup-Newell hierarchy is generated, then a nonlinear integrable coupling of the super D-Kaup-Newell hierarchy is constructed. The super Hamiltonian structures of coupling equation hierarchy is derived with the aid of the super variational identity. Finally, the self-consistent sources of super integrable coupling hierarchy is established. It is indicated that this method is a straight- forward and efficient way to construct the super integrable equation hierarchy.     

关于任意随机适应序列部分和增长阶的估计

设(Ω,F,P)为概率空间,{Xn,Fn,n 0}为定义在上面的随机适应序列.目的是要研究任意随机适应序列的一个强极限定理.作为推论,推广了Freedman的一个定理以及任意随机适应序列部分和增长阶估计定理.     

THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS

Suppose {Xn} is a random walk in time-random environment with state space Zd,|Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index a. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.     

全变差有界函数列的一致(R)可积性

给出了一致有界单调函数列一致可积性定理 ,由此得出全变差序列有界的收敛函数列的一致可积性 .说明了该结论可判断一些非一致收敛函数列的逐项积分性质 .     

赋Orlicz范数的Musielak-Orlicz序列空间的单调点

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间中上（下）单调点以及上（下）局部一致单调点的充分必要条件．     

The uniform convergence of thin plate spline interpolation in two dimensions

Summary. Let be a function from to that has square integrable second derivatives and let be the thin plate spline interpolant to at the points in . We seek bounds on the error when is in the convex hull of the interpolation points or when is close to at least one of the interpolation points but need not be in the convex hull. We find, for example, that, if is inside a triangle whose vertices are any three of the interpolation points, then is bounded above by a multiple of , where is the length of the longest side of the triangle and where the multiplier is independent of the interpolation points. Further, if is any bounded set in that is not a subset of a single straight line, then we prove that a sequence of thin plate spline interpolants converges to uniformly on . Specifically, we require , where is now the least upper bound on the numbers and where , , is the least Euclidean distance from to an interpolation point. Our method of analysis applies integration by parts and the Cauchy--Schwarz inequality to the scalar product between second derivatives that occurs in the variational calculation of thin plate spline interpolation. Received November 10, 1993 / Revised version received March 1994     

强相依高斯序列对高水平超过的弱收敛

设{Xn}为标准化非平稳高期序列，rij=cov(Xi,Xj),Nn为{Xn}对水平un=x/an bn的超过数形成的点过程。当rijlog(j-i)→r∈（0，∞),(j-i→ ∞),且n→∞时，点过程Nn依分布收敛到Cox-过程。     

Conservation laws and self-consistent sources for a super integrable equation hierarchy

In this paper, a super integrable equation hierarchy is considered based on a Lie superalgebra and supertrace identity. Then, a super integrable equation hierarchy with self-consistent sources is established. Furthermore, we introduce two variables F and G to construct conservation laws of the super integrable equation hierarchy and the first two conserved densities and fluxes are listed. It would be specially mentioned that the Fermi variables play an important role in super integrable systems which is different from the ordinary integrable systems.     

Geometric singular perturbation theory for stochastic differential equations

We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths of the stochastic system are concentrated in a neighbourhood of the slow manifold, which we construct explicitly. Depending on the dynamics of the reduced system, the results cover time spans which can be exponentially long in the noise intensity squared (that is, up to Kramers’ time). We obtain exponentially small upper and lower bounds on the probability of exceptional paths. If the slow manifold contains bifurcation points, we show similar concentration properties for the fast variables corresponding to non-bifurcating modes. We also give conditions under which the system can be approximated by a lower-dimensional one, in which the fast variables contain only bifurcating modes.     

On the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity

This paper is concerned with a Cauchy problem where and is a nonnegative radially symmetric function in with compact support. Denote the solution of (P) by . Let if and $p^{\ast} = 1+6/(N-10) N \geq 11 p_{\ast} < p < p^{\ast} \lambda_{\varphi} > 0 $ such that: (i) If $ \lambda < \lambda_{\varphi} u_{\lambda} $ exists globally in time in the classical sense and converges to zero locally uniformly in as . (ii) If , then $ u_{\lambda} $ blows upincompletely in finite time. (iii) If , then blows upcompletely in finite time. Received: 20 December 1999; in final form: 26 May 2000 / Published online: 4 May 2001     

On different forms of self similarity

Fractal geometry is mainly based on the idea of self-similar forms. To be self-similar, a shape must able to be divided into parts that are smaller copies, which are more or less similar to the whole. There are different forms of self similarity in nature and mathematics. In this paper, some of the topological properties of super self similar sets are discussed. It is proved that in a complete metric space with two or more elements, the set of all non super self similar sets are dense in the set of all non-empty compact sub sets. It is also proved that the product of self similar sets are super self similar in product metric spaces and that the super self similarity is preserved under isometry. A characterization of super self similar sets using contracting sub self similarity is also presented. Some relevant counterexamples are provided. The concepts of exact super and sub self similarity are introduced and a necessary and sufficient condition for a set to be exact super self similar in terms of condensation iterated function systems (Condensation IFS’s) is obtained. A method to generate exact sub self similar sets using condensation IFS’s and the denseness of exact super self similar sets are also discussed.     

Hilbert空间上凸函数的上、下指数的共轭性质

本文引入Ｈｉｌｂｅｒｔ空间上非负凸函数具有一般性的上下指数的概念，得到相互共轭凸函数的上下指数的共轭性质，也讨论了由内积范数导出的正ｐ（ｐ＞１）次齐次函数与正ｑ（ｑ＞１，１ｐ＋１ｑ＝１）之间的关系     

连续时间集值(上、下)鞅Doob-停时定理

本文首先给出了Ｊ_L意义下的集值鞅的正则性,然后证明了几种连续时间集值（上、下）鞅Ｄｏｏｂ－停时定理．     

Hilbert-值半鞅序列的弱收敛

本文在条件UT下研究了Hilbert-值半鞅序列到连续Hilbert-值半鞅的收敛性,并在弱收敛的条件下研究了形如X^n=∫oa^n(X^n.,s)dY^ns ∫ob^n(X^n.,s)dA^ns,X^no=O,任意n≥1随机微分方程的稳定性,其中Y^n和A^n分别为Hilbert-值半鞅和分量为增过程的Hilbert-值有限变差过程。     

A localic theory of lower and upper integrals

An account of lower and upper integration is given. It is constructive in the sense of geometric logic. If the integrand takes its values in the non‐negative lower reals, then its lower integral with respect to a valuation is a lower real. If the integrand takes its values in the non‐negative upper reals, then its upper integral with respect to a covaluation and with domain of integration bounded by a compact subspace is an upper real. Spaces of valuations and of covaluations are defined. Riemann and Choquet integrals can be calculated in terms of these lower and upper integrals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Orlicz空间的各类强端点与（R1）—（R3）性质

给出Ｏｒｌｉｃｚ空间超强端点、超端点与次强端点的判别准则和弱中点局部一致凸，（Ｒ１）、（Ｒ２）、（Ｒ３）性质的充分必要条件。     

离散参数集值（上下）鞅的停时定理

本文建立了更广泛的各种集值（上下）鞅的停时定理；推广并改进了N．S．Papageoriou[10]和张，汪，高[13]中的结果。     

Riemann integrability and Lebesgue measurability of the composite function

If f is continuous on the interval [a,b], g is Riemann integrable (resp. Lebesgue measurable) on the interval [α,β] and g([α,β])⊂[a,b], then f○g is Riemann integrable (resp. measurable) on [α,β]. A well-known fact, on the other hand, states that f○g might not be Riemann integrable (resp. measurable) when f is Riemann integrable (resp. measurable) and g is continuous. If c stands for the continuum, in this paper we construct a c²-dimensional space V and a c-dimensional space W of, respectively, Riemann integrable functions and continuous functions such that, for every f∈V?{0} and g∈W?{0}, f○g is not Riemann integrable, showing that nice properties (such as continuity or Riemann integrability) can be lost, in a linear fashion, via the composite function. Similarly we construct a c-dimensional space W of continuous functions such that for every g∈W?{0} there exists a c-dimensional space V of measurable functions such that f○g is not measurable for all f∈V?{0}.     

Goal uncertainity in a generalized information system: convergence properties of the estimated expected utilities ∗

The concept of goal uncertainty in a generalized information system is modeled by treating utility functions as interval valued rather than real valued. Furthermore, since the system is dynamic, the intervals shrink as information accumulates. The lower (upper) endpoints of these intervals are shown to be sub(super) martingales. Decision rules are formulated to select the appropriate course of action for each cycle through the decision-information feedback loop which is the heart of this information system. Finally, the theory of multifunctions is used to obtain convergence theorems for the estimated expected utilities generated by this system