时间随机环境中一维紧邻随机游动的常返性质

设环境q={q(n)}∞0是取值于[0,1]上一列独立同分布的随机变量列,且Eq(0)=p;{Sn}∞0是随机环境q中取整数值随机游动,S0=0,且满足:对任意的整数xi(i≥0),x,y,P(Sn+1=y|S1=x1,…,Sn-1=xn-1,Sn=x,q)={q(n),y=x+1,1-q(n),y=x-1,0,其他.我们证明了:p>1/2时,Sn→+∞,a.e.,n→∞;p<1/2时,Sn→-∞,a.e.,n→∞;p=1/2时,-∞=(lim infSn)/(n→+∞)<(lim supSn)/(n→+∞)=+∞,a.e.,n→∞.     

On Cayley-Transform Methods for the Discretization of Lie-Group Equations

In this paper we develop in a systematic manner the theory of time-stepping methods based on the Cayley transform. Such methods can be applied to discretize differential equations that evolve in some Lie groups, in particular in the orthogonal group and the symplectic group. Unlike many other Lie-group solvers, they do not require the evaluation of matrix exponentials. Similarly to the theory of Magnus expansions in [13], we identify terms in a Cayley expansion with rooted trees, which can be constructed recursively. Each such term is an integral over a polytope but all such integrals can be evaluated to high order by using special quadrature formulas similar to the construction in [13]. Truncated Cayley expansions (with exact integrals) need not be time-symmetric, hence the method does not display the usual advantages associated with time symmetry, e.g., even order of approximation. However, time symmetry (with its attendant benefits) is attained when exact integrals are replaced by certain quadrature formulas. March 7, 2000. Final version received: August 10, 2000. Online publication: January 2, 2001.     

林木生长影响模型及其在人工林林地质量评价中的应用

本文基于对立地因子影响林木生长的系统分析，采用途径分析等方法建立了林木生长影响模型，并将其应用于我国长白山林区红松人工林林地质量的评价。     

Boundaries for algebras of holomorphic functions on Marcinkiewicz sequence spaces

Let Ab(E) be the Banach algebra of all complex-valued bounded continuous functions on the closed unit ball BE of a complex Banach space E and holomorphic in the interior of BE and let Au(E) be the closed subalgebra of those functions which are uniformly continuous on BE. For the case whose bidual is a Marcinkiewicz sequence space Mw, we describe some sufficient conditions for a set to be a boundary of either Ab(E) or Au(E). Moreover, we consider some analogous problems on to those which were studied on the Gowers space Gp of characteristic p by Grados and Moraes [L.R. Grados, L.A. Moraes, Boundaries for algebras of holomorphic functions, J. Math. Anal. Appl. 281 (2003) 575-586; L.R. Grados, L.A. Moraes, Boundaries for an algebra of bounded holomorphic functions, J. Korean Math. Soc. 41 (1) (2004) 231-242].     

On Korn's Inequality

The author first reviews the classical Korn inequality and its proof. Following recent works of S. Kesavan, P. Ciarlet, Jr., and the author, it is shown how the Korn inequality can be recovered by an entirely different proof. This new proof hinges on appropriate weak versions of the classical Poincare and Saint-Venant lemma. In fine, both proofs essentially depend on a crucial lemma of J. L. Lions, recalled at the beginning of this paper.     

Packing dimension of the range of a Lévy process

Let denote a Lévy process in with exponent . Taylor (1986) proved that the packing dimension of the range is given by the index

We provide an alternative formulation of in terms of the Lévy exponent . Our formulation, as well as methods, are Fourier-analytic, and rely on the properties of the Cauchy transform. We show, through examples, some applications of our formula.

     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality

In this paper,we consider the equivalent conditions with L^p-version(1相似文献   

模糊连续映射和开映射的新特征

给定模糊格Ｌ及ＬＦ拓扑空间（Ｌ＾ｘ,δ）,对Ｌ的素元素ｒ及分子ａ,在（Ｌ＾ｘ,δ）中引入了ｒ－开集及α－闭集的概念。证明了所有的ｒ－开集Ｏｒ（δ）和α－闭集Ｃａ（δ）分别形成一个ＬＦ拓扑和ＬＦ余拓扑,借助于它俩得到了ＬＦ连续映射和ＬＦ开映射的若干新特征。     

带双势的非线性Schr dinger方程爆破解的L^2集中性质和L^2集中率

本文研究一类带双势的具有临界幂的非线性Schrodinger方程的初值问题.得到该方程爆破解的L2集中性质并在此基础上得到其爆破解为径向对称情形的L2集中速率.     

L-统计量的Edgeworth展开和随机加权逼近

文［１］讨论了Ｌ－统计量的一种能达到Ｏ１√ｎ精确度的随机加权逼近,本文则给出了Ｌ－统计量的Ｅｄｇｅｗｏｒｔｈ展开和一种能达到ｏ１√ｎ精确性的新的随机加权逼近     

Stability of the Cournot process – experimental evidence

We report results of experiments designed to test the predictions of the best-reply process. In a Cournot oligopoly with four firms, the best-reply process should theoretically explode if demand and cost functions are linear. We find, however, no experimental evidence of such instability. Moreover, we find no differences between a market which theoretically should not converge to Nash equilibrium and one which should converge because of inertia. We investigate the power of several learning dynamics to explain this unpredicted stability. Received May 1997/Revised June 2002     

Absolute monotonicity of rational functions occurring in the numerical solution of initial value problems

Summary This paper deals with rational functions ø(z) approximating the exponential function exp(z) related to numerical procedures for solving initial value problems. Motivated by positivity and contractivity requirements imposed on these numerical procedures we study the greatest nonnegative numberR, denoted byR(ø), such that ø is absolutely monotonic on (–R, 0]. An algorithm for the computation ofR(ø) is presented. Application of this algorithm yields the valueR(ø) for the well-known Padé approximations to exp(z). For some specific values ofm, n andp we determine the maximum ofR(ø) when ø varies over the class of all rational functions ø with degree of the numerator m, degree of the denominator n and ø(z)=exp(z)+(z ^p+1 ) (forz0).     

Brouwer and cardinalities

This note is a somewhat personal account of a paper that L.E.J. Brouwer published in 1908 and that dealt with the possible cardinalities of subsets of the continuum. That paper is of interest because it represents the first time that Brouwer presented his ideas on foundations in an international forum.I found Brouwer’s notions and arguments at times hard to grasp if not occasionally perplexing. I hope that this note contributes to a further discussion of the definitions and reasonings as presented in Brouwer’s paper.     

对两道未定式解法的分析与探讨

以一道未定式的求解为例,通过对使用洛必达法则求解时求导过程比较复杂的原因分析,提出在求导前对函数进行预处理的思想,并指出等价无穷小替换是有效的处理方法.而针对另一道未定式问题,指出相关文献为论证一种错误的解法而使用的反例是错的,给出该解法存在错误的具体说明.     

Hopf-Lax type formula for non monotonic autonomous Hamilton Jacobi equations

We give an explicit formula for a solution of Hamilton-Jacobi equation u_t+H(u,Du)=0 in with initial condition u(x,0)=u₀(x), where p H(u,p) is convex, positively homogeneous of degree one and the Hamiltonian H need not satisfy the monotonicity condition in u.     

Partial regularity for minimizers of convex integrals with L log L-growth

We prove -partial regularity of minimizers with for a class of convex integral functionals with nearly linear growth whose model is In this way we extend to any dimension n a previous, analogous, result in [FS] valid only in the case Received December 1998