双分式Brown运动的自相交局部时和相遇局部时

考虑一个双分式Brown运动的局部时、自相交局部时和两个独立的双分式Brown运动的相遇局部时问题．通过双分式Brown运动的强局部不确定性、L^2收敛和混沌展开,验证自相交局部时和相遇局部时的存在性和光滑性．     

Local Functional Law of the Iterated Logarithm for Increments of a Brownian Sheet北大核心CSCD

本文利用Brown单与Brown单增量的大偏差,得到了Brown单与Brown单增量的局部泛函重对数律.     

分次环的分次根

给出了建立分次环根的一般方法．作为其应用，建立了分次环的分次Brown—McCoy根，并给出了Brown—McCoy半单分次环的结构定理．     

关于无穷参数Wiener过程的随机积分

本文试讨论并建立与无穷参数Wiener过程相应的无穷参数指标集上的随机积分。     

部分信息的完全耦合正倒向系统的随机最大值原理

本文研究了系统为Brown运动驱动的完全耦合的非线性正倒向随机微分方程的随机最优控制问题．系统要求可允许控制过程适应于标的Brown运动生成的盯域流的一个子盯域流．对于这种部分信息的随机最优控制问题,在控制区域为凸集和控制变量可以进入控制系统正向扩散系数的情形下,证明了最优性的一个充分条件（验证定理）和一个必要条件．     

基于构造的Brown单Lévy连续模

该文利用Schauder函数建立了Brown单的级数表示．基于该表示，作者得到它的Lévy连续模的简化证明．     

无穷迭代函数系统的遍历定理

度量空间的压缩映射的一个集合称为一个迭代函数系统．凝聚迭代函数系统可以被看成无穷迭代函数系统．研究了紧度量空间上的无穷迭代函数系统．利用Banach极限的特性和均匀压缩性,证明了紧度量空间上无穷迭代函数系统的随机迭代算法满足遍历性．于是,凝聚迭代函数系统的随机迭代算法也满足遍历性．     

参数的变化对F分布密度函数之影响

该文运用对无穷级数的一些特殊处理方法,深入分析了与г函数有关的一些特殊函数 的性质,揭示了参数变化时F分布密度函数极值变化的一些深刻规律．该文指明,n增大时 F分布的密度函数fm,n(x)的极大值单调增加,而m增大时该密度函数的极大值或单调减 少,或先减后增．     

两参数Brown运动增量的局部泛函重对数律

该文利用两参数Brown运动和两参数Brown运动增量的大偏差,得到了两参数Brown运动增量的局部泛函重对数律.     

独立风景中一般Kesten-Spitzer随机游动的强逼近

证明了若一个一维的随机游动S_n可用Brown运动逼近,则其在独立随机风景中的游动可用Brown风景中的Brown运动逼近.     

Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems

In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.

     

Asymptotic behavior of solutions to the perturbed simple pendulum problems with two parameters

We consider the perturbed simple pendulum equation –u ″(t) + μ |u (t)|^{p –1}u (t) = λ sin u (t), t ∈ I ? (–T, T), u (t) > 0, t ∈ I, u (±T) = 0, where p > 1 is a constant,λ > 0 and μ ∈ R are parameters. The purpose of this paper is to clarify the structure of the solution set. To do this, we study precisely the asymptotic shape of the solutions when λ ? 1 as well as the asymptotic behavior of variational eigenvalue μ (λ) as λ → ∞. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

各种停点及其关系

给出 了一个 尽可能 完善 的各种 停点的 关系． 仿照 Ｂａｋｒｙ 引 入 ｉ强停点, 对亚强 停点 本文给出了它的准 确位置,它处于 停点和强停点之 间,且可以像停 点和强停点一样 用停时点来刻画     

双参数B值鞅Hardy空间的实内插

利用原子分解方法,研究了双参数Ｂ值鞅Ｈａｒｄｙ空间之间的实内插。     

Some Laws of the Iterated Logarithm for Two Parameter Martingales

We prove some laws of the iterated logarithm for two parameter martingale differences of the following type: E(X _t|(X _s, s ₁<t ₁ or s ₂<t ₂))=0 a.s.     

二参数广义Rayleigh分布

为了研究某些工程过程的寿命,需要一个能够适应这些过程性质的寿命模型.与简单模型相比,基于寿命分布的广义模型在建模过程中更具有直观的适用性和吸引力.本文介绍一个二参数广义Rayleigh分布,推导出了其矩生成函数和k阶矩的表达式,通过对样本点进行归一化,得到了它的近似分布函数、概率密度函数、生存函数、风险率函数等.在此基...     

Two Dimensional Landau-Lifshitz Equation

In this paper, we consider the Cauchy problem for two dimensional Landau-Lifshitz equation on 2-dimenslonal Riemannian manifold M without boundary. We proved that if u: M × R_+ → S², is a weak solution, then u is unique and smooth on M × R_+ with the exception of finitely many points.     

Existence of turbulent behavior for non-chaotic two dimensional jets

The classic models of mass transfer for free turbulent jets very often contain neglected terms. This is because these terms are considered so small that their effect can be neglected; however, because the models are usually structurally unstable, these neglected terms, even if they are small, may change the behavior of the system. Furthermore, the existing classic models cannot simulate the far behavior of the fluid, for example, the eddies existing in the jet region of the fluid stream. In this paper, we consider a general implicit small perturbation of the classic model and study the effect of it on the system. We will show that the local bifurcations may imply the existence of eddies for the fluid stream; for example, we will see that, under some conditions, the Hopf bifurcation generates permanent eddies for the system.     

Single machine scheduling problem with two synergetic agents and piece-rate maintenance

This paper attempts to study on the single machine scheduling problems with two synergetic agents, each has a set of nonpreemptive jobs and a regular objective function depending on the completion times of its jobs only. It is not only necessary to satisfy the constraints of each agents objective function, it is necessary to minimize an aggregate increasing objective function of two agents’ objective function. Furthermore, this paper proposes a new kind of machine maintenance: piece-rate maintenance, which depicts the scenario that machine maintenance is implemented once every a fixed number of jobs is completed. Hence, it explores into the single machine scheduling problems with two synergetic agents and piece-rate maintenance. If the regular objective function of each job is polynomial, it can be observed that these problems are all polynomially solvable.