Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

The rank of Hankel operators on harmonic Bergman spaces

We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

     

On Oscillation Criteria of Fourth Order Linear Differential Equations

The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.     

Probing the Stau-Stau-Higgs Couplings in the MSSM at NLC

In the minimal supersymmetric standard model (MSSM) with CP violating phases, this paper discussesthe production of the lightest neutral Higgs boson in association with tau sleptons at future high-energy e e- linearcolliders. In parameter space of the constrained MSSM, the production cross section of e e- → h0τ1 τ1- can be verysubstantial at high energies. This process would provide a production mechanism for probing couplings of neutral Higgsbosons to tau sleptons as well as some soft supersymmetric breaking parameters at next linear colliders.     

求线性规划初始可行基的新方法

本文提出一个求线性规划初始可行基的新算法，该算法不仅避免了人工变量，而且理论分析及初步的数值实验结果表明其效率更高。     

线性规划联合算法的理论与应用

本在[1]的基础上．较系统的叙述了线性规划联合算法的步骤、相关理论及其应用，指出该算法具有避免人工变量、减少迭代次数、使用灵活、应用方便等特点。     

求解一类非单调线性互补问题的宽邻域内点方法及其计算复杂性

对于一类非单调线性互补问题给出了一种新的算法——宽邻域内点算法，并讨论了其计算复杂性。     

线性规划问题的规范型算法

提出了线性规划问题的两种规范标准形式；证明了任意一个线性规划问题都可化为这两种形式之一；给出了不需引入人工变量的线性规划问题的求解算法。     

MC模式下顾客需求与厂商供应的纳什均衡

在大规模定制(MC，Mass Customization)模式下，基于市场需求的复杂化，厂商对个性化的顾客需求很难做出及时准确的反应，而且由于其自身生产能力的限制，不可能对所有的个性化用户进行一一地满足，只可能对已经存在的个性化需求，根据自身的生产能力和规模，以利润最大化及顾客对产品的满意度为目标，对个性化需求进行较准确地预测，从而正确指导生产。本通过博弈论的方法，提出了一个基于顾客对产品的满意度及企业的利润的一个非合作博弈模型，并给出求解纳什均衡的方法。     

A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.