A Skorokhod Problem formulation and large deviation analysis of a processor sharing model

Generalized processor sharing has been proposed as a policy for distributing processing in a fair manner between different data classes in high-speed networks. In this paper we show how recent results on the Skorokhod Problem can be used to construct and analyze the mapping that takes the input processes into the buffer content. More precisely, we show how to represent the map in terms of a Skorokhod Problem, and from this infer that the mapping is well defined (existence and uniqueness) and well behaved (Lipschitz continuity). As an elementary application we present some large deviation estimates for a many data source model. This revised version was published online in June 2006 with corrections to the Cover Date.     

完备格上基于Sup-T合成算子的矩阵的平方根

对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S⊙S=R,则称S为R的平方根,其中I表示指标集|I|的基数,⊙在本文中指的是sup-T合成算子并且T是无限∨分配的保序的算子。本文给出了完备格上基于sup-T合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根。     

拉单晶问题数学模型弱解的存在性和唯一性

本文考虑楔形区域Ｇ０Ｔ上的二相自由边界问题：其中ａ，ｂ，ｂ１，νｐ，ｈ２为正常数。本文在适当的假设之下，证明了上述定解问题弱解的存在性和唯一性。     

一类半线性卷积积分微分方程的初边值问题

本文考虑具线性粘弹性杆受粘性阻尼的横振动所引出的积分微分方程的初边值问题，在某些条件下，得到了解的存在性、唯一性、稳定性和正则性的结论。     

A Degenerate Stefan Problem with Two Free Boundaries

ＡＤｅｇｅｎｅｒａｔｅＳｔｅｆａｎＰｒｏｂｌｅｍｗｉｔｈＴｗｏＦｒｅｅＢｏｕｎｄａｒｉｅｓ￥（李辉来）ＬｉＨｕｉｌａｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）Ａｂｓｔｒａｃｔ...     

Three Classes of Reaction-Diffusion Systems with Neumann Boundary Condition

ＴｈｒｅｅＣｌａｓｓｅｓｏｆＲｅａｃｔｉｏｎ－ＤｉｆｆｕｓｉｏｎＳｙｓｔｅｍｓｗｉｔｈＮｅｕｍａｎｎＢｏｕｎｄａｒｙＣｏｎｄｉｔｉｏｎ￥（严子谦）ＹａｎＺｉｑｉａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈ...     

非线性波动方程解的Blow up

本文主要讨论高维空间非线性波动方程的Ｃａｕｃｈｙ问题整体解的非存在性，我们证明对Ｕｕ－△ｕ＝ｆ（ｕ），ｆ（ｕ）＝ｃ｜ｕ｜ｐ－１ｕ，当１＜ｐ≥时，若初始能量非正，则无论初值数据的ｃｋ－范数（连续空间范数）多么小，解按Ｃｋ－范数或按Ｈｓ（Ｒｎ）（Ｓ≥１）都在有限时间内Ｂｌｏｗｕｐ，并且有相同的生命跨度．     

New solutions for charge distribution on conductor surface

In the paper, a problem of electrostatics for charge distribution on a conductor surface is analytically solved for three new particular cases of conducting surfaces with complicated shape and specified value of electrostatic potential. The exact analytical expressions for surface charge density for the bodies are obtained. All the solutions are represented in a clear view of 3D graphs. It is shown that the proposed method of electrostatic problem for conductors allows to obtain infinitely many numerical solutions for the problem but only several special cases can be solved analytically.     

关于n阶微分方程边值问题（Ⅲ）——奇摄动的渐近展开

本文研究n阶非线性过值问题(NB)的奇异摄动。在较一般的条件下,应用高阶微分不等式理论证明了摄动解的存在性,并给出了摄动解直到n阶导函数的一致有效渐近展开式,推广和改进了已有的结果。     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.