Linear Approximation and Asymptotic Expansion of Solutions in Many Small Parameters for a Nonlinear Kirchhoff Wave Equation with Mixed Nonhomogeneous Conditions

In this paper, we consider the following nonlinear Kirchhoff wave equation

$\left\{\begin{array}{l}u_{tt}-\frac{\partial }{\partial x}(\mu (u,\Vert u_{x}\Vert ^{2})u_{x})=f(x,t,u,u_{x},u_{t}),\quad 0

(1)

where \(\widetilde{u}_{0}\), \(\widetilde{u}_{1}\), μ, f, g are given functions and \(\Vert u_{x}\Vert ^{2}=\int_{0}^{1}u_{x}^{2}(x,t)dx.\) To the problem (1), we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the Faedo–Galerkin method and the weak compact method. In particular, motivated by the asymptotic expansion of a weak solution in only one, two or three small parameters in the researches before now, an asymptotic expansion of a weak solution in many small parameters appeared on both sides of (1)₁ is studied.

     

Limit theorem and uniqueness theorem of backward stochastic differential equations

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.     

矩阵连分式序列的收敛性

本文研究了矩阵连分式的性质，获得了关于矩阵连分式序列收敛性的一些结果．     

HI—V族化合物半导体的高能重离子辐照缺陷研究·

用正电子湮没寿命谱技术研究了2.4×1O15/cm2、2.2×1016/cm2注量的85MeV19F离子辐照N型GaP和1.6×1016/cm 2注量的85MeV19F离子辐照P型InP所产生的辐照缺陷.结果表明:两种注量辐照在GaP中均产生较高浓度的单空位.其浓度随着辐照注量的增大而增加;辐照也在InP中产生较高浓度的单空位.     

A new condition for solvable groups

A subgroup H of G is called complemented in G if there exists a subgroup K of G such that $G=HK$ and $H\cap K=1$. The aim of this paper is to prove the following: A finite group G is solvable if and only if its Sylow 3-, 5- and 7-subgroups are complemented in G.     

Synthesis and characterization of a series of 2‐aminopyridine nickel(II) complexes and their catalytic properties toward ethylene polymerization

A series of 2‐aminopyridine Ni(II) complexes bearing different substituent groups {(2‐PyCH₂NAr)NiBr, Ar = 2,4,6‐trimethylphenyl ( 3a) , 2,6‐dichlorophenyl ( 3b ), 2,6‐dimethylphenyl ( 3c) , 2,6‐diisopropylphenyl ( 3d ), 2,6‐difluorophenyl ( 3e ); (2‐PyCH₂NHAr)₂NiBr₂, Ar = 2,6‐diisopropylphenyl ( 4a )} have been synthesized and investigated as precatalysts for ethylene polymerization in the presence of methylaluminoxane (MAO). High molecular weight branched polymers as well as short‐chain oligomers were simultaneously produced with these complexes. Enhancing the steric bulk of the ortho‐aryl‐substituents of the catalyst resulted in higher ratio of solid polymer to oligomer and higher molecular weight of the polymer. With ortho‐haloid‐substitution, the catalysts afforded a product with low polymer/oligomer ratio ( 3b ) and even only oligomers ( 3e ) in which C₁₄H₂₈ had the maximum content. Compared with complex 3d containing ionic ligand, complex 4a containing neutral ligand exhibited obviously low catalytic activity for ethylene polymerization. The molecular weight, molecular weight distribution, and microstructure of the resulted polymer were characterized by gel permeation chromatography and ¹³C NMR spectrogram. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1618–1628, 2008     

抗坏血酸钛对鱼类、贝类及无尾两栖类的毒性研究

抗坏血酸钛对鲢鱼、草鱼、金鱼及泥鳅的毒性都很低,其96h TLm值为1736～10930mg/l。（敏感性顺序:鲢鱼>草鱼>金鱼>泥鳅）抗坏血酸钛对湖螺的48h TLm值与对蟾蜍蝌蚪的96hTLm值分别为12847.2与1886.5mg/l。经皮下注射,抗坏血酸钛对中华大蟾蜍的LD50为2.87g/kg。微核试验表明,钛试