对流扩散方程带罚函数项的有限体积格式及其分析

1引言 有限体积方法[l]一l’]作为守恒型的离散技术，被广泛应用于工程计算领域.文【2，3} 基于分片常数和分片常向量函数空间，对二维驻定对流扩散方程提出了一类非协调混合 有限体积(Covolume)格式，证明了格式具有。(hl/2)收敛精度.但该格式要求对偶剖分 比较规则，即采用重     

组合原则回溯

从组合原则产生的背景和关键入手，分析和叙述了里兹的组合原则在光谱学上的重要意义，同时，也阐述了它与玻尔氢原子理论之间的关系。     

水准折光及双波长激光效应

本文从“同温度层不完全平行于地面,且在变化”的“任意分层”假设出发,导出了水准折光修正公式,并利用光的色散效应在10~(-6)的精度要求下,求得r=r_T=h_1/h_2=(n_(01)-1)/(n_(02)-1)=常数最后指出,研制双波长激光水准仪的必要性和可能性,并提出了研制此种仪器的技术参数.     

PREPARATION OF POLY（METHYL METHACRYLATE）/LAYERED DOUBLE HYDROXIDES NANOCOMPOSITES via in situ SOLUTION POLYMERIZATION

An exfoliated layered double hydroxides/poly(methyl methacrylate)(LDHs/PMMA)nanocomposite was prepared by in situ solution polymerization of methyl methacrylate(MMA)in the presence of 4-vinylbenzenesulfonate intercalated LDHs(MgAl-VBS LDHs).MgAl-VBS LDHs was prepared by the ion exchange method,and the structure and composition of the MgA1-VBS LDHs were determined by X-ray diffraction(XRD),infrared spectroscopy and elemental analysis.XRD and transmission electron microscopy(TEM)were employed to examine the structure of LDHs/PMMA nanocomposite.It was indicated that the LDHs layers were well exfoliated and dispersed in the PMMA matrix.The grafting of PMMA onto LDHs was confirmed by the extraction result and the weight fraction of grafted PMMA increased as the weight fraction of LDHs in the nanocomposites increased.     

PROGRESS IN PHASE INVERSION EMULSIFICATION FOR EPOXY RESIN WATERBORNE DISPERSIONS

In this review, our recent work in phase inversion emulsification （PIE） for polymer （especially epoxy resin） waterborne dispersions is summarized. Based on experimental results about PIE process, the physical model is proposed which can guide the synthesis of the waterborne dispersions such as polymer/nanoparticle composite dispersion. In the presence of a latent curing catalyst, PIE can give a crosslinkable epoxy resin waterborne dispersion. The dispersions can form cured transparent coatings with some unique properties such as UV shielding. They are promising in functional coatings, waterborne resin matrices for composites, and sizing for high performance fibers.     

一类非线性半向量二层规划问题的罚函数方法

本文研究了一类非线性-线性半向量二层规划问题的罚函数求解方法.对于该类半向量二层规划问题,首先基于下层问题的加权标量化方法和Karush-Kuhn-Tucker最优性条件,将其转化为一般的二层规划问题,并取下层问题的互补约束为罚项,构造出相应的罚问题;然后分析罚问题最优解的相关特征以及最优性条件,进而设计了相应的罚函数算法;最后以相关算例验证了罚函数算法的可行、有效性.     

A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD

针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。     

带五次项的非线性Schrödinger方程的守恒差分格式

本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件（1.6）.针对此问题,我们研究了一个守恒差分格式,在条件（1.6）下,差分解的$L^{\infty}$模先验估计被得到.在此基础上,我们得到了差分解最优$L^2$模的误差估计.     

含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*

在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|²dx) Δu + λV (x)u = μf(x)|u|^q?2u + |u|^p?2u, x ∈ R³,u ∈ H¹(R³),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到.     

In Situ Fabrication of ZnS Semiconductor Nanoparticles in Layered Organic-inorganic Solid Template

Ordered ZnS semiconductor nanoparticles were in situ synthesized in metal halide perovskite organic/inorganic layered hybrids (CnH2n 1NH3)2ZnCl4 (n=10 and 12) by reaction of their spin-casting films with H2S gas. Transmission electron microscopy, UV-vis spectroscopy and small-angle X-ray diffraction were used to characterize the morphology and the structure of formed nanoparticles. Obtained results indicate an effective way to incorporate functional inorganic nanoparticles into structured organic matrices.