双Jacobi椭圆函数展开法及其对KdV方程求解

本文将双Jacobi椭圆函数展开法以及"秩"的概念应用于求解KdV方程,得到了许多组新的用双椭圆函数表示的准确周期解.应用该方法得到的有些周期解在极限情况下可以退化为相应的孤立波解.这种方法还可以用于求解其它非线性波方程.     

关于带第一特征值λ1具Sobolev临界指数2^＊的一类椭圆方程—△u=λ1u＋｜u｜^2^＊—2u＋τ（x,u）

给出了半线性椭圆方程-△u=λ1u |u|^2^*-2u τ(x,u)的Dirichlet问题在对扰动项τ（x,u）增加适当条件后非平凡解的存在性定理，以及方程-△u=λu-|u 2^*-2u h(x),λ∈[λ1,λk]（这里λk是方程-△u=λu的第κ个互不相等的特征值）的非零解的存在性定理。     

尊重言语的不礼貌性探讨

不礼貌言语的突出特点是言说内容威胁到听者的面子,使之感到不快、尴尬。文章通过对Verschueren的顺应论进行改善,将其分为表层顺应和深层顺应。表层顺应即维氏的语境顺应,增添的深层顺应包括交际策略顺应和交际态度顺应。改善后的顺应模型很好地解释了该类日常生活中,既表达了言者对听者尊重的交际态度,但言说内容又极其不礼貌的言语现象。     

一类半线性椭圆方程解的存在性问题

主要应用环绕定理及一些解的估计来讨论一类半线性椭圆方程:-△u-μ/(|x|2)u=k(x)|u|2*-2u+λu,u∈H01(Ω),当k(x)满足一定条件时,方程存在一个非平凡解。     

积分方法在椭圆型方程解的存在性中的应用

结合ODE标准理论和积分方法,通过Lengendre变换,给出了一类拟线性椭圆型偏微分方程整体径向解存在(不存在)的一个充分必要条件。     

Mathematics and Mathematics Education as Triadic Communication? a Semiotic Framework Exemplified

The article investigates in the first part critically dyadic and essentialist understanding of signs and utterances in mathematics and mathematics education as opposed to a triadic view. However even Peircean semiotics, giving priority to triadic, dynamic sign may face challenges, such as explaining the sign as a pragmatic act and how signs are related to context. To meet these and other hurdles an explicit communicational, pragmatic and triadic view, found in parts of the works of Bühler, Bakhtin, Habermas, and Halliday, is developed. Two basic principles are combined and established in a theoretical framework. Firstly, whenever uttering, there will exist in any semiotic sign system, dynamic reciprocity and simultaneity between expressing through form, referring to content, and addressing as an act. Secondly, meaning will be created by the dynamics between given and new in utterances and between utterances and contextual genres. The latter principle explains how meaning merge in communication dynamically and create the basis for a discursive understanding of semiosis and hence even learning at large. The second part exemplifies each of the three main aspects and the dynamics of utterance and genre and given and new by excerpts from a textbook in mathematics education. The concept ‘positioning’, in use for operationalisation, is explained in relation to main principles of the framework. The article ends focusing crucial implications for validation when moving from a dyadic to a triadic understanding of mathematics and mathematics education.     

关于带第一特征值λ1具Sobolev临界指数2*的一类椭圆方程-Δu=λ1u+|u|2*-2u+τ(x,u)

给出了半线性椭圆方程-Δu=λ1u+|u|2*-2u+τ(x,u)的Dirichlet问题在对扰动项τ(x,u)增加适当条件后非平凡解的存在性定理,以及方程-Δu=λu-|u|2*-2u+h(x),λ∈[λ1,λk](这里λk是方程-Δu=λu的第k个互不相等的特征值)的非零解的存在性定理.     

英汉双语话语组合方式探析

话语分析主要研究大于句子的话语或篇章。它突破了主流语言学以句子为语言研究的最高形式,这就大大拓宽了语言的研究视野。话语分析是进行动态的分析,而理论语言学是进行静态的语言描写;前者是博采式的研究(in-widthapproach),后者是深探式的研究(in-depthapproach),二者呈现出互补的关系。     

一类高阶椭圆组解的部分正则性

考虑一类高阶椭圆组,用Blow up方法证明解的C~(m,(?))部分正则性.     

言语失误及其成因与结果

语言表现并不是语言能力或言语,后者只是前者的一种具体表达形式。在语言表达中,言语的失误常常是与语言的表达意图及表达的结果密切相关的,本文通过对言语失误的类型的分析揭示言语失误与语言的表达意图和结果之间的关系。