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数学进展
  1993年, 第22卷, 第1期 刊出日期:1993-02-25 上一期    下一期
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广义指数二分性与微分方程的不变流形
张伟年
数学进展. 1993, 22 (1): 1-45.  
摘要  
用 Hadamar和 Bogoliubov的方法,在常微分方程、泛函微分方程以及半线性抛物型方程所能满足的条件下对Banach或Hilbert空间上的非自治抽象微分方程建立了不变流形理论。首先,对相应的线性方程提出了“广义指数二分性”概念并讨论了它和线性方程谱的关系,然后,我们给出了不变流形存在性结论以及强稳定(不稳定)流形、弱稳定(不稳定)流形和弱双曲流形的分类。进而,我们对这些不变流形给出了C~k光滑性、周期性、概周期性和吸斥性的结论。
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研究论文
狄氏型及其在数学物理中的应用
马志明
数学进展. 1993, 22 (1): 46-68.  
摘要  
简介狄氏型理论。该理论已成为紧密联系解析位势论与马氏过程理论的强有力数学工具,并因此在数学与物理中有许多应用。
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四元数群上的酉群的K_1
游宏
数学进展. 1993, 22 (1): 69-73.  
摘要  
令π表阶为8的四元数群,Zπ是π关于Z的群环,在Zπ上按自然方法定义一个对合映射“*”,并将“*”扩展为对合*_ω(仍记为*):x→ωx~*ω~(-1),x∈Zπ(ω=1,i,j,k)。定义K_1U~(-1)(Zπ)=U-1(Zπ)/EU-1(Zπ),K中U~(-1)(Zπ)=U_(2n)~(-1)(Zπ),EU~(-1)(Zπ)= EU_(2n)~(-1)(Zπ),而U_(2n)~(-1)(Zπ)={U∈GL_(2n)(Zπ)|UFU~*=F,F},EU_(2n)~(-1)(Zπ)为由初等酉阵生成的U_(2n)~(-1)(Zπ)的子群。主要结果是:(i)如果 Zπ上的对合是*ω,ω=i,j,k,则K_1U~(-1)(Zπ)=1;(ii)如果Zπ上的对合是*_1,则K_1U~(-1)(Zπ)=V,这里V表Klein 4元群。
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群分次环的本原性及分次本原性
陈操宇
数学进展. 1993, 22 (1): 74-78.  
摘要  
设A是一个用有限群G分次的环,本文给出了Smash积A#G~*为本原环的一个判别准则,并证明了群分次环的每一个本原理想必定包含一个分次本原理想。作为一个推论,得到已被Cohen和Montgomery证实的Bergman猜想的另一个证明。此外还得到了A_1为本原环或单环的判别。
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RESEARCH ANNOUNCEMENTS The New Necessary and Sufficient Conditions for the Uniformly Continuous and Continuous of Duality Mappings
陈连昌,武俊德
数学进展. 1993, 22 (1): 79-80.  
摘要  
In[1],Ma shaoqin gave the necessary and sufficient condition for the uniformlycontinuous and continuous of duality mappings.In the note,We give very simplecriteria for the uniformly continuous and continuous of duality mappings.And by[1],the necessary and sufficient conditions for the norm of a real Banach Space to beuniformly Frechet differentiable and Frechet differentiable are described.
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Characterizations of Best L_p(1≤p≤+ ∞) Approximation With Restricted Ranges of Derivatives
许树声
数学进展. 1993, 22 (1): 81-83.  
摘要  
Let [a,b] be a compact set containing at least n + 1 points. If Φ_n = span(φ_1, φ_2,…, φ_n) is an n-dimensional subspace of L,[a, b] m φ_1~(s), φ_2~(s)…, φ_n~(s)exist (s≥0is an integer) and have a maximal linearly independent subset which is an extendedChebyshev system of order rs on [a,b], then write
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Geometry of Multinomial Distribution Models
韦博成
数学进展. 1993, 22 (1): 84-85.  
摘要  
In this paper, we present a new differential geometric framework to study mul-tinomial distribution models in which a p-vector parameter θ is of interest. Thegeometry and models discussed here are different from those of Efron and Amari(EA) and Bates and Watts (BW). In brief, the models we study are close to thoseof EA and the geometry we present is close to that of BW. We try to combine bothEA and BW advantages into our models. Suppose that Y = (y_1,…,y_n)~T are multinomial random variables whose densityfunction has the form
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On a Conjecture of S.Halperin
黄华乐
数学进展. 1993, 22 (1): 86-87.  
摘要  
If X is a finite simply connected CW complex, then H_*(X,Q) is finitedimensional, let n_X = max{i|H_i(X,Q)≠0}. On the other hand,π_i(X) is the directsum of finitely many copies of Z and finite Abelian group. We call an interval[k,l] a torsion gap for X if π_k(X) and π_l (X) both coutain copies of Z, andπ_i (X)(k Related Articles
Longest Cycles in 3-Connected k-Regular Claw-Free Graphs
李国君
数学进展. 1993, 22 (1): 88-89.  
摘要  
All graphs considered here are undirected aud finite without loop or multipleedges. A graph is called claw-free if it do not contain a K_(1,3) as an inducedsubgraph. Let δ(G) denote the minimum degree of a graph G, and let V(G) andE(G) be the vertex set and edge set of G, respectively. For a subset S of V(G)and a subgraph H of G,G[S] and G-H denote the subgraphs of G induced by the
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Extension Principle and α-upper (α-lower) Fuzzy Set Category
翟建仁,何清
数学进展. 1993, 22 (1): 90-91.  
摘要  
In this paper the definitions of class of α-upper (resp. α-lower) fuzzy sets andweak extension principle and α-upper (resp. α-lower) fuzzy set category are givenand rationality of weak extension priuciple is illustrated. By the way we popularizeTheorem 2.3 in [1]. Let L be a complete lattice, 0 and 1 respectively the least and the greatestelement of L.
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On Self-dual Gauge Field
陆启铿
数学进展. 1993, 22 (1): 92-93.  
摘要  
Let M be a 4-dimensional differentiable manifold with a pseudo-Riemann metric ds~2 = g_(jk)dx~i dx~k,where x~j is an admissible local coordinate of M. Here we use summation conventionand the indices j,k,l, …,ran from 0 to 3. Let ω~α=e_j~odx~j, α= 0, 1, 2, 3be a set of pseudo-orthogonal frame, i.e.
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国家自然科学基金数学动态报导
数学进展. 1993, 22 (1): 94-95.  
摘要  
一、数学天元基金设立以来,我们在广泛征求数学家意见的基础上,制定了“数学天元基金管理试行办法”,又同我委国际合作局共同制定了“数学天元基金国际合作与交流的暂行规定”,这两个办法都已经我委批准在“数学进展”1992年第21卷第3期上刊登,前者在中国数学会通讯1992年第2期上也已公布。 二、为便于数学界申请,最近我们又制定了“数学天元基金申请审批表”和“数学天元基金国际合作与交流申请审批表”。
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书讯
数学进展. 1993, 22 (1): 96-96.  
摘要  
韦博成等著 东南大学出版社 1991年出版 定价:5.25元 本书为国内唯一的一本系统论述“统计诊断”的专著。全书分两大部分,前六章介绍线性回归的诊断,包括异常点分析、残差分析、影响分析、数据变换及其诊断等;后五章介绍统计诊断的新进展,包括广义影响分析,多元线性模型的诊断,多元分析中影响分析,其它模型(广义线性、非线性、时间序列等)的诊断,统计诊断的Bayes方法等。书中列举了各种实例近100个,并有各种诊断图表。
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