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数学进展
  1992年, 第21卷, 第1期 刊出日期:1992-01-15 上一期    下一期
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Topos理论简介
孟晓青
数学进展. 1992, 21 (1): 1-24.  
摘要  
Topos概念的提出(即elementary topos的公理化)是在研究了如下几类范畴之后:Grothendieck topos,集合的范畴S,以及集合论的布尔值模型。 Grothendieck提出用拓扑空间X上的set valued sheaf的全体做成的范畴Sh(X)作为推广了的拓补空间X,用以研究空间X上的上同调.他把拓扑的概念推广到小范畴(smallcategory)C上,称为一个site(或称为Grothendieck拓扑,参看第2节)。这样就可以考虑给出的site(C,J)上的set valued sheaf的全体做成的范畴Sh(C,J),用它来研究site(C,J)
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研究论文
Harmonic L~p-functions on Complete Riemannian Manifolds
王斯雷
数学进展. 1992, 21 (1): 25-55.  
摘要  
This survey paper concerns some existence theorems of harmonic functions belonging to LP (M), M being a complete Riemannian manifold. It is well known that a function which is analytic and bounded on the whole complex plane must reduce to a constant.This classical result, known as Liouville's theorem, is also true on a higher-dimensional Euclidean spaces. The generalization of this theorem to other Riemannian manifolds is very interesting. Besides its beauty, the proof usally requires sharp estimates which provide deeper understanding of the Laplacian and hence give broad applications to problems in global analysis.The basic problem in this paper is to study how the geometric conditions of a complete Riemannian manifold affect the validity of the Liouville theorem. The paper consists of two parts. Part I describes the results systematically and Part I will be more technical and will contain the detailed proofs of the results given in the first part.
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Some Developments on Algebraic Number Theory in China
冯克勤,陆洪文
数学进展. 1992, 21 (1): 56-78.  
摘要  
In this paper, a survey of the work of Chinese mathematicians on Algebraic Number Theory is given, mainly the work from 1970 years to 1930 years.
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On the Overconvergence of Hermite Interpolating Polynomials
娄元仁
数学进展. 1992, 21 (1): 79-92.  
摘要  
In this paper we study the overconvergence of Hermite interpolating polynomials. A new extension of a theorem of J.L.Walsh is obtained and a conjecture is posed.
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On the Quotient Compact Images of Metric Spaces
林寿
数学进展. 1992, 21 (1): 93-96.  
摘要  
This paper gives an internal characterization of the quotient compact images of metric spaces, which answers a question posed by Arhangel'skii; and an example is constructed to show that the quotient compact images of metric spaces are not preserved by perfect maps.
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Amenability With Respect to a Closed Subgroup of a Product Group
Jean-Paul Pier
数学进展. 1992, 21 (1): 97-112.  
摘要  
In this paper, the concept of amenability with respect to a closed subgroup of a product group (г-amenability), which is a generalization of amenability and inner-amenability under the usual sense, is introduced. Various characterizations of г-amenability reflecting classical descriptions of amenability,and comments on related problems are also elaborated.
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Large Deviation of a Capacity Related to the Ornstein-Uhlenbeck Operator
高付清
数学进展. 1992, 21 (1): 113-118.  
摘要  
We discuss the large deviation estimates of a capacity related to the Ornstein-Uhlenbeck operator and present a refinement of Strassen's form of the law of the iterated logarithm for Brownian metion from the viewpoint of the Dirichlet space theory.
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沉痛悼念沈燮昌同志
数学进展. 1992, 21 (1): 119-119.  
摘要  
沈燮昌同志是北京大学数学系和数学研究所教授,苏州大学和河南大学兼职教授,本刊和《数学研究与评论》副主编。因患癌症医治无效于1991年9月19日下午6时10分不幸逝世,终年57岁。 沈燮昌同志1934年9月10日生于浙江海宁市。1952—1956年就读于北京大学数学力学系,1957—1961年为苏联科学院数学研究所(莫斯科)研究生,获副博士学位。从1961年起一直在北京大学数学系任教。1981年6月加入中国共产党。1981—1983年任数学系副系主任,1984—1988年任北京大学研究生院副院长。1981年起任本刊副主编,1985-1989年任《逼近论及其应用》(英文版)副主编。
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Longest Cycles in 2-Connected Regular Claw-Free Graphs
李明楚
数学进展. 1992, 21 (1): 120-120.  
摘要  
All graph considered In this paper are undirected and finite,without loops ormultip1e edges.A graph is called claw-free if it does not contain a copy of K_(1,3)as an induced subgraph.For a graph C,let δ(G)denote the minimum degree of G.There have been a great many results in recent years dealing with longest cycles.for example, M.Matthews and D.Summer have shown the following result:
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Characterization in Approximation with Restricted Ranges
许树声
数学进展. 1992, 21 (1): 121-122.  
摘要  
Let [a,b] be a compact set containing at least n+1 points,C the set ofall continuous real valued functions defined on with uniform norm If φ_n=span{φ_1,…,φ_n),φ_i∈C([a,b])and φ_1,…,φ_n is an extended Chebyshev system of or-der,r(1≤r≤n),then we call K={q∈φ_n:l(x)≤q(x)≤u(x),x∈[a,b]} the set ofgeneralized polynomials having restricted ranges,where l and u are extended real
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Residual Finiteness of Finitely Generated Quasi-commutative Semigroups
江中豪
数学进展. 1992, 21 (1): 123-123.  
摘要  
A semigroup S is called residually finite if for any pair of distinct elements a,b∈S, there exists a congruence P on S such that S/p is finite and (a,b) P. In1958, Malcev proved the following theorem: Any finitely generated abelian semigroupis residually finite . In this paper,we prove that a finitely generated quasi-commu-tative semigroup is residually finite. It generalizes the above theorem.
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On Ravenel Telescope Conjecture
彭天堂
数学进展. 1992, 21 (1): 124-125.  
摘要  
In the last two decades, the most important achievement in stable homotopy the-ory is that Ravenel established his chromatic point of view. When H. Miller, D.Ravenel, and W. Wilson published their algebraic chromatic spectral sequence (i.e. the chromatic filtration of EXT(BP_*) is by "V_n-periodic families" for various
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Hypersurface With Constant Mean Curvature in Hyperbolic Space Form
吴报强
数学进展. 1992, 21 (1): 125-126.  
摘要  
In [1], S. T. Yau proved the following theorems: (1) If M is compact hyper-surface with constant mean curvature and non-negative Ricci curvature in the Eucli-dean space, then M is umbilical. (2) If M is compact hypersurface with constantscalar curvature in hyperbolic space form and M has positive sectional curvature, thenM is totally umbilical. In this paper, we shall generalize the theorems as follows
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ABSTRACTS OF DOCTORIAL DISSERTATIONS
数学进展. 1992, 21 (1): 127-127.  
摘要  
Free boundary problems for de-generate quasilinear parabolic equa-tions, Li Huilai (李辉来), Jilin Univer-sity, Supervisor: Wu Zhuoqun (伍卓群),Approved: 1987, 12.
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