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数学进展
  1990年, 第19卷, 第1期 刊出日期:1990-01-15 上一期    下一期
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Subgroups of Finite Symmetric Groups
Cheryl E.Praeger
数学进展. 1990, 19 (1): 1-11.  
摘要  
Recent results about primitive permutation groups are surveyed.
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研究论文
Nonlinear Programming——a Review
袁亚湘
数学进展. 1990, 19 (1): 12-24.  
摘要  
Nonlinear programming problems are to minimize general nonlinear functions, possibly subject to some nonlinear constraints. In this paper, we review some recent results on nonlinear optimization.
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An Introduction to Plateau's Problem
Friedrich Tomi
数学进展. 1990, 19 (1): 25-37.  
摘要  
In this paper, the recent development to Plateau's problem for minimal surfaces of prescribed topological type is given briefly.
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An Introduction to the Normal Form Theory of Ordinary Differential Equations
王铎
数学进展. 1990, 19 (1): 38-71.  
摘要  
In this article the author gives a detailed introduction to three basic methods of calculating normal forms of ordinary differential equations, and a brief introduction to a method of getting normal forms of parameter dependent systems. The versa-lity of normal forms with parameters is also discussed.
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Problems Concerning Embeddings of Manifolds
Elmer Rees
数学进展. 1990, 19 (1): 72-79.  
摘要  
Very little is known in general about estimating the smallest integer l such that a manifold Mn emheds in Rn+k +l if it immerses in Rn+k. Indeed there are relatively few examples where k and l can be estimated accurately. There are old examples for which l is known to be arbitrarily Iarge; for those examples l can grow like logn and there are recent examples where l can grow linearly with n. The main difficulty in resolving questions of this kind is that the only general methods known for proving non-embedding and non-immersion results involve doing calculations with characteristic classes and the estimates that they give are very similar for the two problems. In this paper an account is given of various methods that can be used to study examples.
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Blow-up of Solutions of Heat Flows for Harmonic Maps
丁伟岳
数学进展. 1990, 19 (1): 80-92.  
摘要  
Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0) Related Articles
Order of Approximation by Hermite-Fejer Interpolating Polynomials in the Complex Plane
沈燮昌
数学进展. 1990, 19 (1): 93-104.  
摘要  
Suppose that either the outer mapping function of a domain D has continuous second derivatives or D is a strictly star domain. In this paper we first establish two inequalities concerning polynomials at Fejer's points with multiplicity (3 + 1). Using these two inequalities, we obtain the order of approximation in Lp(dD), 0 Related Articles
On the Winding of Stationary Diffusions
龚光鲁,钱敏平
数学进展. 1990, 19 (1): 105-113.  
摘要  
In this paper, the winding of stationary diffusions are studied. It is shown that, differently from Brownian motions,stationary diffusions wind up to time t angles in order of t, while Brownian motions wind up angles in order of logt,and the winding rates tend to , where c, an-i c2 are constants and is a Cauchy random variable.Moreover, it is proved that a stationary diffusion is reversible iff c2=0 for the winding around every point.
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Lower Semicontinuity w.r.t. Decreasing Sequence and its Applications
方曙红
数学进展. 1990, 19 (1): 114-115.  
摘要  
In this paper,we introduce the lower semicontinuity w.r.t.(with respect to)adecreasing sequence,which can replace the lower semicontinuous condition in somewell-known results. Definition Let X be a topological space,a function φ:X→RU{+∞)is said
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L'-Estimates for the Gradient of Weak Solutions to a Class of Degenerate Nonlinear Elliptic Systems
陈宝耀,林长好
数学进展. 1990, 19 (1): 115-116.  
摘要  
We call that λ(x)belongs to Muckenhoupt class A_p if λ(x)≥0 and satisfiesfor all balls in R,where|B_R| denotes the Lebesgue measure of a ball with centerx_0 and radius R,andLet be a bounded domain.Define normHere,denotes the Banach space of all measurable functions defined on
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On the Branching Mechanisms of Superprocesses
李增沪
数学进展. 1990, 19 (1): 117-118.  
摘要  
A superprocess is a continuous analogue of an infinite particle branching pro-cess.The branching mechanism of a superprocess is a function ψ(λ)of the form(cf.[3])
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Approximation by Szasz-Mirakjan Type Operators in L'
周定轩
数学进展. 1990, 19 (1): 118-120.  
摘要  
M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:
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The Prediction Theory of Stationary Random Field (Ⅲ) Four-fold Wold Decompositions
江泽培
数学进展. 1990, 19 (1): 120-122.  
摘要  
Let{X(m,n)}_(m,m=0,±1,±2…)be a stationary random field.The closed linearspace spanned by all X(m,n):m,n=0,±1,±2,…is denoted by L(X).Throughoutthe following pages L_1(x:s)will denote the subspace generated by all X(m,n):m≤s,-∞ Related Articles
Estimates of Orders and Parameters in General ARMA Models
李贵斌
数学进展. 1990, 19 (1): 123-126.  
摘要  
Let X(n)be a time series satisfying the following general ARMA(p,d,r,q)model: E(B)U(B)A(B)X(n)=C(B)W(n),whereC(z)is relatively prime with the polynomial E(z)U(z)A(z),B is the backshiftoperator such that BX(n)=X(n-1),and(W(n),F(n),n≥1)is a sequence ofmartingale differences. For simplicity,we shall assume throughout that the initial values(X(-p-d
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ABSTRACTS OF DOCTORIAL DISSERTATIONS
杜一宏,郭大钧
数学进展. 1990, 19 (1): 127-127.  
摘要  
The thesis is divided into twochapters.In chapter one,we study bycombining topological method with conetheory the nonlinear eigenvalue pro-blem x=f(λ,x),where f:[0,+∞]×P→P is a completely continuous map-ping with f(λ,0)≠0,P is a cone in aBanach space.A detailed description
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