检索结果-南通市图书馆

DIMENSIONS OF SELF-AFFINE SETS WITH OVERLAPS

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2003年第3期24卷 275-284页

作者： HUA Su department of mathematics, tsinghua university, beijing 100084, china. Tsing Hua Univ Dept Math Beijing 100084 Peoples R China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

RECOGNITION AND CLASSIFICATION FOR O(n)-EQUIVARIANT BIFURCATIONS WITH O(n)-CODIMENSION LESS THAN 5

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 1998年第4期19卷 391-400页

作者： WANG XIAOFENG (department of applied mathematics, tsinghua university, beijing 100084, china.)TANG YUN (department of applied mathematics, tsinghua university, beijing 100084, china.)WANG DUO (School of Mathematical Science, Peking universityl Beliing 10 Tsing Hua Univ Dept Appl Math Beijing 100084 Peoples R China Peking Univ Sch Math Sci Beijing 100080 Peoples R China

Bifurcation problems equivariant under the standard action of the orthogonal group O(n) up to O(n)-codimension 4 are classified into 19 classes. For each class the normal form and one universal unfolding are calculate... 详细信息

关键词： O(n)-equivariant bifurcation Normal form Universal unfolding Recognition problem

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2001年第4期22卷 513-518页

作者： BU SHANGQUAN department of applied mathematics, tsinghua university, beijing 100084, china. E-mail: sbu@*** department of applied mathematics Tsinghua University Beijing 100084 China

Let X be a complex Banach space without the analytic Radon-Nikodym property. The author shows that G = {f∈H∞(D,X) there exists∈＞ 0, such that for almost allθ∈[0, 2], lim sup f(reiθ) - f(seiθ)≥∈ } is a dense open subset of H∞(D, X). It is also shown that for every open subset B of T, there exists F∈H∞ (D, X), such that F has boundary values everywhere on Bc and F has radial limits nowhere on B. When A is a measurable subset of T with positive measure, there exists f∈H∞ (D, X), such that f has nontangential limits almost everywhere on Ac and f has radial limits almost nowhere on A.

关键词： Analytic Radon-Nikodym property Radial limits and vector-valued Hardy space

THE NAGUMO EQUATION ON SELF-SIMILAR FRACTAL SETS

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2002年第4期23卷 519-530页

作者： HU JIAXINdepartment of mathematics, tsinghua university, beijing 100084, china. department of mathematics Tsinghua University Beijing 100084 China

The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.

关键词： Fractal set Spectral dimension Sobolev-type inequality Strong (Weak) solution

THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational mathematics 1998年第3期16卷 239-256页

作者： Wei-zhu Bao (department of applied mathematics, tsinghua university, beijing 100084, P.R. china. 清华大学应用数学系北京

We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective.

关键词： Oseen equations artificial boundary artificial boundary condition finite element approximation error estimate

SOME PROPERTIES OF LSQR FOR LARGE SPARSE LINEAR LEAST SQUARES PROBLEMS

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2010年第4期23卷 815-821页

作者： Zhongxiao JIA department of Mathematical Sciences,tsinghua university,beijing 100084,china. department of Mathematical Sciences Tsinghua University

It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual *** not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes *** for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov ***,there has not yet been an analogouslyelegant formula for residual *** paper derives such kind of *** addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.

关键词： CGLS krylov subspace lanczos bidiagonalization least squares lsqr normal equations.

Median cross-validation criterion

在线全文

学校读者我要写书评

暂无评论

Chinese Science Bulletin 1997年第23期42卷 1956-1959页

作者： YANG Yingdepartment of applied mathematics, tsinghua university, beijing 100084, china department of applied mathematics Tsinghua University Beijing China

CONSIDER the nonparametric median regression model Yni = g (xni) + εni, 1≤i≤n （1）where g: [0, 1]|→R is an unknown function of interest; {xni, 1≤i≤n} is the fixed design pointsin the interval [0, 1]; {εni, 1≤i≤n} is a triangular array of row iid random variables having medi-an zero, and {Yni, 1≤i≤n} is the observation. For each x∈[0, 1], n≥1, let Dnj（x） denotethe jth nearest neighber of x, j=1, 2,…, n, i. e. {Dn1（x）, Dn2（x）,…, Dnn（x）} is a trans-position of {xn1, xn2,…, xnn} satisfying |Dn1（x）-x|≤|Dn2（x）-x|≤…≤|Dnn（x）-x|.The tie is broken by the chronological order. The

关键词： median cross validation Bahadur’s representation asymptotic oplimality.

Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields

在线全文

学校读者我要写书评

暂无评论

Chinese Science Bulletin 1998年第10期43卷 824-826页

作者： LIU Tong department of applied mathematics, tsinghua university, beijing 100084, china department of applied mathematics Tsinghua University Beijing China

Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, Zhang Xianke from 1948 to 1988.

关键词： real cyclic sextic number fields class number fundamental relative unit.

THE EXISTENCE OF J-HOLOMORPHIC CURVES AND APPLICATIONS TO THE WEINSTEIN CONJECTURE

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 1999年第4期20卷 425-434页

作者： MA RENYI(department of applied Mathmatics, tsinghua university, beijing 100084, china. tsinghua Univ Dept Appl Math Beijing 100084 Peoples R China

The author first proves the existences of J-holomorphic curves in the symplectizations of Legendre fibrations and then as an application confirms the Weinstein conjectures on contact manifolds of Legendre fibrations. As a corollary a new proof on the theorem due to Hofer,Viterbo, Gluck, Ziller, Weinstein and Ljusternik-Fet Theorem is provided, which is quite different from their original proofs.

关键词： Symplectic geometry J-holomorphic curves Periodic orbit