检索结果-南通市图书馆

Approximation of functions on the Sobolev space with a Gaussian measure

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2010年第2期53卷 373-384页

作者： WANG HePing 1, ZHANG YanWei 2 & ZHAI XueBo 1 1 School of Mathematical Sciences, capital normal university, beijing 10004., china 2 Department of mathematics, Zaozhuang university, Zaozhuang 277160, china 1. School of Mathematical Sciences Capital Normal University Beijing 100048 China2. Department of Mathematics Zaozhuang University Zaozhuang 277160 China

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

关键词： average width best approximation approximation by linear operators Sobolev space Gaussian measure

ON THE VARIATIONS OF G_2

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 387-394页

作者： LIU DONG LIN LEI Department of mathematics, East china normal university, Shanghai 200062, china. Department of mathematics, East china normal university, Shanghai 200062, china. Department of mathematics East China Normal University Shanghai 200062 China

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G2. In this paper, the authors investigate their derivation algebras. It is shown that G2 and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of ViG for i = 3,4, 5, 6, and thereby construct some left-symmetric structures on Vi G for i = 3,4,5,6. Some errors about the variations of sl(3, F) in [1] are corrected.

关键词： Variation Derivation Associative form Left-symmetric structure

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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 473-478页

作者： MENG ZAIZHAO(Department of mathematics, Peking university, beijing 100871, china) Peking Univ Dept Math Beijing 100871 Peoples R China

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2). It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

关键词： Divisor function Multiplicative function Congruence

A New Almost Periodic Type Solution of First Order Neutral Delay Differential Equations with Piecewise Constant Argument

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2001年第3期17卷 403-412页

作者： Rong YUAN Department of mathematics,beijing normal university,beijing 100875,P.R.china E-mail:ryuan@*** Department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference *** the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).

关键词： Pseudo almost periodic solutions Pseudo almost periodic sequences Neutral delay equation Piecewise constant argument

Existence of the solutions and the attractors for the large-scale atmospheric equations

在线全文

学校读者我要写书评

暂无评论

Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2 1. Department of mathematics, beijing normal university, beijing 100875, china 2. Institute of Applied Physics and Computational mathematics, beijing 100080, china 1. Department of mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Asymptotic distributions in the projection pursuit based canonical correlation analysis

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2010年第2期53卷 485-498页

作者： JIN Jiao & CUI HengJian Department of Statistics and Financial mathematics, School of Mathematical Sciences, beijing normal university, Laboratory of mathematics and Complex Systems (beijing normal university), Ministry of Education, beijing 100875, china 1. Department of Statistics and Financial mathematics School of Mathematical Sciences Beijing Normal University Beijing 100875 China2. Ministry of Education Laboratory of Mathematics and Complex Systems (Beijing Normal University) Beijing 100875 China

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and we... 详细信息

关键词： asymptotic distribution canonical correlation analysis influence function robust statistics

Groups whose elements have given orders

在线全文

学校读者我要写书评

暂无评论

Chinese Science Bulletin 1997年第21期42卷 1761-1764页

作者： SHI WujieInstitute of mathematics, Southwest china normal university, Chongqing 630715, china Institute of mathematics Southwest China Normal University Chongqing 630715 China

'ELEMENT orders' is one of the most fundamental concepts in group theory. It plays an impor-tant role in the research of group theory, which can be seen from the famous Burnside’s prob-lem. Some well-known group theory specialists, such as Neumann, Higman, Suzuki and oth-ers, have studied the groups whose element orders take the special values. In 1981 wediscussed the finite groups of all those whose elements are of prime order except identity ele-

关键词： finite group element order simple group.

Near generalized balanced tournament designs with block sizes 4 and 5

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2009年第9期52卷 1927-1938页

作者： SHAN XiuLing1, 2 1 Department of mathematics, beijing Jiaotong university, beijing 10004., china 2 College of mathematics and Information Science, Hebei normal university, Shijiazhuang 050016, china Department of mathematics Beijing Jiaotong University Beijing 100044 China College of mathematics and Information Science Hebei Normal University Shijiazhuang 050016 China

A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.

关键词： near generalized balanced tournament designs frame generalized doubly resolvable packing constructions existence 05B05

Reliability analysis of M/G/1 queues with general retrial times and server breakdowns

在线全文

学校读者我要写书评

暂无评论

Progress in Natural Science:Materials International 2006年第5期16卷 464-473页

作者： WANG Jinting (Department of mathematics, beijing Jiaotong university, beijing 10004., china) Department of mathematics Beijing Jiaotong University Beijing 100044 China

This paper concerns the reliability issues as well as queueing analysis of M/G/1 retrial queues with general retrial times and server subject to breakdowns and repairs. We assume that the server is unreliable and customers who find the server busy or down are queued in the retrial orbit in accordance with a first-come-first-served discipline. Only the customer at the head of the orbit queue is allowed for access to the server. The necessary and sufficient condition for the system to be stable is given. Using a supplementary variable method, we obtain the Laplace-Stieltjes transform of the reliability function of the server and a steady state solution for both queueing and reliability measures of interest. Some main reliability indexes, such as the availability, failure frequency, and the reliability function of the server, are obtained.

关键词： retrial queues general retrial times reliability server breakdowns and repairs.