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COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE

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Acta Mathematica Scientia 2005年第3期25卷 439-448页

作者：房艮孙叶培新 school of mathematical sciences beijing normal university school of mathematical sciences and LPMC Nankai university

The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.

关键词： worst (deterministic) case stochastic case average case setting bounded linear functional error estimate

L^2-Algebraic Decay Rate for Transient Birth-Death Processes

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 583-594页

作者： Lijuan CHENG1 Yingzhe WANG2 1Laboratory of Mathematics and Complex Systems, the Ministry of Education of china school of Mathe-matical sciences, beijing normal university, beijing 100875, china. 2Laboratory of Mathematics and Complex Systems, the Ministry of Education of china school of mathematical sciences, beijing normal university, beijing 100875, china. Laboratory of Mathematics and Complex Systems the Ministry of Education of China school of mathematical sciences Beijing Normal University Beijing China

This paper is a continuation of the study of the algebraic speed for Markov processes. The authors concentrate on algebraic decay rate for the transient birth-death processes. According to the classification of the boundaries, a series of the sufficient conditions for algebraic decay is presented. To illustrate the power of the results, some examples are included.

关键词： Transient Birth-death processes Algebraic decay

Romanoff theorem in a sparse set

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Science china Mathematics 2010年第9期53卷 2195-2202页

作者： CHEN Yong-Gao school of mathematical sciences,Nanjing normal university,Nanjing 210046,china 1. school of mathematical sciences Nanjing Normal University Nanjing 210046 China

Let A be any subset of positive integers,and P the set of all positive *** of our results are:(a) the number of positive integers which are less than x and can be represented as 2k + p(resp.p-2k) with k ∈ A and p ∈ P is more than 0.03A(log x/log 2)π(x) for all sufficiently large x;(b) the number of positive integers which are less than x and can be represented as 2q + p with p,q ∈ P is(1 + o(1))π(log x/log 2)π(x).Four related open problems and one conjecture are posed.

关键词： Romanoff theorem Polignac conjecture asymptotic density

Relative n-widths of periodic convolution classes with NCVD-kernel and B-kernel

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Science china Mathematics 2010年第1期53卷 165-172页

作者： YANG Wei & LIU YongPing school of mathematical sciences,beijing normal university Laboratory of Mathematics and Complex Systems,Ministry of Education,beijing 100875,china 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China

In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q a... 详细信息

关键词： relative n-width periodic convolution class NCVD-kernel B-kernel

Implications of micro-compositions of garnet and biotite from high-grade meta-pelites

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Progress in Natural Science:Materials International 2006年第2期16卷 209-214页

作者： ZHOU Xiwen, WEI Chunjing, and ZHANG Shangkun ( Institute of Geology, CAGS, beijing 100037, china school of Earth and Space sciences, Peking university, beijing 100871, china china university of Geo-sciences, beijing 100083, china) Institute of Geology CAGS Beijing 100037 China school of Earth and Space sciences Peking University Beijing 100871 China china university of Geo-sciences Beijing 100083 China

Based on detailed studies on the compositional zoning of garnet and biotite in pelitic rocks from the Jingshan group of granulite facies in north Jiaodong, P-T pseudosections with isopleths of Fe/(Fe + Mg) in garnet and biotite were calculated in the KF-MASH system for two representative rocks of sillimanite-garnet-cordierite-biotite gneiss ( Vbi/ Vg>1 ) and sillimanite-garnet gneiss (Vbi/ Vg 1 can nearly preserve their peak compositions, and biotites in garnet-rich rocks with Vbi/Vg<0. 2 cannot preserve their peak compositions due to the influence of grain-boundary fluid.

关键词： high-grade meta-pelites THERMOCALC P-T pseudosection peak compositions of garnet and biotite.

Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of Mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI school of mathematical sciences, Fudan university, Shanghai 200433, china school of Mathematics and Statistics, Northeast normal university, Changchun 130024, china. school of mathematical sciences Fudan University Shanghai 200433 China school of Mathematics Statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

Finite Groups in Which Sylow normalizers Admit Supplements

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Acta Mathematica Sinica,English Series 2007年第3期23卷 417-422页

作者： Tian Ze LI school of mathematical sciences,Peking university,beijing 100871,P.R.china school of mathematical sciences Peking University Beijing 100871 P. R.China

For a group G and a subgroup M of G,we say that a subgroup A of G is a supplement toM in G,if G=*** prove that a finite group in which every Sylow normalizer admits a nilpotentsupplement is *** particular we confirm a... 详细信息

关键词： Sylow normalizer Supplement Wreath product

THE REGULARITY OF THE FREE BOUNDARY FOR STRIKE RESET OPTION

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Acta Mathematica Scientia 2010年第5期30卷 1721-1729页

作者：杨舟 school of mathematical sciences South China Normal University

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.

关键词： strike reset option free boundary variational inequality the comparison principle

Structure of augmentation quotients of finite homocyclic abelian groups

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Science china Mathematics 2007年第9期50卷 1280-1288页

作者： Guo-ping TANG school of mathematical sciences,Graduate university of Chinese Academy of sciences,beijing 100049,china 1. school of mathematical sciences Graduate University of Chinese Academy of Sciences Beijing 100049 China

Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p r , i.e., a finite homocyclic abelian group. Let Δ n (G) denote the n-th power of the augmentation ideal Δ(G) of the integral group ring ?G. The paper gives an explicit structure of the consecutive quotient group Q n (G) = Δ n (G)/Δ n+1(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.

关键词： integral group ring augmentation ideal consecutive quotient of augmentation ideal 16S34 20C05