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On the error term in Weyl’s law for the Heisenberg manifolds (Ⅱ)

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Science china Mathematics 2009年第5期52卷 857-874页

作者： ZHAI WenGuang school of mathematical sciences, Shandong normal university, Jinan 250014, china 1. school of mathematical sciences Shandong Normal University Jinan 250014 China

In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.

关键词： Heisenberg manifold Weyl’s law error term mean square

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science china Mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2 1 Department of Mathematics,Fuzhou university,Fuzhou 350002,china 2 Department of Mathematics,south china normal university,guangzhou 510631,china 1. Department of Mathematics Fuzhou University Fuzhou 350002 China 2. Department of Mathematics South China Normal University Guangzhou 510631 China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

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Science china Mathematics 2010年第8期53卷 1995-2010页

作者： HU Tao 1,2 & CUI HengJian 1,2 1 school of mathematical sciences,Beijing normal university,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,china 2 school of mathematical sciences,Capital normal university,Beijing 100048,china 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China

This article considers a semiparametric varying-coefficient partially linear regression *** semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are *** main object is to estimate the nonparametric component and the unknown parameters *** is easier to compute and the required computation burden is much less than the existing two-stage estimation ***,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally *** experiments are carried out to investigate the performance of the proposed method.

关键词： partly linear model varying-coefficient robustness optimal convergence rate asymptotic normality

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

Quasirational dynamic system

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Chinese Science Bulletin 2000年第14期45卷 1277-1279页

作者： SUN Daochun & YANG Lo1. Department of Mathematics, south china normal university, guangzhou 510631, china 2. Institute of Mathematics, Academy of Mathematics and System sciences, Chinese Academy of sciences, Beijing 100080, china Department of Mathematics South China Normal University Guangzhou China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Using the iterations of quasirational mappings, the theorems on dynamic system are generalized to the quasirational dynamic system. Some different results are also obtained.

关键词： quasirational mapping dynamic system covering surface.

The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： CHEN Ercai and XIONG Jincheng Department of Mathematics , Nanjing normal university , Nanjing 210097, china Department of Mathematics , south china normal university, guangzhou 510631 , china Department of Mathematics Nanjing Normal University Nanjing China Department of Mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

Holocene climate variation denoted by Barkol Lake sediments in northeastern Xinjiang and its possible linkage to the high and low latitude climates

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Science china Earth sciences 2011年第4期54卷 603-614页

作者： XUE JiBin & ZHONG Wei 1 school of Geography,south china normal university,guangzhou 510631,china 2 Key Laboratory of Oasis Ecology(Ministry of Education) ,Xinjiang university,Urumqi 830046,china 3 Key Laboratory of Western china's Environmental Systems(Ministry of Education) ,Lanzhou university,Lanzhou 730000,china 1. school of Geography South China Normal University Guangzhou 510631 China2. Key Laboratory of Oasis Ecology (Ministry of Education) Xinjiang University Urumqi 830046 China3. Key Laboratory of Western China’s Environmental Systems (Ministry of Education) Lanzhou University Lanzhou 730000 China

The climate over the closed inland Barkol Lake,which is located in northeastern Xinjiang Uygur Autonomous Region,is significantly influenced by westerly winds *** improve our understanding of past climate processes in westerly wind influenced regions in northwestern china,a 250-cm sediment section was retrieved from this *** taking the carbon reservoir effect into consideration,the chronological sequence of this section was reconstructed based on seven conventional radiocarbon dates of bulk samples,and the bottom age of this section was determined to be about 9400 cal a ***-proxy datasets,includingδ18O car,δ13C car of authigenic carbonate,and total organic carbon were examined using wavelet analysis and singular spectrum analysis *** show that the Holocene in the Barkol Lake region can be divided into four stages:(1) a cold and dry early stage before～8000 cal a BP;(2) a moderately warm and wet middle stage between～8000 and 6000 cal a BP;(3) a warm and dry stage,along with a cooling-wetting tendency from 6000 to 2700 cal a BP;and(4) a fluctuating cooling and wet stage between 2700-800 cal a BP,and a drier stage since 800 cal a *** general trend of Holocene climatic changes revealed by Barkol Lake sediments was in agreement with that of adjacent *** infer that climatic changes during the Holocene in the Barkol Lake region were influenced not only by high latitudes,especially the North Atlantic region climate,but also tropical low-latitude processes,such as the El Nio/La Nia-southern *** study demonstrates that the enhanced activities of ENSO may have played an important role in climatic changes in northeastern Xinjiang during the *** results also suggest that climatic patterns may be temporally different in the northern Xinjiang area in response to the changing predominant control of either the Westerly or the Asian summer monsoon,depending on the contrast of their relative strengths.

关键词： Barkol Lake Holocene climate change tropical processes northern high-latitude climate

Entire Function Sharing Small Function with Its Difference Operators or Shifts

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Journal of mathematical Research with Applications 2012年第4期32卷 431-438页

作者： Baoqin CHEN ,Zongxuan CHEN school of mathematical sciences,south china normal university,Guangdong 510631,P.R.china school of mathematical sciences South China Normal University Guangdong 510631

In this paper,we give some interesting results concerning the entire function f(z) sharing a small function a CM with its difference operators or shifts.

关键词： Brck conjecture shift difference shared value.

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