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Acta Mathematica Sinica,English Ser.es 2002年第3期18卷 615-624页

作者： Zai Hong WANG department of mathematics, Cap.tal Nor.al university. Beijing 100037.{2. department of mathematics Capital Normal University Beijing P. R. China

We p.ovide sufficient conditions for.the existence and multip.icity of p.r.odic solutions for.Duffing's equations with jump.ng nonlinear.ties under.r.sonance conditions.

关键词： p.r.odic solution Jump.ng nonlinear.ties Sp.ctr.m cur.e Time map

New Families in the Stable Homotop. of Sp.er.s r.visited

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Acta Mathematica Sinica,English Ser.es 2002年第1期18卷 95-106页

作者： LIN Jin Kun department of mathematics. Nankai university. Tianjin 300071.{2. department of mathematics Nankai University Tianjin P. R. China

This p.p.r.constr.cts a new family in the stable homotop. of sp.er.s π_(t-)S r.p.esented by h_ngoY_3 ∈E_2.6(,t) in the Adams sp.tr.l sequence which r.visits the b_(n-1goY3)-elements ∈π_(-7)S con- str.ctced in[3]. ... 详细信息

关键词： Stable homotop. of sp.er.s Adams sp.ctr.l sequence Toda-Smith sp.ctr.m Adams r.solution

Dynamics of Two Extensive Classes of r.cur.ive Sequences

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Jour.al of Mathematical r.sear.h and Exp.sition 2010年第5期30卷 929-935页

作者： Bin ZHAO1,2.1.department of mathematics,{2. Agr.cultur. & For.str. university,Shaanxi 712.00,p.r.china 2.department of mathematics,{2. university,Shaanxi 71012.,p.r.china department of mathematics Northwest Agriculture & Forestry University Shaanxi 712100

We investigate the dynamics of two extensive classes of r.cur.ive sequences：Xn＋1 =c∑j=0^k（i0,i1…,i2.）∈A2. ∑xn-i0xn-i1… xn-i2.＋.f（xn-i0, xn-i1,..., xn-i2.）/c∑j=1^k（i0,i1,…,i2.-1）∈A2.-1∑ xn-i0xn-i1… xn-i2.-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2.）and Xn＋1c∑j=1^k（i0,i1,…,i2.-1）∈A2.-1∑ xn-i0xn-i1… xn-i2.-1 ＋ c ＋ f（xn-i0, xn-i1,…, xn-i2.）/c∑j=0^k（i0,i1…,i2.）∈A2. ∑xn-i0xn-i1… xn-i2.＋.f（xn-i0, xn-i1,..., xn-i2.）We p.ove that their.unique p.sitive equilibr.um 5 = 1 is globally asymp.otically stable. And a new access is p.esented to study the theor. of r.cur.ive sequences.

关键词： r.cur.ive sequence equilibr.um dynamics.

On Hyp.r.nvar.ant Subsp.ces of Contr.ction Op.r.tor. on a Banach Sp.ce Whose Sp.ctr.m Contains the Unit Cir.le

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Acta Mathematica Sinica,English Ser.es 2008年第9期24卷 1471-1474页

作者： Ming Xue LIU department of mathematics Guangdong p.lytechnic Nor.al university Guangzhou 510665{2. department of mathematics Guangdong Polytechnic Normal University Guangzhou 510665 P. R. China

In this p.p.r. we p.ove that ever. op.r.tor.in a class of contr.ction op.r.tor. on a Banach sp.ce whose sp.ctr.m contains the unit cir.le has a nontr.vial hyp.r.nvar.ant subsp.ce.

关键词： Banach sp.ce contr.ction op.r.tor invar.ant subsp.ce

Exact r.tes of Conver.ence of Functional Limit Theor.ms for.Csor.o-r.vesz Incr.ments of a Wiener.p.ocess

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Acta Mathematica Sinica,English Ser.es 2002年第4期18卷 727-736页

作者： Wen Sheng WANG department of mathematics. Zhejiang university, Hangzhou 31002.,{2. department of mathematics. Hangzhou Teacher.s College. Hangzhou 310012.{2. department of mathematics Zhejiang University Hangzhou 310028

Let {W(t): t≥0} be a standar. Wiener.p.ocess and S be the Str.ssen set of functions. We investigate the exact r.tes of conver.ence to zer. (as T→∞) of the var.ables sup.(0≤≤T-a_T inf_(f∈S sup.(0≤r.1 |Y_t, T(x)-f(x)] and inf_(0≤t≤T-a_T sup.(0≤x≤1|Y_(t.T)(x)-f(x)| for.any given f∈S, wher. Y_(t.T)(x)=(W(t+xa_T)-W(t))(2._T(logTa_T^(-1)+log logT))^(-1/2.. We establish a r.lation between how small the incr.ments ar. and the functional limit r.sults of Csr.-r.vesz incr.ments for.a Wiener.p.ocess. Similar.r.sults for.p.r.ial sums of i.i.d, r.ndom var.ables ar. also given.

关键词： Wiener.p.ocess Csor.o-r.vesz incr.ment Str.ssen's law of the iter.ted logar.thm

On the Cayley-Bachar.ch p.op.r.y and the constr.ction of vector.bundles

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Science china mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2.1 department of mathematics and Statistics,Huazhong Nor.al university,Wuhan 430079,{2. 2.0},East {2. Nor.al university,Shanghai 2.02.1,{2. 1. department of mathematics and Statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bachar.ch p.op.r.y on comp.ex p.ojective smooth var.eties of dimension n≥2.for.zer. dimensional subscheme defined by the zer. set of the wedge of r.n + 1 global sections of a r.nk r.n vector.bund... 详细信息

关键词： Cayley-Bachar.ch p.op.r.y vector.bundle r.flexive sheaf k-ver. amp.e

Dimension and measur. theor.tic entr.p. of a subshift in symbolic sp.ce

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Chinese Science Bulletin 1997年第14期42卷 1193-1196页

作者： CHEN Er.ai and XIONG Jincheng1. department of Astr.nomy, Nanjing university, Nangjing 2.0093, {2. 2. department of mathematics, South {2. Nor.al university, Guangzhou 510631, {2. department of Astr.nomy Nanjing University Nangjing China department of mathematics South China Normal University Guangzhou China

1 Definitions and r.sultsWITH the develop.ent of the theor. of dynamical systems and fr.ctal geometr., one p.ovedthat symbolic dynamics is a p.wer.ul tool to study chaos and fr.ctals. It is useful to study thefr.ctal char.cter.stics of symbolic dynamics. In the p.esent note we shall p.int out the r.lationbetween the dimension and measur. theor.tic entr.p. of any subshift in symbolic sp.ce. Wep.ove her. that the Bowen’s for.ula for.Hausdor.f dimension holds without Mar.ov str.c-tur.. A var.ational p.incip.e for.dimension is obtained.

关键词： symbolic sp.ce subshift measur. theor.tic entr.p. dimension.

Emp.r.cal likelihood confidence r.gions of the p.r.meter. in a p.r.ially linear.single-index model

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Science china mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. College of Ap.lied Sciences,Beijing university of Technology,Beijing 10002.,china 2.{2.,Hong Kong Bap.ist university,Hong Kong,china 1. College of Ap.lied Sciences Beijing University of Technology 100022 Beijing China 2. department of mathematics Hong Kong Baptist University Hong Kong China

In this p.p.r. a p.r.ially linear.single-index model is investigated, and thr.e emp.r.cal log-likelihood r.tio statistics for.the unknown p.r.meter. in the model ar. suggested. It is p.oved that the p.op.sed statistics ar. asymp.otically standar. chi-squar. under.some suitable conditions, and hence can be used to constr.ct the confidence r.gions of the p.r.meter.. Our.methods can also deal with the confidence r.gion constr.ction for.the index in the p.r. single-index model. A simulation study indicates that, in ter.s of cover.ge p.obabilities and aver.ge ar.as of the confidence r.gions, the p.op.sed methods p.r.or. better.than the least-squar.s method.

关键词： p.r.ially linear single-index model, emp.r.cal likelihood, confidence r.gion, chi-squar. distr.bution, cover.ge p.obability.

The r.gular.r.p.esentation and r.gular.covar.ant r.p.esentation of cr.ssed p.oducts of Wor.nowicz C^(*)-algebr.s

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Science china mathematics 2005年第9期48卷 1245-1259页

作者： zhang Xiaoxia~(1,2. & GUO Maozheng~(1,3) 1. School of Mathematical Sciences,p.king university,Beijing 100871,{2. 2. department of mathematics,Yantai university,Yantai 2.4005,{2. 3. LMAM,p.king university,Beijing 100871,{2. 1. School of Mathematical Sciences Peking University 100871 Beijing China 2. department of mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this p.p.r.it is shown that the r.gular.r.p.esentation and r.gular.covar.ant r.p.esentation of the cr.ssed p.oducts A×α G cor.esp.nd to the twisted multip.icative unitar. op.r.tor.,wher. A is a Wor.nowicz C~*-algebr. acted up.n by a discr.te gr.up.***,it is also shown that the r.gular.covar.ant C~*-algebr. is the Wor.nowicz C~*-algebr. which cor.esp.nds to a multip.icative ***,an exp.icit descr.p.ion of the multip.icative unitar. op.r.tor.for.C(SU_q(2. )×α (?) is given in ter.s of those of the Wor.nowicz C~*-algebr. C(SU_q(2. ) and the discr.te gr.up.G.

关键词： multip.icative unitar. op.r.tor. Wor.nowicz C*-algebr., cr.ssed p.oduct.

On the p.r.odic solutions of a typ. of differ.ntial-iter.tive equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengr.ng 2.and YU Yuanhong 3 1. department of Ap.lied mathematics, Beijing Institute of Technology, Beijing 100081, {2. 2. department of mathematics, Yunnan university, Kunming 650091, {2. 3. Institute of Ap.lied mathematics, C department of Ap.lied mathematics Beijing Institute of Technology Beijing China department of mathematics Yunnan University Kunming China Institute of Ap.lied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for.the existence of p.r.odic solutions to a typ. of nonautonomous differ.ntial_iter.tive equations ar. given.

关键词： differ.ntial_iter.tive equation p.r.odic solution fixed p.int.