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The G Class of Functions and Its Ap.lications

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Acta Mathematica Sinica,English Ser.es 2000年第3期16卷 455-468页

作者： Shenghong li department of mathematics,zhejiang university,hangzhou,310027,p.r.chinaXiangao liu department of mathematics,Fudan university,Shanghai,200433,p.r.china department of mathematics Zhejiang University Hangzhou 310027 P. R. China department of mathematics Fudan University Shanghai 200433 P. R. China

In this p.p.r.we intr.duce the concep. of the G class of functions of the p.r.bolic class, and show the Hlder.continuity of the G class of *** intr.duction *** concep. contr.butes to the p.oof of the r.gular.ty and ex... 详细信息

关键词： p.r.bolic equation r.gular.ty and existence G class of functions

liL and the Ap.r.ximation of r.ctangular.Sums of B-valued r.ndom Var.ables when Extr.me Ter.s ar. Excluded

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Acta Mathematica Sinica,English Ser.es 2002年第3期18卷 605-614页

作者： li Xin ZHANG department of mathematics Xixi Camp.s. zhejiang university, hangzhou 310028, p. r. china department of mathematics Xixi Camp.s Zhejiang University Hangzhou P. R. China

Let {X, X_; ∈N^d} be a field of i.i.d, r.ndom var.ables indexed by d-tup.es of p.sitive integer. and taking values in a Banach sp.ce B and let X_^((r.)=X_(m) if ‖X_‖ is the r.th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r.)S_=S_-(X_^((1))+…+X_^((r.). We ap.r.ximate the tr.mmed sums ^((r.)_n, by a Br.wnian sheet and obtain sufficient and necessar. conditions for.^((r.)S_ to satisfy the comp.ct and functional laws of the iter.ted logar.thm. These r.sults imp.ove the p.evious wor.s by Mor.ow (1981), li and Wu (1989) and Ledoux and Talagr.nd (1990).

关键词： Str.ng ap.r.ximation Tr.mmed sums The law of iter.ted logar.thm

The Equivalence r.lations between the Best Ap.r.ximation and linear.Op.r.tor. Ap.r.ximation in a Besov Sp.ce

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Acta Mathematica Sinica,English Ser.es 1997年第4期13卷 527-536页

作者： li song department of Ap.lied mathematics, zhejiang university, hangzhou 310027, china 浙江大学应用数学系浙江杭州

In this p.p.r. we char.cter.ze Besov typ. sp.ce intr.duced by the best ap.r.ximation, best ap.r.ximating elements and a kind of linear.op.r.tor..

关键词： Sp.ce of Besov typ. the best ap.r.ximation Best ap.r.ximating elements linear.op.r.tor.

Bior.hogonal multip.e wavelets gener.ted by vector.r.finement equation

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Science china mathematics 2007年第7期50卷 1015-1025页

作者： song li~(1+) Jun XIAN~2 1 department of mathematics,zhejiang university,hangzhou 310027,china 2 department of mathematics,Sun Yat-Sen university,Guangzhou 510275,china 1. department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Sun Yat-Sen University Guangzhou 510275 China

Bior.hogonal multip.e wavelets ar. gener.ted fr.m r.finable function vector. by using the multir.solution analysis. In this p.p.r.we p.ovide a gener.l method for.the constr.ction of comp.ctly sup.or.ed bior.hogonal multip.e wavelets by r.finable function vector. which ar. the solutions of vector.r.finement equations of the for. $$\var.0}i (x) = \sum\limits_{\alp.a \in \mathbb{Z}^s } {a(\alp.a )\var.0}i (Mx - \alp.a ), x \in \mathbb{r.^s } ,$$ wher. the vector.of functions ? = (? 1, …, ? r.T is in $(L_2 (\mathbb{r.^s ))^r.,a = :(a(\alp.a ))_{\alp.a \in \mathbb{Z}^s } $ is a finitely sup.or.ed sequence of r.× r.matr.ces called the r.finement mask, and M is an s × s integer.matr.x such that lim n→∞ M ?n = 0. Our.char.cter.zations ar. in the gener.l setting and the main r.sults of this p.p.r.ar. the r.al extensions of some known r.sults.

关键词： r.finement equation bior.hogonal multip.e wavelets r.finable function vector 42C40 41A10 41A15 41A25

Multivar.ate r.finement equation with nonnegative masks

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Science china mathematics 2006年第4期49卷 439-450页

作者： li song & ZHOU Xinlong department of mathematics, zhejiang university, hangzhou 310027, china Instititute of mathematics, university of Duisbur.-Essen, D-47057, Duisbur., Ger.any 1. department of mathematics Zhejiang University Hangzhou 310027 China 2. Institute of mathematics University of Duisburg-Essen D-47057 Duisburg Germany

This p.p.r.is concer.ed with multivar.ate r.finement equations of the typ. wher. (?) is the unknown function defined on the s-dimensional Euclidean sp.ce r., a is a finitely sup.or.ed nonnegative sequence on Zs, and M is an s×s dilation matr.x with m := |detM|. We char.cter.ze the existence of L2-solution of r.finement equation in ter.s of sp.ctr.l r.dius of a cer.ain finite matr.x or.tr.nsition op.r.tor.associated with r.finement mask a and dilation matr.x M. For.s = 1 and M = 2, the sufficient and necessar. conditions ar. obtained to char.cter.ze the existence of continuous solution of this r.finement equation.

关键词： nonnegative mask, subdivision schemes, multivar.ate r.finement equation.

A Sufficient Condition for.a Smash p.oduct as a Tr.nsfinite Left Fr.e Nor.alizing Extension and Its Ap.lication

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Acta Mathematica Sinica,English Ser.es 2000年第1期16卷 71-78页

作者： Fang li department of mathematics,zhejiang university Xixi Camp.s,hangzhou 310028,p.r.chinaZhongkui liu department of mathematics,Nor.hwest Nor.al university,Lanzhou 730070,p.r.china department of mathematics Zhejing University Xixi Campus Hangzhou 310028 P.R. China

In this p.p.r.a sufficient condition is given under.which the smash p.oduct A#H is a tr.nsfinite *** nor.alizing extension of an algebr. ***,the r.sult is ap.lied to a skew semigr.up.r.ng,a skew gr.up.r.ng and the qua... 详细信息

关键词： Smash p.oduct Tr.nsfinite left fr.e nor.alizing extension Skew semigr.up.r.ng Quantum gr.up

Global Analyses of a Class of Cubic Systems

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Acta Mathematica Sinica,English Ser.es 1997年第2期13卷 207-220页

作者： li Jinming Cai Suilin (department of Ap.lied mathematics,zhejiang university,hangzhou 310027,china) department of Ap.lied mathematics Zhejiang University

In this p.p.r.we use the canonical for.s of homogeneous p.lynomials of degr.e 3 to study the global p.op.r.ies of cubic systems =x+p.（x,y）,=y+Q3（x,y）（0.1） wher. p. and Q3 ar. homogeneous p.lynomials of degr.e 3 ... 详细信息

In this p.p.r.we use the canonical for.s of homogeneous p.lynomials of degr.e 3 to study the global p.op.r.ies of cubic systems =x+p.sub>3（x,y）,=y+Q3（x,y）（0.1） wher. p.sub>3 and Q3 ar. homogeneous p.lynomials of degr.e 3 in x,*** this wor.,we dr.w an over.ll outline of such systems.

关键词： p.ase-p.r.r.it limit cycle Cubic systems

limit theor. of r.str.cted r.nge ap.r.ximations of comp.ex-valued continuous functions

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Science china mathematics 2007年第10期50卷 1427-1440页

作者： Xian-fa LUO~1 Chong li~(2+) ~1 School of mathematics and Comp.ter.Science,Jishou university,Jishou 416000,china ~2 department of mathematics,zhejiang university,hangzhou 310027,china 1. School of mathematics and Comp.ter.Science Jishou University Jishou 416000 China 2. department of mathematics Zhejiang University Hangzhou 310027 China

This p.p.r.is concer.ed with the p.oblem of the best r.str.cted r.nge ap.r.ximations of comp.ex-valued continuous functions. Sever.l p.op.r.ies for.the ap.r.ximating set p. such that the classical char.cter.zation r.sults and/or.the uniqueness r.sults of the best ap.r.ximations hold ar. intr.duced. Under.the ver. mild conditions, we p.ove that these p.op.r.ies ar. equivalent that p.is a Haar.subsp.e.

关键词： r.str.cted r.nge ap.r.ximation, Haar subsp.ce, char.cter.zation, uniqueness

Dynamic analysis and bifur.ation contr.l of a delayed fr.ctional-or.er.eco-ep.demiological migr.tor. bir. model with fear.effect

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Inter.ational Jour.al of Biomathematics 2024年第3期17卷 1-33页

作者： Caihong song Ning li College of Sciences Northeastern University 110819 ShenyangLiaoningP.R.China

In this p.p.r.a new delayed fr.ctional-or.er.model including suscep.ible migr.tor. bir.s,infected migr.tor. bir.s and p.edator. is p.op.sed to discuss the sp.ead of diseases among migr.tor. *** of p.edator. is consider.d in the model,as fear.can r.duce the r.p.oduction r.te and disease tr.nsmission r.te among ***,some basic mathematical r.sults of the p.op.sed model ar. ***,time delay is r.gar.ed as a bifur.ation p.r.meter.and the delay-induced bifur.ation conditions for.such an uncontr.lled system ar. established.A novel p.r.odic p.lse feedback contr.ller.is p.op.sed to sup.r.ss the bifur.ation *** is found that the contr.l scheme can successfully sup.r.ss the bifur.ation behavior.of the system,and the p.lse width can be ar.itr.r.ly selected on the p.emise of ensur.ng the contr.l *** with the tr.ditional time-delay feedback contr.ller.the contr.l scheme p.op.sed in this p.p.r.has mor. advantages in p.actical ap.lication,which not only embodies the advantages of low contr.l cost and easy op.r.tion but also cater. to the p.r.odic changes of the *** p.op.sed contr.l scheme,in p.r.icular.r.mains effective even after.the system has been disr.p.ed by a *** simulation ver.fies the cor.ectness of the theor.tical r.sults.

关键词： Delayed fr.ctional-or.er migr.tor. bir.s fear Hop. bifur.ation p.r.odic p.lse feedback