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Acta Mathematica Sinica,English Ser.es 2000年第2期16卷 261-270页

作者： Shaoyi Zhangdepartment of mathematics.beijing normal university.beijing 100875.p.r.china department of mathematics.Hubei normal university.Huangshi 435002,p.r.china department of mathematics Beijing Normal University Beijing 100875 P. R. China department of mathematics Hubei Normal University Huangshi 435002 P. R. China

In this p.p.r.for.two given tr.nsition p.obabilities,the existence of the op.imal Mar.ovian coup.ing with r.sp.ct to a non-negative lower.semi-continuous function is *** an ap.lication of this r.sult,the well-known Str.ssen’s theor.m is ***,it is p.oved that the existence of an or.er.p.eser.ing Mar.ovian coup.ing of two given jump.p.ocesses is equivalent to their.stochastical comp.r.bility.

关键词： Tr.nsition p.obability Mar.ovian coup.ing Jump.p.ocess

Linear.estimation and distr.bution of the limit cycles bifur.ated fr.m a kind of degener.te p.lycycles

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Science china mathematics 2007年第3期50卷 334-344页

作者： Li-qin ZHAO department of mathematics. beijing normal university. beijing 100875. china department of mathematics Beijing Normal University Beijing China

In this p.p.r. we investigate the number.and the distr.bution of the limit cycles bifur.ated fr.m a kind of degener.te p.anar.p.lycycles thr.ugh thr.e singular.p.ints: a saddle-node p., a fine saddle p. with finite or.er.m∈N, a contr.ctive (attr.cting) saddle p. with the hyp.r.olicity r.tio q2(0)■Q. The connection between p. and p. is of hh-typ. and the connection between p. and p. is of hp.typ.. It is assumed that the connections between p. to p. and p. to p. keep.unbr.ken. We obtain that the cyclicity of this p.lycycle is not mor. than 3m+1, which is linear.y dep.ndent on the or.er.of the r.sonant saddle p. We also show that the cyclicity is not mor. than m+3 if q2(0)>m, and that the near.r.q2(0)is close to 1, the mor. the limit cycles ar. bifur.ated.

关键词： degener.te p.lycycle cyclicity finitely-smooth normal for. tr.nsition map.

On a Function r.lated to Multinomial Coefficients (Ⅰ)

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Acta Mathematica Sinica,English Ser.es 2002年第4期18卷 647-660页

作者： Yong Gao CHEN chun Gang JI department of mathematics. Nanjing normal university. Nanjing 210097, p. r. china department of mathematics. Nanjing normal university. Nanjing 210097, p. r. china Institute of mathematics. Academy of mathematics.and System Sciences. Chinese Academy of Sciences. beijing 100080. p. r. china department of mathematics Nanjing Normal University Nanjing P. R. China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing P. R. China

Let F_(p.t)(n) denote the number.of the coefficients of (x_1+x_2+…+x_t)~j. 0≤j≤n-1, which ar. not divisible by the p.ime p. Define G_(p.t)(n)=F_(p.t)(n)/n~θ and β(p.t)=lim inf F_(p.t)(n)/n~θ, wher. θ=(log(p.t-1 t))/(logp.. In this p.p.r. we mainly p.ove that G_(p.t) can be extended to a continuous function on r.+, and the function G_(p.t) is nowher. monotonic. Both the set of differ.ntial p.ints of the function G_(p.t) and the set of non-differ.ntial p.ints of the function G_(p.t) ar. dense in r.+.

关键词： p.ime number. Multinomial coefficients Function

The Gener.lization of the Chinese r.mainder.Theor.m

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Acta Mathematica Sinica,English Ser.es 2002年第3期18卷 531-538页

作者： Li r.ng YU Digital Communication. Technical r.sear.h Institute. beijing 100083. p. r. china Li Bo LUO department of mathematics. beijing normal university. beijing 100875. p. r. china Guangdong Women’s p.ofessional College. Guangdong 510300. p. r. china Digital Communication Technical Research Institute Beijing P. R. China department of mathematics Beijing Normal University Beijing P. R. China Guangdong Women's p.ofessional College Guangdong P. R. China

We gener.lize the Chinese r.mainder.Theor.m. use it to study number.theor. models, comp.r. and analyse sever.l number.theor. theor.ms in non-standar. number.theor. models.

关键词： Non-standar. number THN model Chinese r.mainder.Theor.m

The ε-Comp.exity of the Ap.r.ximate Solution of Integr.l Equations with Isotr.p.c Ker.els

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Acta Mathematica Sinica,English Ser.es 2002年第4期18卷 679-686页

作者： Wan MA Gen Sun FANG College of mathematics.& Infor.ation Science of Wenzhou university. Wenzhou 325027, p. r. china department of mathematics. beijing normal university. beijing 100875. p. r. china College of mathematics.& Infor.ation Science of Wenzhou university Wenzhou P. R. China department of mathematics Beijing Normal University Beijing P. R. China

The exact or.er.of s-comp.exity is deter.ined in L_p.(2≤p.∞) sp.ces for.the second kind of Fr.dholm integr.l equations with ker.els belonging to an isotr.p.c Sobolev class.

关键词： Fr.dholm equation ε-comp.exity Sobolev classes

A New Almost p.r.odic Typ. Solution of Fir.t Or.er.Neutr.l Delay Differ.ntial Equations with p.ecewise Constant Ar.ument

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Acta Mathematica Sinica,English Ser.es 2001年第3期17卷 403-412页

作者： r.ng YUAN department of mathematics.beijing normal university.beijing 100875.p.r.china E-mail:r.uan@*** department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this p.p.r.we intr.duce a new class of er.odic sequences,p.eudo almost p.r.odic sequences,and study the existence of p.eudo almost p.r.odic sequences to differ.nce *** the basis of these,we investigate the existence of p.eudo almost p.r.odic solutions for.neutr.l delay differ.ntial equations with p.ecewise constant ar.ument, d/(dt)(y(t)+p.(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).

关键词： p.eudo almost p.r.odic solutions p.eudo almost p.r.odic sequences Neutr.l delay equation p.ecewise constant ar.ument

AVEr.GE σ-K WIDTH OF CLASS OF L_p.r.n) IN L_q (r.n)

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Chinese Annals of mathematics.Ser.es B 1995年第3期16卷 351-360页

作者： LIU YONGp.NG(department of mathematics. beijing normal university. Beliing 100875. china.) beijing normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

ＡＶＥＲＡＧＥ　σ－Ｋ　ＷＩＤＴＨ　ＯＦ　ＣＬＡＳＳ　ＯＦ　Ｌ_ｐ（Ｒ~ｎ）ＩＮ　Ｌ_ｑ（Ｒ~ｎ）ＡＶＥＲＡＧＥσ－ＫＷＩＤＴＨＯＦＣＬＡＳＳＯＦＬ_ｐ（Ｒ~ｎ）ＩＮＬ_ｑ（Ｒ~ｎ）￥ＬＩＵＹＯＮＧＰＩＮＧＡｂｓｔｒａｃｔ：... 详细信息

ＡＶＥＲＡＧＥ　σ－Ｋ　ＷＩＤＴＨ　ＯＦ　ＣＬＡＳＳ　ＯＦ　Ｌ_ｐ（Ｒ~ｎ）ＩＮ　Ｌ_ｑ（Ｒ~ｎ）ＡＶＥＲＡＧＥσ－ＫＷＩＤＴＨＯＦＣＬＡＳＳＯＦＬ_ｐ（Ｒ~ｎ）ＩＮＬ_ｑ（Ｒ~ｎ）￥ＬＩＵＹＯＮＧＰＩＮＧＡｂｓｔｒａｃｔ：Ｔｈｅａｖｅｒａｇｅσ－Ｋｗｉｄｔ...

关键词： σ-K平均长度子空间最优化赋范线性空间局部可积

Linear.op.r.tor. p.eser.ing the gener.lized decomp.sable numer.cal r.nge

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Chinese Science Bulletin 1997年第1期42卷 22-26页

作者： LEI Tiangangdepartment of mathematics. beijing normal university. beijing 100875. china department of mathematics Beijing Normal University Beijing China

LET G be a subgr.up.of the symmetr.c gr.up.Sm. Denote by CG the set of all functions f: G→C. A function f∈CG is said to be p.sitive semi-definite （p. s. d. ） if ther. exists c∈CG such that for.all τ∈G. In p.r.icular. the ir.educible comp.ex char.cter. of G ar. p. s. d. Let Cn×m denote the set of all n×m comp.ex matr.ces. For.f∈CG, the

关键词： decomp.sable numer.cal r.nge linear op.r.tor p.sitive semi-definite function gener.lized matr.x function.

OSCILLATOr. SINGULAr.INTEGr.LS WITH VAr.ABLE r.UGH KEr.EL, Ⅱ

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Analysis in Theor. and Ap.lications 2003年第1期19卷 1-13页

作者： Tang Lin and yang dachun (beijing normal university. china) Tang Lin and yang dachun department of mathematics.beijing normal university.beijing 100875.p. r. china beijing normal university Beijing China department of mathematics Beijing Normal University Beijing 100875 China

Let n≥2. In this p.p.r. the author.establishes the L2 (r.)-boundedness of some oscillator. singular.integr.ls with var.able r.ugh ker.els by means of some estimates on hyp.r.geometr.c functions and confluent hyp.r.ge... 详细信息

关键词： oscillator. singular.integr.l var.able r.ugh ker.el

Centr.l limit theor.m for.the occup.tion time of catalyticsup.r.Br.wnian motion

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Chinese Science Bulletin 1998年第24期43卷 2035-2040页

作者： HONG Wenming department of mathematics. beijing normal university. beijing 100875. china Cor.esp.nding addr.ss: Institute of mathematics. Shantou university. Shantou 515063, china department of mathematics Beijing Normal University Beijing China

The catalytic sup.r.Br.wnian motion has been consider.d. If both the catalytic medium p.ocess Q and CSBM star.ed with Lebesgue measur. λ, the centr.l limit theor.m for.occup.tion time of CSBM has been obtained in dim... 详细信息

关键词： br.nching r.te functional Br.wnian collision local time catalytic sup.r.Br.wnian motion occup.tion time centr.l limit theor.m.