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ON THE LAp.ACIAN Sp.CTr.L r.DII OF Tr.ES WITH NEAr.Y p.r.ECT MATCHINGS

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Jour.al of Systems Science & Comp.exity 2009年第3期22卷 533-540页

作者： li ZHANG Jiayu SHAO Dep.r.ment of Ap.lied Mathematics Shanghai Finance University Shanghai 201209 China. Dep.r.ment of Mathematics Tongji University Shanghai 200092 China.

Let ：T2k＋1 be the set of tr.es on 2k＋ 1 ver.ices with near.y p.r.ect matchings, and let S2k＋2 be the set of tr.es on 2k ＋ 2 ver.ices with p.r.ect matchings. The lar.est Lap.acian sp.ctr.l r.dii of tr.es in ：T2k＋l and S2k＋2 and the cor.esp.nding tr.es wer. given by Guo （2003）. In this p.p.r. the author. deter.ine the second to the sixth lar.est Lap.acian sp.ctr.l r.dii among all tr.es in T2k＋1 and give the cor.esp.nding tr.es.

关键词： Tr.e Lap.acian eigenvalue near.y p.r.ect matching p.r.ect matching.

Exp.icit Analytical Solutions for.the Shear.ngand r.dial Str.sses in Cur.ed Beams

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Communications in Nonlinear.Science and Numer.cal Simulation 1999年第2期4卷 151-156页

作者： Aiming YU+ Xiangr.ng li+++ (tongji university, shanghai 200092, china.++ (shanghai university, shanghai 200072, china. tongji university Shanghai 200092 China shanghai university Shanghai 200072 China

The shear.ng str.sses in cur.ed beams can be solved exp.icitly fr.m anintegr.l equation, which is obtained by differ.ntiation & integr.l manip.lations. Twonovel for.ulae for.shear.ng & r.dial str.sses ar. also p.esented in the p.p.r. The r.sultsof an examp.e r.veal that the shear.ng & r.dial str.sses ar.ive at their.maximum valuesslightly below the centr.id of the section.

关键词： cur.ed beam shear.ng str.ss r.dial str.ss integr.l equation

Nor.alization of Hydr.dynamic Coefficients in Mor.son Equation

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china.Ocean Engineer.ng 1999年第2期14卷 125-132页

作者： li Yucheng professor, the State Key Labor.tor. of Coastal and Offshor. Engineer.ng, Dalian university of Technology, Dalian 116024, p. r. china. State Key Labor.tor. of Coastal and Offshor. Engineer.ng Dalian University of Technology Dalian 116024 China

The hydr.dynamic coefficients C-d and C-m ar. not only dep.ndent on the size of slender.cylinder. its location in water. KC number.and r. number. but also var. with envir.nmental conditions, i.e., in r.gular.waves or.in ir.egular.waves, in p.r. waves or.in wave-cur.ent coexisting field. In this p.p.r. the nor.alization of hydr.dynamic coefficients for.var.ous envir.nmental conditions is discussed. When a p.op.r.definition of KC number.and p.op.r.char.cter.stic values of ir.egular.waves ar. used, a unified r.lationship.between C-d, C-m and KC number.for.r.gular.waves, ir.egular.waves, p.r. waves and wave-cur.ent coexisting field can be obtained.

关键词： Mor.son Equation dr.g for.e coefficient iner.ia for.e coefficient hydr.dynamic coefficient nor.alization

p.eudo-r.ndom Sequences Gener.tor.Based on Discr.te Hyp.r.haotic Systems

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Jour.al of Systems Engineer.ng and Electr.nics 2003年第4期14卷 84-89页

作者： li Changgang & Han Zhengzhi Dep.r.ment of Automation, shanghai Jiaotong university, shanghai 200030, p. r. china Dep.r.ment of Automation Shanghai Jiaotong University Shanghai 200030 P. R. China

We fir.t design a discr.te hyp.r.haotic system via p.ece-wise linear.state feedback. The states of the closed loop.system ar. locally exp.nding in two dir.ctions but absolutely bounded on the whole, which imp.ies hyp.r.haos. Then, we use thr.e suchlike hyp.r.haotic systems with differ.nt feedback gain matr.ces to design a p.eudo-r.ndom sequence gener.tor.(p.SG). Thr.ugh a thr.shold function, thr.e sub-sequences gener.ted fr.m the outp.t of p.ecewise linear.functions ar. changed into 0-1 sequences. Then, followed by XOr.op.r.tion, an unp.edictable p.eudo-r.ndom sequence (p.S) is ultimately obtained. The analysis and simulation r.sults indicate that the p.S, gener.ted with hyp.r.haotic systems, has desir.ble statistical featur.s.

关键词： discr.te hyp.r.haotic system p.ecewise linear.state feedback p.eudo-r.ndom sequences.

r.GULAr.TY r.SULTS FOr.SOME QUASI-liNEAr.ELlip.IC SYSTEMS INVOLVING Cr.TICAL EXp.NENTS

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Chinese Annals of Mathematics,Ser.es B 2005年第1期26卷 119-126页

作者： HUYEXIN liJUAN Dep.r.mentofMathematics ShanghaiJiaotongUniversityShanghai200240China Dep.r.mentofMathematics ShanghaiJiaotongUniversityShanghai200240China.

The author. show the r.gular.ty of weak solutions for.some typ.cal quasi-linear.ellip.ic systems gover.ed by two p.Lap.acian op.r.tor.. The weak solutions of the following p.oblem with lack of comp.ctness ar. p.oved t... 详细信息

关键词： Ellip.ic equation system p.Lap.acian op.r.tor Cr.tical Sobolev exp.nent r.gular.ty

Nonlinear.constitutive law for.fer.oelectr.c/fer.oelastic mater.al and its finite element r.alization

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Science china.p.ysics,Mechanics & Astr.nomy) 2007年第1期50卷 70-86页

作者： li YaoChen Dep.r.ment of Aer.sp.ce Engineer.ng and Ap.lied Mechanics,tongji university,shanghai 200092,china Dep.r.ment of Aer.sp.ce Engineer.ng and Ap.lied Mechanics Tongji UniversityShanghai 200092 China

The hyster.sis p.enomena of fer.oelectr.c/fer.oelastic mater.al in p.lar.zation p.ocedur. ar. investigated. Some assump.ions ar. p.esented based on the p.blished exp.r.mental data. The electr.cal yielding cr.ter.on, mechanical yielding cr.ter.on and isotr.p.c har.ening model ar. established. The flow theor. in incr.mental for.s in p.lar.zation p.ocedur. is p.esented. The nonlinear.constitutive law for.electr.cal-mechanical coup.ing is p.op.sed p.enomenologically. Finally, the nonlinear.constitutive law exp.essed in a for. of matr.ces and vector., which is immediately associated with finite element analysis, is for.ulated. In the examp.e p.oblem of a r.ctangular.sp.cimen subjected to a uniaxial electr.c field, the p.ocedur. fr.m vir.in state to fully p.lar.zed state is simulated. After.ar., a uniaxial comp.essive loading is ap.lied to dep.lar.zing the sp.cimen. r.sults ar. in agr.ement with the exp.r.mental data.

关键词： fer.oelectr.c/fer.oelastic mater.al constitutive law nonlinear finite element method.

Analytical solution for.wave-induced r.sp.nse of isotr.p.c p.r.-elastic seabed

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Science china.Technological Sciences) 2010年第10期53卷 2619-2629页

作者： ZHANG Yongli & li Jie Dep.r.ment of Building Engineer.ng, tongji university, shanghai 200092, china 1. Dep.r.ment of Building Engineer.ng Tongji University Shanghai 200092 China

By use of sep.r.tion of var.ables,the gover.ing equations descr.bing the Biot consolidation model is fir.tly tr.nsfor.ed into a comp.ex coefficient linear.homogeneous or.inar. differ.ntial equation,and the gener.l solution of the hor.zontal disp.acement of seabed is constr.cted by emp.oying a comp.ex wave number.thus,all the exp.icit analytical solutions of the Biot consolidation model ar. deter.ined. By comp.r.ng with the exp.r.mental r.sults and analytical solution of Yamamoto etc. and the analytical solution of Hsu and Jeng,the validity and sup.r.or.ty of the suggested solution ar. ver.fied. After.investigating the influence of seabed dep.h on the wave-induced r.sp.nse of isotr.p.c p.r.-elastic seabed based on the p.esent theor.,it can be concluded that the influence dep.h of wave-induced hydr.dynamic p.essur. in the seabed is equal to the wave length.

关键词： linear wave dynamic water p.essur. seabed analytical solution Biot consolidation model

The p.omoting Effect on the Activities ofFe Dop.d TiO_2 p.otocatalysts

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Chemical r.sear.h in Chinese Univer.ities 2001年第2期17卷 187-192页

作者： YU Xi-bin, WANG Gui-hua and li He-xing (Dep.r.ment of Chemistr., shanghai Nor.al university, shanghai 200234, p. r. china. shanghai Nor.al Univ Dept Chem Shanghai 200234 Peoples R China

The p.r.icles of titanium-ir.n (Ti/Fe) comp.ex with differ.nt Fe contents wer. p.ep.r.d by means of the sol-gel method and used as a p.otocatalyst. The activity of the catalyst was investi- gated as a function of the Fe content dur.ng the liquid-p.ase oxidation of tetr.cycline, which showed an enhancement at the low Fe content. The Xr., r.man, Xp., and UV-Vis absor.0} tion sp.ctr. indicated that the cr.stalline str.ctur. of the Ti/Fe comp.ex p.r.icles changed fr.m anatase p.ase to r.tile p.ase when the Fe content incr.ased. The isolated Fe203, Fe304, FeO sp.cies wer. obser.ed and Fe3+ ions wer. highly disp.r.ed in the TiO2 matr.xes, then Ti-O-Fe sp.cies wer. for.ed. These sp.cies incr.ased the sur.ace defects of the Ti/Fe p.r.icles. Also, ac- tive hydr.xyl r.dicals could be gener.ted in the catalytic tr.nsfor.ation, which led to the higher. activity of the catalyst than bar. Ti02 for.the degr.dation of tetr.cycline.

关键词： Titanium Fe dop.d p.otocatalyst p.otocatalytic activity Tetr.cycline

A　SEp.r.TED－LAYEr.FINITE　ANALYTIC　METHOD　FOr.NUMEr.CAL　SIMULATION　OF　A　THr.E－DIMENSIONAL　VISCOUS　FLOW　FIELD　Ar.UND　A　SHIp.STEr.

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Jour.al of Hydr.dynamics 1994年第1期6卷 50-57页

作者： li Ting-qiu Miao Guo-p.ng liu Ying-zhong (shanghai Jiao Tong university, shanghai 200030, p. r. china. shanghai Jiaotong Univ Shanghai China

A calculation code of numer.Cal simulation of comp.ete r.ynolds-aver.ged Navier.Stokes(r.NS) equations for.thr.e-dimensional viscous flow ar.und a ship.is develop.d in this p.p.r.using an imp.oved sep.r.ted-layer.finite analytic(SLFA) method. And the k-εmodel is used to comp.te the tur.ulent str.ss. An imp.ovement is also made for.gr.d gener.tion in the asp.ctS of saving the r.n time and contr.lling the gr.d density in the near.wall r.gion. The SIMp.EM algor.thm, sup.r.or.to the well-known SIMILEr.algor.thm, is adop.ed for.sp.eding up.the iter.tions of the coup.ing between the p.essur. and velocity under.the unstagger.d *** satisfied agr.ements with the exp.r.mental r.sults ar. achieved for.the Wigley mathematic hull at the r.ynolds number.of 1. 0×106.

关键词： the SLFA method the r.NS equations the SIMp.EM algor.thm.