ON LIAPOUNOFF’S METHOD IN THE THEORY OF STABILITY OF LAMINAR FLUID FLOWS

In[1]Zhou extended some Liapounoff‘s theorems of the theory of stability in the case of plane laminar fluid flows.In[2]Zhou and Li investigated the eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation,and obtained some new results.In this paper,based on the results of[1]and[2]we shall prove:(1)For the linearized problem the definition of stability according to the eigenvalues of Orr-Sommerfeld equation and that according to the perturbation.energy are equivalent;(2)The method of linearization is admissible for the stability pro-blem of plane laminar fluid flows for sufficiently small initial disturbance.     

BLOW-UP OF THE SOLUTIONS FOR THE INITIAL-BOUNDARY PROBLEMS OF THE NONLINEAR SCHR?DINGER EQUATIONS

Ｔｈｅｒｅａｒｅｍａｎｙｄｏｃｕｍｅｎｔｓｔｈａｔｄｉｓｃｕｓｓｂｌｏｗ＿ｕｐｏｆｔｈｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖｌｕｅｐｒｏｂｌｅｍｓｏｆｔｈｅｎｏｎｌｉｎｅａｒＳｃｈｒ ｄｉｎｇｅｒｅｑｕａｔｉｏｎｓ,ｓｕｃｈａｓｐａｐｅｒ [1 ] .Ｂｕｔｔｈｅｐａｐｅｒ [1 ]ｈａｓｏｎｅｗｅａｋｐｏｉｎｔ,ｔｈａｔｉｓ,ｉｔｃａｎｎｏｔｕｎｉｔｅｄｉｓｃｕｓｓｉｏｎｆｏｒｂｌｏｗ＿ｕｐｏｆｔｈｅｓｏｌｕｔｉｏｎｓｆｏｒｔｈｅｉｎｉｔｉａｌ＿ｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌ…     

THE ASYMPTOTIC ANALYEICAL SOLUTION OF THE STRAINHARDENING ELASTO-PLASTIC PLATE CONTAINING A CIRCULAR HOLE UNDER SIMPLE TENSION

In this paper the general asymptotic analytical solution ofplane problem of elasto-plasticity with strain-hardening[2]isused in solving the problem of an infinitely large plate con-taining a circular hole under simple tension,and the analy-tical expressions of stress components of the first two approxi-mations,are given,These results are compared with the numeric-al and the experimental results given by other authors[4,5],and a good agreement is obtained.At the end of this paper theauthors inspect the correctness of Neuber’s formula[9]for thisproblem.     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR'E SYSTEMS

IntroductionInpractice ,thereexistmanyexamplesofimpulsivecontrolsystems (seeRefs.[1 ,2 ,3 ] ) .Recently ,impulsivecontrolhasbeenwidelyusedtostabilizeandsynchronizechaoticsystems(seeRefs.[4～ 1 5] ) .Forexample,thepredictivePoincarecontrol[4 ]andtheoccasionalproportionalfeedbackcontrol[5 ]aretwoimpulsivecontrolschemeswithvaryingimpulsiveintervals.Yangetal.inRefs.[7,1 1 ]studied ,respectively ,thestabilizationandsynchronizationofaclassofchaoticsystemscalledLorenzsystems .YangandChuainRef.[1 …     

THE FINITE ROTATION PARAMETER OF A DEFORMABLE BODY AND GYROMAGNETIC EFFECT

The derivation of synge[2]for the finite rotation formula interms of Euler parameter is put into tensor form.Hence a fur-ther clarification of the geometric meaning of the orthogonaltransformation obtained in the author’s paper[7]is made.Thetensor properties of rotation axis vector are also discussed.By means of the method of co-moving coordinate system establi-shed in[8],[9],we explain the gyromagnetic effect.and derivea simple formula for calculating bodg couple which is inducedby magnetization.     

关于“非均匀各向同性介质弹性力学平面问题”

文献[1]讨论了指定位移的边界条件用应力函数表示的问题。阅读之后,感到有几个问题值得提出来讨论。 一、文献[1]导出的位移边界条件(3.1)有错误,现在重新简略推导如下: 在指定位移的边界S上,边界条件为: u(s)=(s),v(s)=(s), (1) 这里,分别代表边界线上的法向和切向指定位移(凡末加说明的符号均与文献[1]所     

THE CREEPING MOTION IN THE ENTRY REGION OF A SEMI-INFINITE CIRCULAR CYLINDRICAL TUBE

In 1969,Lew and Fung[1]considered the inlet flow into a se-mi-infinite circular cylinder at low Reynolds number.Dagan etal.[2]in1982 obtained a series solution for the creeping motionthrough a pore of finite length directly.The numerical resultsobtained in[1]also describe the entrance flow in a tube of afinite length as the Fourier integrals in the general solutions arereplaced by Fourier series.In the present paper,the Fourier in-tegralss are evaluated numerically and the velocity,pressure dis-tribution and the stream function in the entry region of a semi-infinite circular cylindrical tube is close to the factor1.3 sug-gested by Lew and Fung[1].The collocation technique applied inthe present paper is shown to converge rapidly and it should beuseful in other similar problems.     

THE SEMI-DISCREIXTE METHOD FOR SOLVING HIGH-DIMENSION WAVE EQUATION

1.IntroductionWaveequationiswidelyusedinsuchsubjectsasgeophysics,elasticmechanics,andsoon.Therefore,how'tosolvewaveequationbecomesaveryimportantproblem.Althoughpeoplehaveachievedalotinthetheoryandcalculationofwaveequationl']'121,newproblemsandsolutionskeep.comingoutl3]'141.Oneofthemethodsgiveninpaper[5]istoreducetwodimensionequationtoone-dimensionequationsystem.However,itisdifficulttoextendhighdimensionwave'equationandwaveequationwithvariablecoefficient.Bythesemi-discrete'methoddiscussedinthi…     

ON THE CRITICAL POINTS OF THE MAP F_p:X→‖AXB-C‖_p~p

1　ＰｒｅｌｉｍｉｎａｒｉｅｓＬｅｔＨｂｅａＨｉｌｂｅｒｔｓｐａｃｅ,ａｎｄＬ(Ｈ) ,ｂｅｔｈｅｓｐａｃｅｏｆａｌｌｔｈｅｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｏｎＨ ,ａｎｏｐｅｒａｔｏｒＴ- ｉｓｓａｉｄｔｏｂｅａｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｏｆｔｈｅｏｐｅｒａｔｏｒＴｉｆＴＴ- Ｔ =Ｔ .ＡｎｏｐｅｒａｔｏｒＴｉｎＬ(Ｈ)ｈａｓａｇｅｎｅｒａｌｉｚｅｄｉｎｖｅｒｓｅｉｆａｎｄｏｎｌｙｉｆｔｈｅｒａｎｇｅｏｆＴ ,ｄｅｎｏｔｅｄｒａｎ(Ｔ) ,ｉｓｃｌｏｓｅｄ[1].ＲＰｅｎｒｏｓｅ[1]ｓｈｏｗｅｄｔ…     

The Hamiltonian equations in some mathematics and physics problems

IntroductionHamiltoniansystemsareveryimportantinmathematics,physicsandmechanics.SpeciallyafterFengKang[1]firstproposedthesymplecticnumericalmethodforfinitedimensionalHamiltoniansystemin 1 980s,thestudyofHamiltoniansystemhasbeenfurtherimprovedinboththeoryandapplication .ItisthereforenaturaltoconsidertheproblemaboutwhichkindofpartialdifferentialequationscanberewrittenorrepresentedbyHamiltoniansystem .SuchkindofproblemhasnowbeenwarmlystudiedbymanymathematiciansandphysicianssuchasinRefs.[2 -5] …     

THE WILD SOLUTIONS OF THE INDUCED FORM UNDER THE SPLINE WAVELET BASIS IN WEAKLY DAMPED FORCED KdV EQUATION

I.IntroductionTheInethodtostudytheAIMbyusingthesplinewaveletbasisoriginatesfi.onl[l],adiscussiononthesoft'adjointtypenonlinearevolutionaryequations.However,itisstillaquestionwhetherthereexistsAIMonnonselfadjointtypenonlinearevolutiollaryequations.[2]l.esultsinthatthereexistsAIMbyusingtheFourierbasisinnonselftlcljointtype'sWDFKdVequatioll.[3]getstheAIMbyusillgthesplinewaveletbasisinperturbedperiodicKdVequation.[4]setsuptheglobalattractoranditsestimationoffractaldimensioninWDFKdVequati…     

Maximum principles for generalized solutions of quasi-linear elliptic equations

1　IntroductionandMainRrsultsSincethe 1 950s,therehasbeenarapidprogressinthestudyoftheregularitytheoryforgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceformwithseveralvariables,whichhasplayedanimportantroleinthestudyofquasi_linearequations (seeRefs.[1 ,2 ] ) .But,inspiteofthefactthatMorry[3 ]provedtheFredholmAlternativetheoremwithrespecttotheexistenceofgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceform (whichisageneralizationoftheclassicaltheory)a…     

ON THE PERTURBATIONAL GLOBAL ATTRACTIVITY OF NONAUTOMOUS DELAY DIFFERENTIAL EQUATIONS

I.Introductionillthispaper,wewillstudytheglobalattractivityofzerosolutionofnonautonomouslineardelaydit'ferentialequationswiththeperturbedtermft(t)=--a(t)x(t--r) F(t,x,),t30(1.l)whereF:[0,ac)xC[-6,0]~Riscontinuous,C[-a,0]isthespaceofcontilluousfunctions(di:[--8,0]-R),F(t,0)-0,t30.a(t)eC((0,co),(0,co)),andr>0.Fortheasylllptoticstabilityoflilleardiflbrentialequatiollwithperturbedtcrlns,mostoftheknownpapershaveonlybeenconcernedwiththelocalbehaviorll--sl.Evenfortheglobalbehavior,theauthorsonlyde…     

APPLICATION OF RECIPROCAL THEOREM FOR CALCULATING THE TRANSVERSE DISPLACEMENT EQUATIONS OF THE THIN ELASTIC CIRCULAR PLATES

On the basis of[1] and [2], this paper further extends the Reciprocal Theorem to the thin elastic circular plates and proposes a general convenient new method, which can easily solve the transverse displacement equations of the circular plates with various complex edges and loads.     

ON CAUCHY PROBLEMS FOR THE RLW EQUATION IN TWO SPACE DIMENSIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｓｙｓｔｅｍｏｆｔｈｅｎｏｎｌｉｎｅａｒｄｉｓｐｅｒｓｉｖｅ ,ｔｈｅｐａｐｅｒｓ [1 ]ａｎｄ [2 ]ｈａｖｅｓｔｕｄｉｅｄｔｈｅｍｏｄｅｌｅｑｕａｔｉｏｎｏｆｓｉｍｐｌｅｗａｖｅｓｐｒｏｐａｇａｔｉｏｎｏｆｌｏｎｇｗａｖｅ ,ｕｔ+αｕｘ+ βｕｕｘ-γｕｘｘｔ=0　　ｘ∈Ｒ ,ｔ≥ 0ｉｓｃａｌｌｅｄｔｈｅＲＬＷｅｑｕａｔｉｏｎ .ＳＨＡＮＧ[3]ｏｂｔａｉｎｅｄｔｈｅｅｘａｃｔｓｏｌｉｔａｒｙｗａｖｅｓｏｌｕｔｉｏｎｓｏｆｔｈｅｔｗｏｄｉｍｅｎｓｉｏｎａｌＲＬＷｅｑｕａｔｉｏｎ .Ｉｎ…     

FORMING MICHELL TRUSS IN THREE-DIMENSIONS BY FINITEELEMENTMETHOD

IntroductionTheMichell’s[1]theoryforoptimizingstructuraltopologyforstressconstraintsunderoneloadconditionplaysanimportantroleinstructuraloptimizationfield .TheoptimumstructuresbasedonsuchtheoryarecalledasMichelltruss,orleast_weighttruss.Subsequently ,thistheorydevelopedgreatlyinmanyaspects[2 - 8].ItisprovedthatMichelltrussisidenticalwiththeleast_weighttrussforcomplianceconstraints.TheMichelltrussesundersomeloadcasesweregainedbyanalyticalmethod[8- 10 ].Michelltrussisestablishedbasedonstrict…     

THE OPTIMAL POINT OF THE GRADIENT OF FINITE ELEMENT SOLUTION

We consider the first boundary value problem of the second order elliptic equation andserendipity rectangular elements.Papers[2,3,9]proved that the gradients of finite elementsolution possess superconvergence at Gaussianpoint.In this paper,we extend the results inpapers[2,3,9]in the sense that the coefficients of the elliptic equations are discontinuous ona curve S which lies in the bounded domain Ω.     

SECOND-ORDER CNOIDAL WAVES AT THE FREE SURFACE AND INTERFACE OF A TWO-FLUID SYSTEM

In this paper, using the PLK method and reductive perturbation method,we obtainedthe second approximation to cnoidal waves at the free surface and ihterface for the two-fluid system considered in[1].The corresponding results in[3]and[4]may be obtained asspecial cases in this paper.     

INVESTIGATION OF THE DYNAMIC BUCKLING OF DOUBLEWALLED CARBON NANOTUBE SUBJECTED TO AXIAL PERIODIC DISTURBING FORCES

IntroductionThediscoveryofthefirstcarbonnanotubes[1]hasattractedwideattentionandstimulatedextensivestudies[2 - 5 ].Thestudiesshowedthatthecarbonnanotubesexhibitsuperiormechanical,electronicandchemicalproperties.Onthemechanicalbehavior,thecarbonnanotubespossessexceptionallyhighstrength ,stiffnessandelasticmodulus.Theestimatemodulusofthecarbonnanotubemayreachashighas 1TPa.Itisthelargestofallknownmaterials.Thestrengthorstiffnessishigherthananyknownfiber[3].Thecarbonnanotubeareusedascompositemat…