NEWTON METHOD FOR SOLVING A CLASS OF SMOOTH CONVEX PROGRAMMING

1ConvexProgrammingandExactPenaltyFunction Weconsiderthefollowingconvexprogramming:(P)minf(x)s.t.x∈S={x∈Rn:gi(x)≤0,i=1,…,m}.SupposethatSisacompactset.ThusthereexistsalargeboundedboxX,suchthatS={x∈Rn:gi(x)≤0,i=1,…,m}intX.Assumethatf(x),gi(x),i=1,…,m     

LOCAL SLIP VELOCITY IN A DOWNER

Based on the EMMS model,the local slip velocity between gas and solid is systematically analyzed and a theoretical correlation of local slip velocity with local voidage for a downer is derived as follows:Us(r)/u1=D^8/7(1-εmf)^-2/7[1-ε(r)/ε(r)]^8/7ε(r)^47/14ε(r)-εmf/ε(r).Using this correlation,the local gas-solid slip velocity in a downer is calculated.The calculated results are well consistent with experimental data.In addition,the variation of the local slip velocity with its corresponding solid holdup is also discussed.     

A Mathematical Interpretation of Dirac δ Function

The two conditions(see[1]p.58)δ(x)=0,for x≠0 (1.1)∫_( ∞)_(-∞)δ(x)dx=1 (1.2)of the Diracδfunction are inconsistent in standard analysis.In this paper,the author began by studying the integral of the func-tions on tbe nucleon a(o),and then,making use of the point function ininfinitesimal analysis to define the Diracδfunctionδ(x)so that it satis-fies the condition(1.2)andδ(x)=0.for x∈R and x≠0Some various examples of Diracδfunctions have been presented andsome properties of theδfunction have been derived.     

GLOBAL ATTRACTIVITY FOR A CLASS OF NONLINEARDELAY DIFFERENCE EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｇｌｏｂａｌａｔｔｒａｃｔｉｖｉｔｙｏｆｔｈｅｎｏｎｌｉｎｅａｒｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎΔｘｎ+ａｎｘｎ+ｆ(ｎ ,∑0ｓ=-ｋ ｑｓ,ｎｘｓ+ｎ) =0　 (ｎ=0 ,1 ,2 ,… ) . ( 1 )ＴｈｅｉｎｉｔｉａｌｖａｌｕｅｏｆＥｑ .( 1 )ｉｓｘｓ =φｓ　 (ｓ=-ｋ ,-ｋ+ 1 ,… ,-1 ,0 ) . ( 2 )Ｉｎｔｈｅｓｅｑｕｅｌ,ｗｅａｌｗａｙｓｓｕｐｐｏｓｅｔｈａｔＤ1) ａｎ ｉｓａｎｏｎｎｅｇａｔｉｖｅｒｅａｌｓｅｑｕｅｎｃｅ ,0 ≤ａｎ <1ａｎｄｋｉｓａｐｏｓｉｔｉｖｅ…     

DYNAMICAL CHARACTER FOR A PERTURBED COUPLED NONLINEAR SCHRDINGER SYSTEM

Introduction WeconsidertheperturbedcouplednonlinearSchr dingerequations(CNLS)iq1t=q1xx 2[|q1|2 |q2|2-ω2]q1 iε(^D1q1-r1),iq2t=q2xx 2[|q1|2 |q2|2-ω2]q2 iε(^D2q2-r2),(1)whereqjis2πperiodicandeveninx.rjisconstant,^Djisboundeddissipativeoperatorand assumedtotaketheform^Djqj=-αjqj βj^Bqj,(2)αjandβjarepositiveconstants,j=1,2.^BisaFouriertruncationofLaplaceoperator xx,i.e.,^Bcos(kx)=-k2cos(kx),k0isasmallperturbation parameter.Th…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

IntroductionConsidertheswitchedlinearsystemwithmultipletime_delaysincontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) + Kk=1Dr(t) ,ku(t -τk) ,(1)wherex(t) ,u(t)andr(t)isdefinedasbefore ,(Ai,Bi,Di,1,… ,Di,K)｜i=1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimplies (Ai,Bi,Di,1,… ,Di,K)ischosenasthesystemrealizationattimet.K <∞isthenumberoftime_delaysinthesystem .0<τ1<… <τKareKfixedtime_delays .Remark 1　Similarly ,wecandescribeswitchingpathbyintroducingswitchingsequ…     

HOPF BIFURCATION IN A THREE-DIMENSIONAL SYSTEM

In this paper,Liapunor-Schmidt reduction and singularity theory are employed todiscuss Hopf and degenerate Hopf bifurcations in global parametric region in a three-dimensional system x=-βx y,y=-x-βy(1-kz),z=β[α(1-z)-ky~2].Theconditions on existence and stability are given.     

A NEW HIGHER-ORDER THEORY TO LAMINATED PLATES AND SHELLS

In this paper a new ltigher-order theory to laminated plates and shells is presented and tIII,I,vhcIlv t1v I)r‘..v(,III‘,lI(IIIIIthen symmetric and antisymmetric cross-ply lammated plates.cylmdric bending andbending of spherical shells are also studied.In order to examine the accuracy of the theory.!(‘IhI‘‘It.l‘uI.at:1‘(!l‘Ih(‘Ih(‘l)I:1..several particular examples have been calculated The numerical results are in goodagreement with the exdct solution.which shows the theory is possessed of higher accuracyand is easy to solve a problem with few unknowns.     

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 ,　　 0 0 ,( 1 )withtheinitialandtheboundaryconditions　　　　　u(x,0 ) =f(x) ,　　 0 相似文献   

STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS

The stability and local bifurcation of a simply-supported flexible beam(Bernoulli- Euler type)carrying a moving mass and subjected to harmonic axial excitation are investigated. In the theoretical analysis,the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales(a perturbation technique).The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance.The results show that some of the parameters,especially the velocity of moving mass and external excitation,affect the local bifurcation significantly.Therefore,these parameters play important roles in the system stability.     

SEDIMENTATION OF CYLINDRICAL PARTICLES IN A VISCOELASTIC LIQUID： SHAPE-TILTING

1.IntroductionItiswell-knownthattheorientationoflongbodieswithonedimensionbeingmuchlargerthantheothertwoinliquidsofdifferentnatureisafundamentalissueinmanyproblemsofpracticalinterest.Theseproblemscoverawiderangeofapplications,includingmanufacturingofshort-fibercomposites(Advani,1994;Leeetal.,1997),separationofmacromoleculesbyelectrophoresis(Grossman&Soane,1990;Hames&Rickwood,1984;Trainor,1990;Tinlandetal.,2000),flow-inducedmicrostructures(Joseph,2000),modelsofbloodflow(Schmid-Schonbein&Wel…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME_DELAY CASE

IntroductionConsideraswitchedlinearsystemwithsingletime_delayinthecontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) +Dr(t) u(t -τ) ,(1)wherex(t) ∈Rnisthestate,u(t) ∈R mtheinput,thepiecewiseconstantscalarfunctionr(t) :R+ → 1,2 ,… ,Nistheswitchingpath ,(Ai,Bi,Di) ｜i =1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimpliesthat(Ai,Bi,Di)ischosenasthesystemrealizationattimet.τ >0isthefixedtimedelayincontrol.Inthispaper ,wewillstudythecontrollabilityofsystem (1) .Theone_per…     

DISCUSSIONS ON“AN ASYMPTOTIC ELASTIC PLASTIC ANALYSIS IN PLANE STRAIN DEFORMATION NEAR A CRACK TIP”

I.In his paper,prof.D.W.Hsueh derived the following functionf(θ)=-[(1 2n)/(1 n)~2-k_1~2]A_1/k_1θ-[(1 2n)/(1 n)~2-k_2~2]A_2/k_2-cosk_2θ(1)In calculation of coefficients A_1,A_2 a mistake occurred.Making use of f′(π)=0 andf(0)=0,     

FLOW OF A TRAIN OF DEFORMABLE FLUID PARTICLES IN A TUBE

I.IntroductionWangandSkalakll]studiedforsolidspheresintubes.HymanandSkalak12--31studiedthemovementofacompactfluidspheres(non-deformable)intubes.Theyonlystudiedcompactdropswhoseradiusesarenotbiggerthan0.7.Pozrikidisl4]studiedthenlotiollofdeformabletluidparticlesintubes.Inthispaper,westudiedtwo-phasenowregime,consistingofaperiodictrainofequallyspacedliquidslugsmovingaxisymmetricallyinacontinuousliquidphasewhichisimmisciblewiththeslugphase(Fig.l(a)).Wereportnumericalsolutionsforthehydrodynamic…     

LAMINAR DISSIPATIVE FLOW IN A POROUS CHANNEL BOUNDED BY ISOTHERMAL PARALLEL PLATES

IntroductionTheproblemofforcedconvectioninaporousmediumchannelorductisaclassicalone (atleastforthecaseofslugflow (Darcymodel) .Therehasrecentlybeenrenewedinterestintheproblembecauseoftheuseofhyperporousmediainthecoolingofelectronicequipment.Recently ,NieldandBejan[1]refertomorethan 3 0papersonthetopic ,butnoneofthemdealsexplicitlywiththecaseofthermaldevelopment.ThisgapintheliteraturehasbeenpartlyfilledbyNieldetal.[2 - 4 ].Lahjomrietal.[5 ,6 ]havesolvedmathematicallysimilarproblemsbyusingthe…     

CONTROL OF POLYMER PARTICLE SIZE USING POROUS GLASS MEMBRANE EMULSIFICATION A REVIEW

1.IntroductionPolymerparticleshavebeenusedinvariousfields.Besidestraditionalapplicationssuchaspaint,ink,andpaperindustries,muchattentionhasinrecentyearsbeenpaidtofineapplications,e.g.,carrierforenzyme(Omietal.,1997),separationmedia(Okubo&Hatorri,1993;Inomataetal.,1995;Ugelstadetal.,1992)forprotein,DNAandcell,andcarrierfordruginDrugDeliverySystem(DDS)(Paulettietal.,1997;Russell-Jones,2000).Controlofpolymerparticlesizeisespeciallyimportantinsuchfineapplications.Forexample,whenporouspartic…     

BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE

Ｃｏｎｓｉｄｅｒｐｌａｎａｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂｅｄｓｙｓｔｅｍ ｘ=ｆ(ｘ) +εｇ(ｔ,ｘ,ε ,δ) ,　　ｘ∈Ｒ2 ,( 1 )ｗｈｅｒｅε∈Ｒ ,δ∈Ｄ ＲｎｗｉｔｈＤｃｏｍｐａｃｔ,ａｎｄｆ,ｇａｒｅＣ3ｆｕｎｃｔｉｏｎｓａｎｄｇｉｓＴ＿ｐｅｒｉｏｄｉｃｉｎｔ,Ｔ >0 .Ｌｅｔｓｙｓｔｅｍ ( 1 )ｈａｓａｌｉｍｉｔｃｙｃｌｅＬ0 :ｘ =ｕ(ｔ) ,0 ≤ｔ≤Ｔ0 ｆｏｒε =0ｗｉｔｈＴ0 ｔｈｅｐｅｒｉｏｄｏｆＬ0 .ＳｕｐｐｏｓｅＴ0 /Ｔｉｓｒａｔｉｏｎａｌ,ｔｈａｔｉｓＴ0 /Ｔ=ｍ/ｋ,　　 (ｍ ,ｋ) =1 . ( 2 )Ａｓｗｅｋｎｏ…     

A NOVEL HYDROTHERMAL SYNTHESIS METHOD FOR BARIUM FERRITE

In the present work, fine barium ferrite powder has been synthesized through a one-step hydrothermal process in an autoclave at [OH^-]/[Cl^-] ratio of 2:1 in the temperature range from 180 to 260℃ using barium chloride(BaCl2), ferrous chloride (FeCl2) and potassium nitrate (KNO3) as the starting materials. Both particle size and saturation magnetization (Ms) increase with increasing hydrothermal reaction temperature, while the intrinsic coercivity (iHc) peaks at 685 Oe at 230℃. Morphology progress from the barium ferrite precursor particles to the barium hexaferrite particles has been monitored with increasing hydrothermal reaction time at 230℃ in the autoclave.     

RECURRENCE FORMULA FOR B-SPLINES WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS

In this paper,we give recurrence formula for normalized B-Splines with respect tostandard system{(?)~(i-1)(x)}_(i-1)~m which is the basic set of solutions to a class of differentialoperators in view of generalized divided difference—Green function—B-Splines.