简介:SeveralcubatureformulasonthecubicdomainsarederivedusingthediscreteFourieranalysisassociatedwithlatticetiling,asdevelopedin[10].ThemainresultsconsistofanewderivationoftheGaussiantypecubaturefortheproductChebyshevweightfunctionsandassociatedinterpolationpolynomialson[-1,1]~2,aswellasnewresultson[-1,1]~3.Inparticular,compactformulasforthefundamentalinterpolationpolynomialsarederived,basedonn~3/4+(?)(n~2)nodesofacubatureformulaon[-1,1]~3.
简介:Inthispaper,aBoussinesqhierarchyinthebilinearformisproposed.ABacklundtransformationforthishierarchyispresentedandthenonlinearsuperpositionformulaisprovedrigorously.
简介:Throughoutthispaper,D=(d1,d2,...,dn)denoteasequenceofnonnegativeinte-gers.Welet(?)(D)denotetheclassofallgraphswithdegreesequenceD,orequally,theclassofallsymmetric(0,1)--matriceswithtrace0androwsumvectorD.ThestructurematrixS=S(D)ofDisamatrixofordern+1,whoseentriesare
简介:LetM1,M2besubmodulesofanalyticHilbertmoduleXonΩ(Cn)suchthatM1M2anddimM1/M2=k<∞.IfM2isanAF-cosubmodule,thenthecodimensiondimM1/M2ofM2inM1equalsthecardinalityofzerosofM2relatedtoM1bycountingmultiplicities.Thecodimensionformulahassomeinterestingapplications.Inparticular,theauthorcalculatesoutthedimensionofRudinquotientmodule,whichisraisedin[14].
简介:Schroedingeroperatorisacentralsubjectinthemathematicalstudyofquantummechanics.ConsidertheSchrSdingeroperatorH=-Δ+VonR,whereΔ=d^2/dx^2andthepotentialfunctionVisrealvalued.InFourieranalysis,itiswell-knownthatasquareintegrablefunctionadmitsanexpansionwithexponentialsaseigenfunctionsof-Δ.AnaturalconjectureisthatanL^2functionadmitsasimilarexpansionintermsof"eigenfunctions"ofH,aperturbationoftheLaplacian(see[7],Ch.XIandthenotes),undercertainconditiononV.
简介:Thispaperre-examinesBagnold’stheoremofsedimenttransport.DifferentfromthestreampowerdefinedbyBagnold,i.e.,τoV,thisstudyshowsthatthetotalloadofsediment-ladenflow,gt,isrelatedtonearbedenergydissipationrate,i.e.,τou*’.Anattemptismadetoexplaintheempiricalrelation.Theratio(=k)ofmeasuredtotalload,gt,totheproductofnearbedvelocity,u*’,andenergydissipationrate,τou*’,isanalyzed.ItisfoundthatkisindependentoftheRousenumber,Z,ifZisgreaterthan2.6,butthecoefficientkdecreaseswiththeincreaseofZwhenZ<2.6.AnempiricalrelationbetweenkandZisdeveloped.Asystematicandthoroughanalysisof1,458setsofdatacollectedfrom16riversandcanalsconfirmsthattheproposedformulacanbeusedtocomputethetotalloadwithaccuracy.
简介:Theshortcomingsofthepresenttwoformulaefordescribingcolumnholdupareanalyzedanddeductionsareadetofindanewformula,Thecolumnholdup,Hw,describedbythenewformulaisdimensional,andrelatedtosoilsoultetransportkinesisandcolumnphysicalproperties,Comparedwiththeothertwocolumnholdups,Hwisfeasibletodescribedimensionalcolumnholdupduringsolutetransportprocess,TherelationshipsbetweenHwandretardationfactor,R,indifferentsolutetransportboundaryconditionsareestablished.
简介:Bysolvingthebasicequationsofmagneticfieldintheanisotropicmagneticmediainwhichthetensorμikissymmetric,anintegralformulaforanisotropicvectorpotentialAisobtained.Bywhichthecharacteristicformulaeforselfandmutualinductancesarederivedinscalarandtensorforms,andtheirtransformationformulaarealsoderived.Finally,theformulaischeckedbypracticalexamples.
简介:ThispaperdevelopsaclaseofquadratureformulawithfirstderivativesItisdemonstratedthatitsdegreeofaccuracyisnotlessthan2k+1forasetofdistinctnodes{x0,x1,...,xn}overinterval[a,b],andjustonly2k+1forequallyspacednodes.FarovercomingtheshortcomingofinvolvingagreatnumberofmanualcomputationsfortheintegrationrulesoftheHermitianinterpolationformula,somesimpleformulasforcomputingautomaticallyβi,γiandE[f]bycomputeraregiven,especiallyforequallyspacednodes.
简介:为Hermite多项式的Mehler公式允许一个维的部分Fourier变换的一个不可分的代表。在这篇论文,我们在克利福德分析的框架介绍amulti维的部分Fourier变换。由证明它与古典tensorial途径与一致,我们能为克利福德分析的概括Clifford-Hermite多项式证明Mehler的公式。
简介:Abstract.WeobtainaBlack-Scholesformulaforthearbitrage-freepricingofEu-ropeanCalloptionswithconstantcoefficientswhentheunderlylngstockgeneratesdividends.TohedgetheCalloption,wewillalwaysborrowmoneyfrombank.WeseetheinfluenceofthedividendtermontheoptionpricingviathecomparisontheoremofBSDE(backwardstochasticdi~erentialequation[5],[7]).WealsoconsidertheoptionpricingproblemintermsoftheborrowingrateRwhichisnotequaltotheinterestrater.ThecorrespondingBlack-Sdxolesformulaisgiven.Wenoticethatitisinfacttheborrowingratethatplaystheroleinthepricingformula.