简介:Anewspectralproblemisproposed,andnonlineardifferentialequationsofthecorrespondinghierarchyareobtained.Withthehelpofthenonlinearizationapproachofeigenvalueproblems,anewfinite-dimensionalHamiltoniansystemonR2nisobtained.Ageneratingfunctionapproachisintroducedtoprovetheinvolutionofconservedintegralsanditsfunctionalindependence,andtheHamiltonianflowsarestraightenedbyintroducingtheAbel-Jacobicoordinates.Atlast,basedontheprinciplesofalgebracurve,thequasi-periodicsolutionsforthecorrespondingequationsareobtainedbysolvingtheordinarydifferentialequationsandinversingtheAbel-Jacobicoordinates.
简介:随便取一个自然数,如果它是偶数,用2除它;如果它是奇数,将它乘3之后再加1,这样反复运算,最终必然得1.比如,取自然数N=6.6是偶数,先用2除,6÷2=3;3是奇数,要将它乘3之后再加1,3×3+1=10;按着上述法则往下做:10÷2=5;5×3+1=16;16÷2=8;8÷2=4;4÷2=2;2÷2=1.从6开始经历了3→10→5→16→8→4→2→1,最后得1.通过大量演算发现最后结果总是得1.于是数学家提出如下猜想:对于任一个自然数N,若N是偶数,就把它变成N2;若N是奇数,就把它变成3N+1.按照这个规则运算下去,最后必然得1.这个猜想到目前还没有人给予证明,不过日本东京大学的米田信
简介:In2010,theBESCollaboration[1]foundaclearenhancementintheK0K0massdistributionintheJ=ψ!ηK0K0decay.SuchanenhancementisusuallyasignatureofanL=0resonancearoundthreshold,whichinthiscasewouldcorrespondstoanh1statewithquantumnumbersIG(JPC)=0??(1+??).Thish1statewaspredictedbytheChiralUnitarytheoryintheKKinteraction.Becauseoftheconversationlaw,thisstatecanonlydecaytoK0K0channel,andcanbestudiedefficientlyintheJ=ψ!ηK0K0decay.
简介:Anecessaryandsufficientconditionofregularityof(0,1,…,m-2,m)interpolationonthezerosof(1-x)Pn-1α,β(x)(α>-1,β≥-1)inamanageableformisestablished,wherePn-1α,β(x)standsforthe(n-1)thJacobipolynomial.Meanwhile,theexplicitrepresentationofthefundamentalpolynomialswhentheyexist,isgiven.
简介:Tostudytheelectromagnetic(EM)backscattercharacteristicsoffreakwavesatmoderateincidenceangles,weestablishanEMbackscatteringmodelforfreakwavesin(1+1)-dimensionaldeepwater.ThenonlinearinteractionbetweenfreakwavesandBraggshortwavesisconsideredtobethebasichydrodynamicspectramodulationmechanisminthemodel.NumericalresultssuggestthattheEMbackscatteringintensitiesoffreakwavesarelessthanthosefromthebackgroundseasurfaceatmoderateincidenceangles.Thenormalisedradarcrosssections(NRCSs)fromfreakwavesarehighlypolarisationdependent,evenatlowincidenceangles,whichisdifferentfromthesituationfornormalseawaves;moreover,theNRCSoffreakwavesismorepolarisationdependentthanthebackgroundseasurface.NRCSdiscrepanciesbetweenfreakwavesandthebackgroundseasurfacewithusinghorizontaltransmittinghorizomtal(HH)polarisationarelargerthanthoseusingverticaltransmittingvertical(VV)polarisation,atmoderateincidentangles.NRCSdiscrepanciesbetweenfreakwavesandbackgroundseasurfacedecreaseswiththeincreaseofincidenceangle,inbothHHandVVpolarisationradars.Asanapplication,inthesynthetic-apertureradar(SAR)imagingoffreakwaves,wesuggestthatfreakwavesshouldhaveextremelylowbackscatterNRCSsforthefreakwavefacetwiththestrongestslope.Comparedwiththebackgroundseasurface,thefreakwavesshouldbedarkerinHHpolarisationechoimagesthaninVVechoimages,inSARimages.FreakwavescanbemoreeasilydetectedfromthebackgroundseasurfaceinHHpolarisationimagesthaninVVpolarisationimages.Thepossibilityofdetectionoffreakwavesatlowincidenceanglesismuchhigherthanathighincidenceangles.
简介:Wehavesuccessfullysynthesized1-(2′-Phenyl)cycloproply1-2,3-epoxypropan-1-ol3,whichwillbeappliedtothekineticsstudyofoxiranylcarbinylradical.
简介:SINGULARITYANDQUADRATUREREGULARITYOF(0,1,...,m-2,m)─INTERPOLATIONONTHEZEROSOF(1-x)Pn-1αβ(x)ShiYingguang(史应光)(ComputingCe...
简介:ThesplittingofpotentialenergylevelsforgroundstateX2ΠgofOx2(x=+1,1)underspin–orbitcoupling(SOC)hasbeencalculatedbyusingthespin–orbit(SO)multi-configurationquasi-degenerateperturbationtheory(SO-MCQDPT).TheirMurrell–Sorbie(M–S)potentialfunctionsaregained,andthenthespectroscopicconstantsforelectronicstates2Π1/2and2Π3/2arederivedfromtheM–Sfunction.TheverticalexcitationenergiesforOx2(x=+1,1)areν[O+12(2Π3/2→X2Π1/2)]=195.652cm1,andν[O12(2Π1/2→X2Π3/2)]=182.568cm1,respectively.Allthespectroscopicdataforelectronicstates2Π1/2and2Π3/2aregivenforthefirsttime.