简介:LetFbeafieldofcharacteristiczero.Wn=F[t(+1/2),t(+1/2),...,t(+1/n)]δ/δt1+...+F[t(+1/2),t(+1/2),...,t(+1/n)]δ/δtnistheWittalgebraoverF,Wn+=F[t1,t2...,tn]δ/δt+...+F[t1,t2...,tn]δ/δtnisLieshbalgebraofWn.ItiswellknownbothWnandWn+aresimpleinfinitedimensionalLiealgebra.InZhao'spaper,itwasconjecturedthatEnd(Wn^+)-{0}=Aut(Wn^+)anditwasprovedthatthevalidityofthisconjectureimpliesthevalidityofthewell-knownJacobianconjecture.Inthisshortnote,wechecktheconjectureaboveforn=1.WeshowEnd(W1^+)-{0}=Aut(W1^+).
简介:Analgorithmofcontinuousstage-spaceMCMCmethodforsolvingalgebraequationf(x)=0isgiven.Itisavailableforthecasethatthesignoff(x)changesfrequentlyorthederivativef'(x)doesnotexistintheneighborhoodoftheroot,whiletheNewtonmethodishardtowork.Letnbethenumberofrandomvariablescreatedbycomputerinouralgorithm.Thenafterrn=O(n)transactionsfromtheinitialvalueXo,X^*canbegotsuchthat[f(x^*)|<e-^cm|f(xo)|bychoosingsuitablepositiveconstantc.Anillustrationisalsogivenwiththediscussionofconvergencebyadjustingtheparametersinthealgorithm.
简介:AdetailedstudyofthepressureoscillationinducedbythefilmboilingofHeⅡispresented.Thefilmboilingstateandthestabilitynofthevapourfilmaredeterminedbythegoverningparameter(i.e.theimmersiondepth).Itisfoundthatthepowerdensityspectrumofthepressureoscillationinducedbythefilmboilingdisplaysthe1/f^α-behaviour.Theexponentαwasfoundtobewithintherangefromonetotwo,whichindicatestheexistenceofself-organizedcriticalityinthefilmboilingofHeⅡ.
简介:Inthispaper,radiation-inducedcrosslinkingmechanismandcharacterizationofthecrosslinkingdensityofF-40andF-4byX-rayphotoelectronspectroscopy(XPS)havebeenstudied.ThedoseofgelationofF-40obtainedfromXPSis4.1×10~4Gy.ItisfoundthatcrosslinkingdensityisthelargestintherangeofcertaindoseforF-40andF-4.