简介:Thefirstexcitedstateandthegroundstateof^17Farestudiedwiththeasymptoticnormalizationcoefficientmethod.Theresultsshowthattheprobabilitiesofthelastprotonbeingoutofthebinding-potentialinboththestatesareP=59.71%andP=27.61%,respectively.Thismeansthatthelastnucleoninboththestatesof^17Fisfar-extendedbeyondtherangeofnuclearforce,especiallyinthefirstexcitedstate.Thisresultisalsoverifiedbythecalculationofthedensitydistributionsofthelastprotonin^17F.Itisquantitativelyconfirmedthatthefirstexcitedstateof^1TFisanuclearhalostateanditsgroundstateisaprotonskinstate.
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.