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:日前,信息产业部无线电管理局就进一步加强450~470MHz频段的管理,保障无线电频谱资源的合理开发发出通知。
简介:TheproblemsofcharacteristicpolynomialassignmentinFomasini-Marchesini(F-M)modelⅡof2-Dsystemsareinvestigated.Thecorrespondingclosed-loopsystemsdescribedbyF-MmodelIIareobtainedviathestatefeedback.Usingthealgebraicgeometrymethod,thecharacteristicpolynomialassignmentinthedosed-loopsystemsisdiscussed.Intermsofthetheoryofalgebraicgeometry,theproblemofcharacteristicpolynomialassignmentistransferredtotheonewhetherarationalmappingisonto.SufficientconditionsforalmostarbitraryassignmentcoefficientsofcharacteristicpolynomialinF-MmodelⅡof2-Dsystemsviastatefeedbackarederived,andtheyareavailableformulti-inputcases.Italsohasbeenshownthatthismethodcanbeappliedtoassignthecharacteristicpolynomialwithoutputfeedback.Thesufficientconditionsforalmostarbitraryassignmentcoefficientsofcharacteristicpolynomialofmulti-input2-DsystemsdescribedbyF-MmodelⅡwithoutputfeedbackareestablished.
简介:Thesimplemodelfor4f-5dtransitionsoflanthanideionsincrystalswasextendedtodealwiththecaseoftheoctahedralcrystalfield,whereforthet2componentof5dorbitalsthespin-orbitinteractioncouldnotbeneglectedduetoincompletequenchingofthe5dorbitalangularmomentum.Theenergylevelsforthe4fN-15dconfigurationandtherelativelinestrengthsforthe4fN4fN-15dtransitionwerecalculatedindetail.Theresultwasappliedtotheinterpretationofthelow-temperature4f-5dexcitationspectrumofCs2NaYCl6∶Tb3+.