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:WeputforthDramaTheoryⅡ(DTⅡ)asaformalmultipleparticipantdecisionmakingframeworkthatcanbeusedtosystematicallymodelcomplexsecuritychallenges,andadvancethefieldofSustainableSecuritySystemsEngineering.DTⅡisdefinedasatheoryof'largeworld'pre-gamecommunicationandequilibriumselection.Whilegametheoretictoolshavebeenwidelyappliedtoresolveenvironmentalconflictsandpromoteglobalsecurity,traditionalgametheoryassumesthatdecisionmakers,options,andpreferencesarefixed.Amathematicaltreatmentofkeydramatheoreticconcepts(i.e.positions,intentions,doubtsanddilemmas)isprovided.Thedynamicsofthedramatheoreticprocessarediscussedandtheexpectedequilibriumsetisderived.Thefundamentaltheoremofdramatheoryisprovenandalltheoreticalresultsareappliedtopromotesustainablesecuritysolutions.ItisemphasizedthatDTⅡrepresentsaflexiblesystemsengineeringtechniquetoaddresstime-sensitive,multi-faceted,andcomplexmultipleparticipantnegotiations.
简介:摘要:DT21材质的钢种属于半钢轧辊,其特点是碳高,磷和硫还要控制的比较低。按照以往一贯的操作方法会出现很多问题:第一、为了保住碳,而磷很难降到工艺规格内出钢;第二、为了降低磷,而导致终点碳很难控制在工艺规格内,炉后增碳后,回磷现象比较严重;第三、为了降低磷含量,大量的换渣操作,不仅增加辅助材料的消耗,而且增加冶炼时间;