简介:左R-模M称为Eω-内射模,如果对环R中任意的ω阶Euclid理想I来说,任何R-模同态能够拓展为R-模同态。左R-模M称为Eω-投射模,若对环R中任意的ω阶Euclid理想I和任何R-模同态f∈HomR(M,R/I),存在R-模同态g∈HomR(M,R)使得f=πg,其中π是自然同态。本文证明P和Q均是Eω-投射模当且仅当PQ是Eω-投射模。进而,又证明了每一个左R-模是Eω-投射的当且仅当每一个左R-模是Eω-内射。
简介:(满分100分,90分钟完成)(/1)基础知识达标检测一、选择题(每小题4分,共40分)1.(,『1+I)x?+r,“一2+,『ii=0是关于r的一元二次方程,邶幺m的值是().({)r,j>一1(B),n>1(C)口‘≠一1(D),H≠02.方程x::x的根是().(1)()(B)l(c)2(D)0或13F列方程中,没有实数根的是().(4)!Y:一7x=0(B)5J!一7J+5=0t、C)!r?+3r一4=0(D)16,+9y=244.,f、等式Ⅲf。。’‘)’0的整数僻的个数足().L2x<5l{)1个(B)!个((j)3个(D)4个5.一啦!
简介:Itisknownfromclassicaldifferentialgeometrythatonecanreconstructacurvewith(n-1)prescribedcurvaturefunctions,ifthesefunctionscanbedifferentiatedacertainnumberoftimesintheusualsenseandifthefirst(n-2)functionsarestrictlypositive.ItisestablishedherethatthisresultstillholdsundertheassumptionthatthecurvaturefunctionsbelongtosomeSobolevspaces,byusingthenotionofderivativeinthedistributionalsense.ItisalsoshownthatthemappingwhichassociateswithsuchprescribedcurvaturefunctionsthereconstructedcurveisofclassC∞.
简介:Numericalestimatesforelectronsandmesonsparticle–antiparticlecreationfromvacuuminthepresenceofstrongelectromagneticfieldsarederived,usingthecompleteprobabilitydensityrelationofPopov’simaginarytimemethod(Popov,JETPLett.13,185(1971);Sov.Phys.JETP34,709(1972);Sov.Phys.JETP35,659(1972);PopovandMarinov,Sov.J.Nucl.Phys.16,449(1973);JETPLett.18,255(1974);Sov.J.Nucl.Phys.19,584(1974));(Popov,Phys.Let.A298,83(2002)),andwithintheframeworkofanexperimentalsetupliketheE144(Burkeetal.,Phys.Rev.Lett.79,1626(1997)).Theexistenceofcrossingpointamongpaircreationefficiencycurvesofdifferentphotonenergiesandtheroleofodd/evenmultiphotonordersintheproductionratesarediscussed.Finallyakindoftunabilityprocessbetweenthetwocreationprocessesisdiscussed.
简介:Usingfourβ-cyclodextrinderivatives,2,6-di-O-benzyl-3-O-heptanonyl-β-CD,2,6-di-O-benzyl-3-O-octanonyl-β-CD,2,3-di-O-benzyl-6-O-heptanonyl-β-CD,and2,3-di-O-benzyl-6-O-octanonyl-β-CD,aschiralstationaryphasesofcapillarygaschromatography(CGC),theenantiomersofSharplessepoxideswerewellseparated.Theenantiomerexcessvalues(e.e.%)ofsomechiralSharplessepoxideswerealsodeterminedsuccessfullyusingtheseCDs.
简介:LetB(E,F)bethesetofallboundedlinearoperatorsfromaBanachspaceEintoanotherBanachspaceF,B+(E,F)thesetofalldoublesplittingoperatorsinB(E,F)andGI(A)thesetofgeneralizedinversesofA2B+(E,F).InthispaperweintroduceanunboundeddomainW(A,A^+)inB(E,F)forA2B+(E,F)andA^+2GI(A),andprovideanecessaryandsufficientconditionforT2W(A,A^+).Thenseveralconditionsequivalenttothefollowingpropertyareproved:B=A^+(IF+(T??A)A^+)??1isthegeneralizedinverseofTwithR(B)=R(A^+)andN(B)=N(A^+),forT2W(A,A^+),whereIFistheidentityonF.Alsoweobtainthesmooth(C¥)diffeomorphismMA(A^+,T)fromW(A,A^+)ontoitselfwiththefixedpointA.LetS=fT2W(A,A^+):R(T)\N(A^+)=f0gg,M(X)=fT2B(E,F):TN(X)R(X)gforX2B(E,F)g,andF=fM(X):8X2B(E,F)g.UsingthediffeomorphismMA(A^+,T)weprovethefollowingtheorem:SisasmoothsubmanifoldinB(E,F)andtangenttoM(X)atanyX2S.ThetheoremexpandsthesmoothintegrabilityofFatAfromalocalneighborhooldatAtotheglobalunboundeddomainW(A,A^+).Itseemstobeusefulfordevelopingglobalanalysisandgeomatricalmethodindifferentialequations.
简介:Alooplessgraphonnverticesinwhichverticesareconnectedatleastbyaandatmostbybedgesiscalleda(a,b,n)-graph.A(b,b,n)-graphiscalled(b,n)-graphandisdenotedbyKbn(itisacompletegraph),itscomplementbyKbn.Anonincreasingsequencep=(d1,…,dn)ofnonnegativeintegersissaidtobe(a,b,n)graphicifitisrealizablebyan(a,b,n)-graph.Wesayasimplegraphicsequencep=(d1,…,dn)ispotentiallyK4—K2[K2-graphicifithasaarealizationcontaininganK4—K2[K2asasubgraphwhereK4isacompletegraphonfourverticesandK2[K2isasetofindependentedges.Inthispaper,wefindthesmallestdegreesumsuchthateveryn-termgraphicalsequencecontainsK4—K2[K2assubgraph.
简介:Itisidentifiedthatbarelypassingelectronsarethedriveofthee-Gshbones,ratherthanthebarelytrappedelectronsatlowfrequency.Thefrequencyjumpine-Bshboneexperimentsisreproducedandanalyzed.Itisfoundthatthee-Bshbonefrequencyincreaseswiththehotelectronenergy,whichisconsistentwiththeexperiments.Thegrowthrateofthemode(m=2,n=2)isgreaterthanthatofthemode(m=1,n=1).
简介:Afusionbreedermightbeanessentialintermediateapplicationoffusionenergyatearlierterm,sinceithasthepotentialtoprovideplentyofcommercialfissilefuel.Basedonfusionphysicsandtechnologiesavailableatpresentandinthenearfuture,therealisticfusionexperimentalbreeder,FEB-Ewasdesigned.
简介:Inthecontextofthetop-color-assistedtechnicolor(TC2)model,theflavor-changingneutral-current(FCNC)interactioninducedbythetop-higgs(h_t~0)arepredictedattreelevel.Westudytherelevantprocessesofe~+e~-(γγ)→th_t~0attheInternationalLinearCollider(ILC).ItisfoundthattheserareprocessesproductionratescanbeenhancedsignificantlyintheTC2model.Especiallyfortheprocessγγ→th_t~0,thetotalcrosssectionwillreachafewfbinthereasonableparameterspace.Wealsocalculatethedistributionsoftransversemomenta,pseudo-rapidandinvariantmassofthetop-higgs.Inviewofthemaindecaymodesoftop-higgsform_(h_t~0)<2m_t,weEndthattherewillbeseveralhundredsFCNCeventsproducedattheILCwithannuallyintegralluminosityof500fb~(-1).Duetothecleanbackground,suchFCNCsignalscanpossiblybedetectedattheILC.