简介:Children'sliterature,whichincludesstories,books,magazines,andpoems,isespeciallyvividforchildren.ThisbookreviewisaboutCharlieandtheChocolateFactory,apopularChildren’sliteraturewrittenbyRoaldDahl.Inthebookreview,Iwillbrieflyintroduceinformationabouttheauthorandthisnovel.Thebookreviewalsoincludesanotherthreemainparts:whathappenedinthewholestory,whichpartsimpressedmemostinthebookandtheauthor’swritingskillsofthebook.Eachpartistobegivenindetail.ExamplesarealsocontainedtoshowwhyIthinkthebookisreadable,interestingandattractive.
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.