简介:A(k;g)-graphisak-regulargraphwithgirthg.A(k;g)-cageisa(k;g)-graphwiththeleastpossiblenumberofvertices.Letf(k;g)denotethenumberofverticesina(k;g)-cage.Thegirthpairofagraphgivesthelengthofashortestoddandashortestevencycle.Afc-regulargraphwithgirthpair(g,h)iscalleda(k;g,h)-graph.A(k;g,h)-cageisa(k;g,h)-graphwiththeleastpossiblenumberofvertices.Letf(k;g,h)denotethenumberofverticesina(k;g,h)-cage.Inthispaper,weprovethefollowingstrictinequalityf(k;h-1,h)
简介:LetZbeatopologicalspaceandmappingA2:Z→B(H)withclosedrangeR(A2)becontinuous.SomenecessaryandsufficientconditionsofthecontinuityofM-PinversesAz+aregivenin[1],[2].ItisoneofthemthatAZ+iscontinuousifanaonlyifAZ+islocallybounded.Inthispaper,wediscussthefollowingproblem:iflimAn=A0inB(H)and||An+||isunbounded(i.e.theabovenecessaryandsufficientconditionfails),whathinHwillmaketheequations:limAm+h=A0+horw-limAn+h=A0+hbetrue.Forthispurposethreetheoremsandanerrorestimationaregiveninthispaper.
简介:SYNTHESISOF3-ARYL-1(2H,4H)ACRIDONESANDTHEIRDERIVATIVES¥RongYIN;GuangFanHAN;YuTianLI(DepartmentofMedicalLaboratory,JilinMediea...
简介:1IntroductionLetA∈Cn×n,B∈Cn×n.WesayBisasquarerootofAifA=B×Bi.e.A=B2.Itiswell-knownthatanysymmetricpositivedefinitematrixexistsoneandonlyonesquarerootwhichisasymmetricpositivedefinitematrix,too(e.g.see[5]).Higham[4]studiedcarefullytherelationofarealnonsingularmatrixbetweenitsrealsquarerootsanditseigenvalues.AlefeldandSchneider[1]pointedoutthatforanynonsingularM-ma-trixthereisoneandonlyoneM-matrixasitssquareroot.Inthispaper,westudyona
简介:Thispaperreportstwolanthanidecomplexesofformula(C9H7)Ln(C8H8)·(THF)2whereLnisProrNd,C9H7isindenyl,andC8H8iscyclooctatetraene(COT).ThecomplexeswerepreparedbythereactionofLnCl3withK(C9H7)andK2(C8H8)inTHF.(C9H7)Pr(C8H8)·(THF)2crystallizesinTHFat-15℃inthemonoclinicspacegroupP21:withunitcelldimensionsa=8.446(0),b=10.083(2),c=13.407(3),β=105.48(1)°,V=1100.43(35)3,Dc=1.52g/cm3andZ=2.ThefinalRvalueis0.033,Rwvalueis0.030,respectively.In(C9H7)Pr(C8H8)·(THF)2afive-memberedringcentroidofC9H7,theC8H8ringcentroidandthetwooxygenatomsfromthetwoTHFmoleculesformadistortedtetrahedralgeometryaroundthemetal.
简介:Thesolidaddofthefirstprotonatedzincoborophosphate,(H3O)Zn(H2O)2BP2O8·H2O(1),wassoventothermallysyn-thesizedbythereactionofZn(NO3)2·6H2OandH3BO3withH3PO4inamixedsolvent,andstructurallycharacterizedbysingle-ystalX-raydiffractionanalysis.ItcrystallizesinthehexagonalP6122,a=0.9604(4)nm,c=1.5297(6)nm,V=1.2218(8)nm^3,Dc=2.921g/cm^3,Z=6,F(000)=1080,μ=3.495mm^-1.Thestmchwefeaturesthatthetetrahedra-te-trahedrahdlcesinterconnectedbyoctahedraandstronghydro-gembondinteractionsformathree-dimensionalframework.Theprotonatedwatermoleculesarelocatedatuniquepositions.othercharacterizationsbyIRandthermalanalysisarealsode-scribed.
简介:Weestablishseveralfundamentalidentities,includingrecurrencerelations,degreeelevationformulas,partitionofunityandMarsdenidentity,forquantumBernsteinbasesandquantumBeziercurves.WealsodeveloptwotermrecurrencerelationsforquantumBernsteinbasesandrecursiveevaluationalgorithmsforquantumBeziercurves.Ourproofsusestandardmathematicalinductionandotherelementarytechniques.
简介:ThispapershowsthatforΩ∈H1(Sn-1),MarcinkiewiczintegraloperatorμΩisLp(Rn)boundedfor1<p<∞,whichimprovessomeknownresults.
简介:Inthispaper,westudythehomogeneouspolynomialsorthogonalwiththeweightfunctionh(x(d))=x2k11green.Itissimplerthantheformulain[2],andcanberegardedasanextensionof[1]undertheweightedcase.
简介:Givennon-negativeintegersm,n,handkwithm≥h>1andn≥k>1,an(h,k)-bipartitehypertournamentonm+nverticesisatriple(U,V,A),whereUandVaretwosetsofverticeswith|U|=mand|V|=n,andAisasetof(h+k)-tuplesofvertices,calledarcs,withatmosthverticesfromUandatmostkverticesfromV,suchthatforanyh+ksubsetsU_1∪V_1ofU∪V,Acontainsexactlyoneofthe(h+k)!(h+k)-tupleswhoseentriesbelongtoU_1∪V_1.Necessaryandsufficientconditionsforapairofnon-decreasingsequencesofnon-negativeintegerstobethelosingscorelistsorscorelistsofsome(h,k)-bipartitehypertournamentareobtained.