简介:本文引进了两个正定自共轭四元数矩阵的算术均值,几何均值,调和均值三概念,给出了正定自共轭四元数矩阵的算术-几何-调和均值不等式,得到了正定自共轭四元数矩阵的几何均值的一个最大性质及其相关的某些性质。
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: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:Weestablishseveralfundamentalidentities,includingrecurrencerelations,degreeelevationformulas,partitionofunityandMarsdenidentity,forquantumBernsteinbasesandquantumBeziercurves.WealsodeveloptwotermrecurrencerelationsforquantumBernsteinbasesandrecursiveevaluationalgorithmsforquantumBeziercurves.Ourproofsusestandardmathematicalinductionandotherelementarytechniques.