简介:TheauthorsmainlyconcernthesetUfofc∈Csuchthatthepowerdeformationzf(z)/zcisunivalentintheunitdisk|z|<1foragivenanalyticunivalentfunctionf(z)=z+a2z2+···intheunitdisk.ItisshownthatUfisacompact,polynomiallyconvexsubsetofthecomplexplaneCunlessfistheidentityfunction.Inparticular,theinteriorofUfissimplyconnected.Thisfactenablesustoapplyvariousversionsoftheλ-lemmafortheholomorphicfamilyzf(z)/zcofinjectionsparametrizedovertheinteriorofUf.ThenecessaryorsufficientconditionsforUftocontain0or1asaninteriorpointarealsogiven.
简介:Letp(z)=beapolynomialdegreenandletThenaccord-ingtoBernstein’sinequality||p’||
简介:Everyoneknowstodayisthestartofthenewyear,butnoteveryoneknowstodayIsalsoZDay.ItsorganizerssaythatonZday,thelastshallbethefirst-andwhatbetterdateforsuchacelebrationthanthefirstdayoftheyear?Sincetodayalsomarksthe1484birthanniversaryoftheSwissReformationleaderUlrichZwingandthestartoftheMexicanZabatlsta