简介:InthispaperweprovesomeinterestingextensionsandgeneralizationsofEnestrom-KakeyaTheoremconcerningthelocationofthezerosofapolynomialinacomplexplane.Wealsoobtainsomezero-freeregionsforaclassofrelatedanalyticfunctions.Ourresultsnotonlycontainsomeknownresultsasaspecialcasebutalsoavarietyofinterestingresultscanbededucedinaunifiedwaybyvariouschoicesoftheparameters.
简介:组G的Wielandt亚群,由w(G)表示了,是G的所有低于正常的亚群的normalizers的交叉。在这份报纸,作者为每整数i为最大的班G,为所有整数i的任何一个wi(G)=i(G)或wi(G)=i+1(G)的p组显示出那,并且为在有K1的G的每正常亚群K的w(G/K)=(G/K)。同时,为最大的班的常规p组的一个必要、足够的条件令人满意的w(G)=2(G)被给。最后,如果G是有基本z(G)的non-abelianp组,作者证明力量自守组PAut(G)是基本abelianp组?\mho1(G)\zeta(G)\cap\mho_1(G)。
简介:Inthispaper,weestablisharesultofLeray-Schauderdegreeontheorderintervalwhichisinducedbyapairofstrictloweranduppersolutionsforasystemofsecond-orderordinarydifferentialequations.Asapplications,weprovetheglobalexistenceofpositivesolutionsforamulti-parametersystemofsecond-orderordinarydifferentialequationswithrespecttoparameters.ThediscussionisbasedontheresultofLeraySchauderdegreeontheorderintervalandthefixedpointindextheoryincones.
简介:AnewapproachforrobustH-infinityfilteringforaclassofLipschitznonlinearsystemswithtime-varyinguncertaintiesbothinthelinearandnonlinearpartsofthesystemisproposedinanLMIframework.TheadmissibleLipschitzconstantofthesystemandthedisturbanceattenuationlevelaremaximizedsimultaneouslythroughconvexmulti-objectiveoptimization.TheresultingH-infinityfilterguaranteesasymptoticstabilityoftheestimationerrordynamicswithexponentialconvergenceandisrobustagainstnonlinearadditiveuncertaintyandtime-varyingparametricuncertainties.Explicitboundsonthenonlinearuncertaintyarederivedbasedonnorm-wiseandelement-wiserobustnessanalysis.
简介:Inthisarticle,first,asufficientconditionforastarlikemappingoforderαf(x)definedontheunitballinacomplexBanachspaceisgiven.Second,thesharpestimateofthethirdhomogeneousexpansionforfisestablishedaswell,wheref(z)=(f1(z),f2(z),...,fn(z))’isastarlikemappingoforderαoranormalizedbiholomorphicstarlikemappingdefinedontheunitpolydiskinCn,andOurresultstatesthattheBieberbachconjectureinseveralcomplexvariables(thecaseofthethirdhomogeneousexpansionforstarlikemappingsoforderαandbiholomorphicstarlikemappings)ispartlyproved.