简介：函数周期性的判定方法秦翠娥，黄永强（太原工业大学）（太原农业学校）进行三角函数教学时，引进了周期函数的概念，讲授“级数”一章时，要求展开成傅里叶级数的函数是周期函数。周期函数对研究函数的性态有很多方便之处。因此，研究周期函数是十分重要的数学问题。本文...

简介：对于单位圆盘内的解析函数f(z)=z+^∞∑(k=2)akz^k，本文根据D^nf(z)/z给出了判别函数f(z)为单叶函数的几条判别法则，其中D^0f(z)=f(z)，D^1f(z)=Df(z)=zf′(z)，D^nf(z)=D(D^(n-1)f(z))，n∈N.

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简介：InthispaperaconnectivestudyofGould'sannihilationcoefficientsandAbel-Gontscharoffpolynomialsispresented.ItisshownthatGould'sannihilationcoefficientsandAbel-Gontscharoffpolynomialsareactuallyequivalenttoeachotherundercertainlinearsubstitutionsforthevariables.Moreover,apairofrelatedexpansionformulasinvolvingGontscharoff'sremainderandanewformofitaredemonstrated,andalsoillustratedwithseveralexamples.

简介：InthispaperwestudythesolutionsandstabilityofthegeneralizedWilson’sfunctionalequation∫_Gf(xty)dμ(t)+∫_Gf(xtσ(y))dμ(t)=2f(x)g(y),x,y∈G,whereGisalocallycompactgroup,σisacontinuousinvolutionofGandμisanidempotentcomplexmeasurewithcompactsupportandwhichisσ-invariant.Weshowthat∫_Gg(xty)dμ(t)+∫_Gg(xtσ(y))dμ(t)=2g(x)g(y)iff≠0and∫_Gf(t.)dμ(t)≠0,where[∫_Gf(t.)dμ(t)](x)=∫_Gf(tx)dμ(t).WealsostudysomestabilitytheoremsofthatequationandweestablishthestabilityonnoncommutativegroupsoftheclassicalWilson’sfunctionalequationf(xy)+χ(y)f(xσ(y))=2f(x)g(y)x,y∈G,whereχisaunitarycharacterofG.

简介：ABanachspaceoperatorsatisfiesgeneralizedRakoevi'sproperty(gw)ifthecomplementofitsuppersemiB-WeylspectruminitsapproximatepointspectrumisthesetofeigenvaluesofTwhichareisolatedinthespectrumofT.Inthisnote,wecharacterizehypecyclicandsupercyclicoperatorssatisfyingtheproperty(gw).

简介：群G的一个子群H称为在G中S-拟正规嵌入的,如果对H阶中的每一个素因子p,H的Sylowp-子群也是G的某个S-拟正规子群的Sylowp-子群.利用子群的S-拟正规嵌入性给出了群为p-幂零群及超可解群的一些特征.

简介：也就是，这篇文章介绍理想的一个新班sπr理想。在一枚戒指的sπr理想上的每个常规方形的矩阵承认斜减小，这被显示出。

简介：Inthispaper,westudyRényi'sproblemandotherrelatedproblemsabouttheadditivefunctionsinshortintervals.Ascorollaries,weimproveIvic'sresults.

简介：ＡＲＯＮＳＯＮ＇ＳＥＳＴＩＭＡＴＥＳＡＮＤＣＯＮＤＩＴＩＯＮＡＬＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＱＩＡＮＺＨＯＮＧＭＩＮ（钱忠民）ＷＥＩＧＵＯＱＩＡＮＧ（魏国强）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｔａｔｉｓｔｉｃｓ，ＥａｓｔＣｈ...

简介：TheConwaypotentialfunction(CPF)forcoloredlinksisaconvenientversionofthemultivariableAlexander–Conwaypolynomial.WegiveaskeincharacterizationofCPF,muchsimplerthantheonebyMurakami.Inparticular,Conway’s"smoothingofcrossings"isnotintheaxioms.Theproofusesareductionschemeinatwistedgroup-algebraP_nB_n,whereB_nisabraidgroupandP_nisadomainofmulti-variablerationalfractions.Theproofdoesnotusecomputeralgebratools.Aninterestingby-productisacharacterizationoftheAlexander–Conwaypolynomialofknots.

简介：Inthispaper,thecycle’sstructureofembeddedgraphsinsurfacesarestudied.Accordingtothemethodoffundamentalcycles,thesetC(Ccontainsallshortest)isfound.AundirectedgraphGwithnverticeshasatmostO(n5)manyshortestcycles;IftheshortestcycleofGisoddcycle,thenGhasatmostO(n3)manyshortestcycles;IfGhasbeenembeddedinasurfaceSg(Ng,gisaconstant),thenithasatmostO(n3)shortestcycles,moreover,iftheshortestcycleofGisoddcycle,then,GhasatmostO(n2)manyshortestcycles.WecanfindacyclebaseofG,thenumberofoddcyclesofG,thenumberofevencyclesofG,thenumberofcontractiblecyclesofG,thenumberofnon-contractiblecyclesofG,arealldecided.IftheΠ-embeddedgraphGhasΠ-twosidedcycles,then,CcontainsashortestΠ-twosidedcycleofG,thereisapolynomiallyboundedalgorithmthatfindsashortestΠ-twosidedcycleofaΠ-embeddedgraphG,thenewandsimplesolutionsabouttheopenproblemofBojanMoharandCarstenThomassenareobtained.

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简介：Thispaperproposesaformallystrongerset-valuedClaxke'sfixedpointtheorem.Bythis-theoremwecanimproveafixedpointtheoremforweaklyinwardcontractionset-valuedmappingofD.DowingandW.A.Kirk.

简介：AradialfunctioncanbeexpressedbyitsgeneratorthroughThepositivedefiniteofthefunctionplaysanimportantroteintheradialbasisinterpolation.WecannaturallyuseBochner’sTheoremtocheckifispositivedefinite.Thisrequireshoweveran-dhnensiotialFouriertransformationanditisnotveryeasytocalculate.Furthermoreinalotofcaseswewilluseforspacesofvariousdimensionstoo,thenforeveryfixednweneeddotheFouriertransformationoncetocheckifthefunctionispositivedefiniteinthen-di-mensionalspace.Thecompletelymonotonefunction:,whichisdiscussedin[4]ispositivedefiniteforarbitraryspacedimensions.Withthistechniquetvecanveryeasilycharacterizethepositivedefinite,ofaradialfunctionthroughitsgenerator.Unfortunatelythereisonlyaverysmallsubsetofradialfunctionwhichiscompletelymonotone.Thusthiscriterionexcludedalotofinterestingfunctionssuchascompactlysupportedradialfunction,whcihareveryusefulinapplic

简介：WeconductedtheresearchonthecalculationoftheJordannormalformofamatrixfrom1993to1998.Inthisperiod,weobtainedsometheoreticalresults,alsodevelopedandimplementedaseriesofalgorithmsforthetheoreticalresults.Nowthisresearchiscompletedtosomedegree.TheGolub-Wilkinson’sProblemComputingtheJordandecompositionofamatrix,introducedbyG.H.GolubandJ.

简介：Mardia(1970)definedameasureofmultivariatekurtosisandderiveditsasymptoticdistributionforsamplesfromamultivariatenormalpopulation.SomenewresultsonellipticaldistributionsareusedtoextendMardia’sresultstosamplesfromanellipticaldistribution.Theseresultsprovideamethodfortestinghypothesesonthekurtosisparameterofellipticaldistributions.AnappendixprovidesextensionsofKendallandStuart’s(1977)standarderrorsofbivariatemomentstothethirdandfourthorder.

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