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简介：ThepurposeofthispaperistogivearelativelyelementaryanddirectproofoftheDeltaInequality,whichplaysaveryimportantroleinthestudyoftheextremalproblemofquasiconformalmappings.

简介：Theproblemofdecisionmakinginanimpreciseenvironmenthasfoundparamountimportanceinrecentyears.Inthispaper,wedefinevaguesoftrelationandsimilaritymeasureofvaguesoftsets.Usingthesedefinitions,somenovelmethodsofobjectrecognitionfromanimprecisemultiobserverdatahasbeenpresented.Moreover,weintroducethenotionofgeneralizedvaguesoftsetsandstudysomeofitsproperties.Thesimilaritymeasureofgeneralizedvaguesoftsetsisalsopresentedandanapplicationofthismeasureindecisionmakingproblemshasbeenshown.

简介：Thispaperusesgraphicmethodtoanalyzethemechanismofprimenumberformationandtheperiodiccharacteristicsofitsmultipleinnaturalnumbers.TheGoldbach’sconjectureisprovedbytheanalysisdiagrams.

简介：Inthispaperusinganargumentfrom[1],weproveoneoftheprobabilisticversionofHardy'sinequality.

简介：AconstructiveproofisgivenfortheinversionformulaforzonalfunctionsonSL(2,R).AconcretelyconstructedsequenceofzonalfunctionsareprovedtosatisfytheinversionformulaobtaAnedbyHarish-Chandraforcompactsupportedinfinitelydifferentiablezonalfunctfons.Makinguseofthepropertyofthissequencesomehowsimilartothatofapproximationkernels,theauthorndeducethattheinversionformulaistrueforcontinuouszonalfunctiotmon8L(2,R)somecondition.Theclassicalresultcanbeviewedasacorollaryoftheresultshere.

简介：Inthispaperwe’llproveafundameutalpropertyofthevectorspacebymeansoftheex-tensionfield,i.e.thenumbersoftheelementsofabasisofthevectorspaceVoverthefieldFequaltothedimensions(V:F).

简介：在这篇文章，我们在用原来被介绍在的相互作用Morawetz估计为Hartree方程散布的精力上给一个简单证明[5]。

简介：SupposethatDisadivisionringinwhichthereisdefinedananti-automorphismα→(?)isinvolutorial,RisaleftvectorspaceoverD.Usingthegivenanti-automorphismα→(?),itiseasytoturnRintoarightvectorspaceoverDbysetingx(?)=ax.Bilinearformg(x,y)connectingtheleftvectorspaceRandtherightvectorspaceRisaHermitianscalar.

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简介：ThefollowingtheoremisprovedTheorem1.Letqbeapolynomialofdegreen（qPn）withndistinctzeroeslyingintheinterval[-1,1]and△’q={-1}∪{τi:q’（τi）=0,i=1,n-1}∪{1}.IfpolynomialpPnsatisfiestheinequalitythenforeachk=1,nandanyx[-1,1]itsk-thderivativesatisfiestheinequality丨pk（x）丨≤max{丨q（k）（x）丨,丨1/k（x2-1）qk+1（x）+xq（k）（x）丨}.ThisestimateleadstotheMarkovinequalityforthehigherorderderivativesofpolynomialsifwesetq=Tn,whereTnisChebyshevpolynomialleastdeviatedfromzero.SomeotherresultsareestablishedwhichgivesevidencetotheconjecturethatundertheconditionsofTheorem1theinequality‖p（k）‖≤‖qk‖holds.

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简介：Softsettheoryhasarichpotentialapplicationinseveralfields.Asoftgroupisaparameterizedfamilyofsubgroupsandafuzzysoftgroupisaparameterizedfamilyoffuzzysubgroups.Theconceptoffuzzysoftgroupisthegeneralizationofsoftgroup.AbdulkadirAygunogluandHalisAygunintroducedthenotionoffuzzysoftgroupsin2009[1].Inthispaper,theconceptoflatticeorderedfuzzysoftgroupsanditsdualityhasbeenintroduced.Thendistributiveandmodularlatticeorderedfuzzysoftgroupsareanalysed.Theobjectiveofthispaperistostudythelatticetheoryoverthecollectionoffuzzysoftgroupinaparametricmanner.Somepertinentpropertieshavebeenanalysedandhenceestablisheddualityprinciple.