简介:WeestablishtheconstructiontheoryoffunctionbaseduponalocalfieldKpasunderlyingspace.Byvirtureoftheconceptofpseudo-differentialoperator,weintroduce"fractalcalculus"(or,p-typecalculus,or,Gibbs-Butzercalculus).Then,showtheJacksondirectapproximationtheorems,BermsteininverseapproximationtheoremsandtheequivalentapproximationtheoremsforcompactgroupD(Kp)andlocallycompactgroupK+p(=Kp),sothatthefoundationofconstructiontheoryoffunctiononlocalfieldsisestablished.Moreover,theJacksontype,Bernsteintype,andequivalentapproximationtheoremsontheH?lder-typespaceCσ(Kp),σ>0,areproved;thentheequivalentapproximationtheoremonSobolev-typespaceWrσ(Kp),σ≥0,1≤r<+∞,isshown.
简介:Inthisstudy,anewmethodologybasedontheHadamardmatrixisproposedtoconstructquantumBooleanfunctionsfsuchthatf=I2n-2P2n,whereI2nisanidentitymatrixoforder2nandP2nisaprojectivematrixwiththesameorderasI2n.TheenumerationofthisclassofquantumBooleanfunctionsisalsopresented.
简介:Inacommonauthenticationcodewitharbitration,thedishonestarbitermaymakeathreattothesecurityofauthenticationsystem.Inthispaper,anauthenticationcodewithdoublearbitersoversymplecticgeometryisconstructed,andtherelevantparametersandtheprobabilitiesofsuccessfulattacksarecalculated.Themodelnotonlypreventsdeceptionfromtheopponentandmembersofthesystem,butalsoeffectivelylimitstheattacksofsinglearbiter.Moreover,thecollusionattacksfromarbitersandparticipatorsaredifficulttosucceed.
简介:AsimpleandefficientcascadeMichael/cyclizationreactionof3-aminoindolin-2-oneswithenones/enalswasidentifiedforthesynthesisofpotentiallybiologicallyactive3’,4’-dihydrospiro[pyrrol-3,2’-oxindoles],usingDBUasanefficientcatalystandethyleneglycolasanenvironmentallybenignsolvent.Morediverse3’,4’-dihydrospiro[pyrrol-3,2’-oxindoles]analoglibrarieswerepreparedingoodyields(upto97%).Thestructureof3’,4’-dihydrospiro[pyrrol-3,2’-oxindoles]wasconfirmedbymassspectrometryanalysis,NMRanalysisandsinglecrystalX-raydiffraction.Themainadvantagesofthismethodincludetheavailabilityofstartingmaterials,simpleexperimentaloperation,shortreactiontime,aswellashighyieldsobserved.
简介:Inthiswork,webrieflydiscussanovelclassofmodifiedgravitylikef(T,TG)gravity.Inthisbackground,weassumethenewagegraphicversionofpilgrimdarkenergyandreconstructf(T,TG)modelsfortwospecificvaluesofs.Wealsodiscusstheequationofstateparameter,squaredspeedofsoundandwDE-wDEplaneforthesereconstructedf(T,TG)models.Theequationofstateparameterprovidesphantom-likebehavioroftheuniverse.ThewDE-wDEplanealsocorrespondstoΛCDMlimit,thawingandfreezingregionsforbothmodels.
简介:《数学课程标准》要求学生所掌握的空间与图形内容如下:能够借助不同的方法探索几何对象的有关性质;能够使用不同的方式表达几何对象的大小、位置与特征;能够在头脑里构建几何对象,进行几何图形的分解与组合,能够对某些图形进行简单的变换;能够借助数学证明的方法确认数学命题的正确性。图形与证明是空间与图形的核心内容之一,课标要求学生掌握基本的图形基础知识与基本技能;了解证明的含义,掌握证明的方法,体会证明的过程;能把所学的公理、定理和基本事实正确运用到证明的过程中,在合情推理的基础上发展初步的演绎推理能力;初步通过观察、实验、归纳、类比、推测获得数学猜想,体验数学活动充满着探索性和创造性,感受证明的必要性、证明过程的严谨性及结论的稳定性,它贯穿在整个几何知识的学习及运用之中.