简介:Theaimofthispaperistogiveasimpleproofoftherestrictiontheoremforthemaximaloperatorsonthed-dimensionalEuclideanspaceRd,whosetheoremwasprovedbyCarro-Rodriguezin2012.Moreover,weshallgivesomeremarksoftherestrictiontheoremforthelinearandthemultilinearoperatorsbyCarro-RodriguezandRodriguez,too.
简介:TwoLatinsquaresofordervarer-orthogonaliftheirsuperpositionproducesexactlyrdistinctorderedpairs.Thetwosquaresaresaidtober-orthogonalidempotentLatinsquaresanddenotedbyr-MOILS(v)iftheyareallidempotent.Inthispaper,weshowthatforanyintegerv≥28,thereexistsanr-MOILS(v)ifandonlyifr∈[v,v~2]\{v+1,v~2-1}.
简介:LongtimebehaviorofdegenerateequationswiththenonlinearityofpolynomialgrowthofarbitraryorderonthewholespaceRNisconsidered.Byusing-trajectoriesmethods,weprovedthatweaksolutionsgeneratedbydegenerateequationspossessan(L2U(RN),L2loc(RN))-globalattractor.Moreover,theupperboundsoftheKolmogorovε-entropyforsuchglobalattractorarealsoobtained.
简介:.Thesingle2dilationorthogonalwaveletmultipliersinonedimensionalcaseandsingleA-dilation(whereAisanyexpansivematrixwithintegerentriesand|detA|=2)waveletmultipliersinhighdimensionalcasewerecompletelycharacterizedbytheWutamConsortium(1998)andZ.Y.Li,etal.(2010).Butthereexistnomoreresultsonorthogonalmultivariatewaveletmatrixmultiplierscorrespondingintegerexpansivedilationmatrixwiththeabsolutevalueofdeterminantnot2inL2(R2).Inthispaper,wechoose2I2=(2002)asthedilationmatrixandconsiderthe2I2-dilationorthogonalmultivariatewaveletY={y1,y2,y3},(whichiscalledadyadicbivariatewavelet)multipliers.Wecallthe3×3matrix-valuedfunctionA(s)=[fi,j(s)]3×3,wherefi,jaremeasurablefunctions,adyadicbivariatematrixFourierwaveletmultiplieriftheinverseFouriertransformofA(s)(cy1(s),cy2(s),cy3(s))?=(bg1(s),bg2(s),bg3(s))?isadyadicbivariatewaveletwhenever(y1,y2,y3)isanydyadicbivariatewavelet.Wegivesomeconditionsfordyadicmatrixbivariatewaveletmultipliers.TheresultsextendedthatofZ.Y.LiandX.L.Shi(2011).Asanapplication,weconstructsomeusefuldyadicbivariatewaveletsbyusingdyadicFouriermatrixwaveletmultipliersandusethemtoimagedenoising.
简介:LetL=L0+VbethehigherorderSchrdigertypeoperatorwhereL0isahomogeneousellipticoperatoroforder2mindivergenceformwithboundedcoefficientsandVisarealmeasurablefunctionasmultiplicationoperator(e.g.,including(-?)m+V(m∈N)asspecialexamples).Inthispaper,assumethatVsatisfiesastronglysubcriticalformconditionassociatedwithL0,theauthorsattempttoestablishatheoryofHardyspaceHpL(Rn)(0
简介:本文在L_p(1≤p〈∞)空间上,研究了种群细胞增生中一类具扰动项的一般边界条件下的L-R模型,给出了这类模型相应的迁移方程解的渐近行为等结果.
简介:Inthispaper,weshowthatnewmodifieddoublecosinetrigonometricsumsintroducedin[1]areinappropriate,theclassofdoublesequencesJdintroducedthereisunusableforsuchsumsandconsequentlytheresultsobtainedinitarecompletelyincorrect.WehereintroduceappropriatemodifieddoublecosinetrigonometricsumsmakingtheclassJdusableconsideringaparticulardoublecosinetrigonometricseries.
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.
简介:首先介绍选举理论中的5种投票方法(简单多数、单轮决胜、系列决胜、Coombs法、Borda计数)和5条公平性准则(多数票、Condorcet获胜者、Condorcet失败者、无关候选人独立性、单调性),并用政治和社会领域的若干实例给以解释。然后给出著名的Arrow不可能性定理的两种不同的版本,以及对Arrow一条公平性准则的修正;按照修正后的准则,存在满足所有公平性准则的投票方法。