简介:在文献中,DNA序列曾被描述为一维游动和三维游动.对前者,一个游动对应于多个DNA序列;对后者,游动和DNA序列一一对应.我们发现在三维游动(xn,yn,zn)中,由xn,yn和zn中任意有序的两个给出的二维游动已经与DNA序列一一对应,且余下的一维游动由该二维游动完全决定.因此,二维游动似乎是描述DNA序列最合适的模型.4个碱基A,C,G和T共有4!=24个排序.每一个排序都给出DNA序列用二维游动的一种描述.两个游动(x'n,y'n)和(x"n,y"n)被看作是等价的,如果(x'n,y'n)=(εx"n,δy"n)或(εy"n,δx"n),这里ε=±1,且δ=±1.于是这24个类型的游动被分成三个等价类;它们的代表分别是(xn,yn),(yn,zn),和(xn,zn),这里(xn,yn,zn)正好是张和张的三维游动.
简介:Inthispaper,thetwo-dimensionalMarcinkewiczintegralintroducedbySteinμ(f)(x)=(∫0x|∫|x-y|≤1|x-y|Ω(x-y)f(y)dy|2t-3dt)2isshowntobeofweaktype(1,1)andweightedweaktype(1,1)withrespecttopowerweight|x|"if-1<α<0,whereΩishomogeneousofdegree0.hasmeanvalue0andbelongstoLlog+L(S1).
简介:Anewspectralproblemisproposed,andnonlineardifferentialequationsofthecorrespondinghierarchyareobtained.Withthehelpofthenonlinearizationapproachofeigenvalueproblems,anewfinite-dimensionalHamiltoniansystemonR2nisobtained.Ageneratingfunctionapproachisintroducedtoprovetheinvolutionofconservedintegralsanditsfunctionalindependence,andtheHamiltonianflowsarestraightenedbyintroducingtheAbel-Jacobicoordinates.Atlast,basedontheprinciplesofalgebracurve,thequasi-periodicsolutionsforthecorrespondingequationsareobtainedbysolvingtheordinarydifferentialequationsandinversingtheAbel-Jacobicoordinates.
简介:随便取一个自然数,如果它是偶数,用2除它;如果它是奇数,将它乘3之后再加1,这样反复运算,最终必然得1.比如,取自然数N=6.6是偶数,先用2除,6÷2=3;3是奇数,要将它乘3之后再加1,3×3+1=10;按着上述法则往下做:10÷2=5;5×3+1=16;16÷2=8;8÷2=4;4÷2=2;2÷2=1.从6开始经历了3→10→5→16→8→4→2→1,最后得1.通过大量演算发现最后结果总是得1.于是数学家提出如下猜想:对于任一个自然数N,若N是偶数,就把它变成N2;若N是奇数,就把它变成3N+1.按照这个规则运算下去,最后必然得1.这个猜想到目前还没有人给予证明,不过日本东京大学的米田信
简介:Anecessaryandsufficientconditionofregularityof(0,1,…,m-2,m)interpolationonthezerosof(1-x)Pn-1α,β(x)(α>-1,β≥-1)inamanageableformisestablished,wherePn-1α,β(x)standsforthe(n-1)thJacobipolynomial.Meanwhile,theexplicitrepresentationofthefundamentalpolynomialswhentheyexist,isgiven.
简介:SINGULARITYANDQUADRATUREREGULARITYOF(0,1,...,m-2,m)─INTERPOLATIONONTHEZEROSOF(1-x)Pn-1αβ(x)ShiYingguang(史应光)(ComputingCe...
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简介:Abosonicconstruction(withcentralchargec=2)ofLiealgebrasW1+∞andW1+∞(glN),aswellasthedecompositionsintoirreduciblemodulesaredescribed.AndforW1+∞,whenrestrictedtoitsVirasorosubalgebraVir,abosonicconstructionandthesamedecompositionforVirareobtained.