简介：我们计算在光滑的度量标准的情况下在FJRW理论定义的真实Cauchy-Riemann操作员的索引。为圆柱的度量标准，我们在加权的Sobolev空格学习在Witten地图和重量的线性化的操作符的索引之间的关系。

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简介：让G是顺序n的一张图并且让1，2，，n是它的特征值。Estrada索引[2]G被定义为EE=EE(G)=。在这份报纸，为EE的新界限被建立，以及在EE和图精力E之间的一些关系。

简介：<正>Inthispaper,weprovethatthesetofallfactorizationindicesofacompletelypositivegraphhasnogaps.Inotherwords,wegiveanaffirmativeanswertoaquestionraisedbyN.KoganandA.Berman[8]inthecaseofcompletelypositivegraphs.

简介：Theq-Wienerindexofunicyclicgraphsaredeterminedinthiswork.Asanexampleofitsapplications,anexplicitexpressionofq-Wienerindexofcaterpillarcyclesispresented.

简介：有单音的补品连接功能的单个索引的模型被调查。第一，连接工作，这被显示出h(·)能被一个图形的方法看。也就是说有水平轴上的适合的反应的阴谋；垂直的轴上的观察y能被用来设想连接功能。甚至当连接功能不是单音的补品时，这条图形的途径也是适用的，这被指出。注意那许多存在非参量的光滑的ers能也被用来估计h(·)。因此，经由与惩罚功能最大化协变性功能的连接功能的我花键近似在现在的工作被调查。标准的一致性被构造。小模拟被执行证实在纸建议的途径的效率。

简介：Basedonsomerecentresultsforinterlacingeigenvalueintervalsfrom1-parameterfamiliesofsequencesofeigenvalueinequalities,anewmethodisgiventosolvingtheindexproblemforSturm-Liouvilleeigenvaluesforcoupledself-adjointboundaryconditionsintheregularcase.ThekeyisanewcharacteristicprincipleforindicesforSturm-Liouvilleeigenvalues.Thealgorithmcorrespondingonthecharacteristicprinciplearediscussed,andnumericalexamplesarepresentedtoillustratethetheoreticalresultsandshowthatthealgorithmisvalid.

简介：Assumethatm≥2,pisaprimenumber,(m,p(p-1))=1,-1(Z/mZ)~*and[(Z/mZ)~*:]=4.Inthispaper,wecalculatethevalueofGausssumG(X)=Σ_(x∈F_q~*)x(x)ζ_p~(T(x))overF_q,whereq=p~f,f=((m))/4xisamultiplicativecharacterofF_qandTisthetracemapfromF_qtoF_p.Underourassumptions,G(x)belongstothedecompositionfieldKofpinQ(ζm)andKisanimaginaryquarticabeliannumberfield.WhentheGaloisgroupGal(K/Q)iscyclic,wehavestudiedthiscycliceaseinanotherpaper:'Gausssumsofindexfour:(1)cycliccase'(acceptedbyActaMathematicaSinica,2003).Inthispaperwedealwiththenon-cycliccase.

简介：Inthisarticle,apartiallylinearsingle-indexmodelforlongitudinaldataisinvestigated.Thegeneralizedpenalizedsplineleastsquaresestimatesoftheunknownparametersaresuggested.Allparameterscanbeestimatedsimultaneouslybytheproposedmethodwhilethefeatureoflongitudinaldataisconsidered.Theexistence,strongconsistencyandasymptoticnormalityoftheestimatorsareprovedundersuitableconditions.Asimulationstudyisconductedtoinvestigatethefinitesampleperformanceoftheproposedmethod.Ourapproachcanalsobeusedtostudythepuresingle-indexmodelforlongitudinaldata.

简介：在线上的顺序三的方程被显示出全球性好的为概括Korteweg-deVries的起始的价值问题为不平的数据摆姿势。我们的证明基于Colliander，龙骨，Staffilani，Takaoka，和道介绍的多线性的估计和我方法。

简介：<正>InthispaperwedisscustherelativeindexfortheAtiyah-Patodi-Singertypeellipticboundaryvalueproblems,asanapplicationwegiveanewapproachtothepairingbetweentherelativeK-homologyandK-cohomology.

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简介：InthispaperwestudytheapproximationonsetoffullmeasureforfunctionsinSobolevspacesL_m~1(R~n)(m∈N)byBochner-RieszmeansofconjugaleFourierintegralsbelowthecriticalindex.AtheoremconcerningthepreciseapproximationorderswithrelationtothenumbermofspaceL_m~1(R~n)andtheindexofBochner-Rieszmeansisobtained.