简介：在这份报纸，我们学习交往的散开的线性系统的一个班的一些各态历经的定理，它是一个寓言的安德森模型。首先，在假设下面转变内核=(一(我，j))我，jS是二倍地随机的，我们获得长期的集中到基于自我两重性从围住的一泛音函数h开始的不变的概率措施h性质，然后我们显示出集中到措施h为起始的分布的一个宽广的类保持的不变的概率。秒(一(我，j))我，jS短暂、对称，并且在阀值下面的散开参数c遗体，我们能决定不变的概率与有限的秒测量的extremal的集合时刻。最后，在情况中转变核(一(我，j))我，jS是二倍地随机的并且满足大小写我(看见大小写我在里面[Shiga，T.：在人口遗传的一个交往的系统。J。数学。京都大学，20，213242(1980)])，我们证明这个寓言的安德森模型局部地灭绝独立于散开参数c。

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简介：Asimplifiedmethodforthesimulationoftheergodicspatiallycorrelatedseismicgroundmotionisproposedbasedonthecommonlyusedoriginalspectralrepresentationmethod.Torepresentthecorrelationinthegroundmotion,thephaseanglesaregivenbyexplicittermswithaclearphysicalmeaning.Bytheseexplicitterms,thecomputationalefficiencycanbeimprovedbyconvertingthedecompositionofthecomplexcross-spectralmatrixintothedecompositionoftherealincoherencecoefficientmatrix.Double-indexingfrequenciesareintroducedtosimulatetheergodicseismicgroundmotion,andtheergodicfeatureoftheimprovedmethodisdemonstratedtheoretically.Subsequently,anexplicitsolutionoftheelementsofthelowertriangularmatrixundertheCholeskydecompositionisgiven.Withthisexplicitsolution,theimprovedmethodissimplified,andthecomputationalefficiencycanbeimprovedgreatlybyavoidingtherepetitiveCholeskydecompositionofthecross-spectralmatrixineachfrequencystep.Finally,anumericalexampleshowsthegoodcharacteristicoftheimprovedmethod.

简介：Inthispaper,weconsiderthespectrumsharingCognitiveRadio(CR)system,whereinSingle-InputMulti-Output(SIMO)cognitivefadingchannelisassumed.Subjecttotheaveragein-terferenceconstraintofprimaryuser,theergodiccapacityofcognitiveuserinvolvingjointbeamformingandpowercontrolisanalyzed.Wederivetheoptimaljointbeamformingandpowercontrolstrategyanddeducethegeneralintegralexpressionforergodiccapacity.Furthermore,underdifferentchannelfadingsincludingRaleighfading,Nakagami-mfadingandLognormalshadowingfading,thespecificexpressionsofergodiccapacityforSIMOcognitivechannelareexhibited.Mostoftheexpressionsarepresentedinclosed-formorwithsomespecialintegralfunctions.Largeamountofsimulationsareconductedtocorroborateourtheoreticalresults.