简介：Kolmogorov的5／3次方律E（k）=Cε^2/3k^-5/3矿乃是20世纪湍流研究最重要的理论研究成果。这里E代表湍流能谱，占为湍流能量耗散率，k为波数，C为一常量。在极高雷诺数流动中-5／3次方律被很多实测数据验证。但是对于有限雷诺数问题，湍流能谱具有-5／3次方律的波数范围一般很窄；湍流实验证实，瞬时湍动能耗散存在时空分布极不均匀的情况，即所谓的间歇性现象，湍流物理量呈明显的非高斯分布，

简介：Analyzingtheaverage-casecomplexityofalgorithmsisaverypracticalbutverydifficultproblemincomputerscience.Inthepastfewyears,wehavedemonstratedthatKolmogorovcomplexityisanimprotanttoolforanalyzingtheaverage-casecomplexityofalgorithms.Wehavedevelopedtheincompressibilitymethod.Inthispaper,sereralsimpleexamplesareusedtofurtherdemonstratethepowerandsimplicityofsuchmethod.Weproveboundsontheaverage-casenumberofstacks(queues)requiredforsortingsequentialorparallelQueuesortorStacksort.

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简介：本文研究了一个广义Kolmogorov系统.这个系统包含了Gause型模型(Kuang和Freeman,1988),广义捕食者-被食者系统(Huang,1988,Huang和Merrill,1989)和其他许多系统(Liu和Zhao,2000,Zheng等,2001,Yang和Liang,2001)为其特例.有关该系统存在极限环的条件以及极限环唯一的条件在本文中已经证明.文献中的许多结果都可容易地作为本文定理的特例而导出.

简介：本文研究kolmogorov捕食系统{（dx/dt）=x（ψ（x）-φ（y）（dx/dt）=y（bx^m-d）得到了极限环存在唯一的条件，从而推广了前人相关的结果．其中：ψ（x）=a0＋a1x＋a2x^2＋…＋a（a-1）x^（n-1）-anx^n;n≥m≥1（n,m∈N）,φ（0）=0,φ（y）〉ε〉0（y〉0）.

简介：Inthispaperwestudytheexistenceoflimitcycleforcubicsystem（E）3,ofKolmogorovtypewithaconicalgebraictrajectoryF2（x,y）=ax2+2bxy+cy2+dx+ey+f=0Ithasbeenprovedinmyformerpapersthat（E）3doesn’thaveanylimitcycleonthewholeplaneIfb2-ac≠0,Nowweareinvestigatingthecasewhereb2-ac=0.Weprovethesufficientandnecessaryformula（2）or（13）witbwhich（E）3musthaveaparabolictrajectoryF2（x,y）=0.Thentherewillnotbeanylimitcycleonthefullplane.Onthebasisofthis,weconclude:ThecubicsystemofKolmogorovtypewithanon-degeneratedquadraticalgebraictrajectoryonthewholeplanehasnolimitcycle.

简介：WemodeltheeffectsofweakfluctuationsontheprobabilitydensitiesandnormalizedpowersofvortexmodelsfortheBessel–Gaussphotonbeamwithfractionaltopologicalchargeintheparaxialnon-Kolmogorovturbulencechannel.Wefindthatprobabilitydensityofsignalvortexmodelsisafunctionofdeviationfromthecenterofthephotonbeam,andthefartherawayfromthebeamcenteritis,thesmallertheprobabilitydensityis.Forfractionaltopologicalcharge,theaverageprobabilitydensitiesofsignal/crosstalkvortexmodesoscillatealongthebeamradiusexceptthehalf-integerorder.Asthebeamwaistofthephotonsourcegrows,theaverageprobabilitydensityofsignalandcrosstalkvortexmodesgrowtogether.Moreover,thepeakoftheaverageprobabilitydensityofcrosstalkvortexmodesshiftsoutwardfromthebeamcenterasthebeamwaistgetslarger.Theresultsalsoshowthatthesmallerindexofnon-Kolmogorovturbulenceandthesmallergeneralizedrefractive-indexstructureparametermayleadtothehigheraverageprobabilitydensitiesofsignalvortexmodesandloweraverageprobabilitydensitiesofcrosstalkvortexmodes.Lower-coherenceradiusorbeamwaistcangiverisetolessreductionofthenormalizedpowersofthesignalvortexmodes,whichisoppositetothenormalizedpowersofcrosstalkvortexmodes.

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