简介:设μ(I,{nk}k≥1,{ck}k≥1)为闭区间I,正整数序列{nk}k≥1及正实数序列{ck}l≥1确定的Moran集,c(I,{nk},{ck})c(I,{nk},{ck})分别为μ{nk}k≥1,{ck}k≥1的齐次Cantor集与偏齐次Cantor集,给出了齐次Cantor集与偏齐次Cantor集的关系及证明。
简介:Inthepaper,weconsiderMoran-typesetsE_agivenbysequences{a_k}_(k=1)~∞and{n_k}_(k=1)~∞.weprovethatE_amaybedecomposeintothedisjointunionoflevelsets.Moreover,wedefinethreetypeofequivalencebetweentwodimensionfunctionsassociatedtotwoMorantypesets,respectively,andweclassifyMoran-typesetsbytheseequivalentrelations.
简介:Byusingageneralizedfitness-dependentMoranprocess,anevolutionarymodelforsymmetric2×2gamesinawell-mixedpopulationwithafinitesizeisinvestigated.Inthemodel,theindividuals’payoffaccumulatingfromgamesismappedintofitnessusinganexponentfunction.Bothselectionstrengthβandmutationrateεareconsidered.Theprocessisanergodicbirth-deathprocess.Basedonthelimitdistributionoftheprocess,wegivetheanalysisresultsforwhichstrategywillbefavouredwhenεissmallenough.Theresultsdependonnotonlythepayoffmatrixofthegame,butalsoonthepopulationsize.Especially,weprovethatnaturalselectionfavoursthestrategywhichisrisk-dominantwhenthepopulationsizeislargeenough.Forarbitraryβandεvalues,the’Hawk-Dove’gameandthe’Coordinate’gameareusedtoillustrateourmodel.Wegivetheevolutionarystablestrategy(ESS)ofthegamesandcomparetheresultswiththoseofthereplicatordynamicsintheinfinitepopulation.Theresultsaredeterminedbysimulationexperiments.
简介:证明了一类整系数齐次线性递归数列,当项数n是素数时,第n项与第1项的n次方模n同余.Fermat小定理,以及与Fibonacci数列、Perrin数列有关的一些定理,都可以看作是这一定理的推论.
简介:研究非齐次边界条件下,含有p—Laplacian算子的微分方程解的存在性,应用上下解方法,得到边值问题可解性的充分条件.