简介:结合环R称为强诣零Armendariz的如果对于R[x]中任意两个多项式f(x),g(x)当f(x)g(x)∈Nil*(R)[x]时,有ab∈Nil*(R),这里a,b分别是f(x),g(x)的任何系数,而N*(R)为R的素根。证明了强诣零Armendariz环R的素根与上诣零根一致;强诣零Armendariz环是诣零Armendariz环;证明了R是强诣零Armendariz环当且仅当R的每个子环是强诣零Armendariz环,当且仅当R的多项式环R[x]是强诣零Armendariz环,当且仅当R的上三角矩阵环Tn(R)是强诣零Armendariz环;R是强诣零Armendariz环当且仅当R/Nil*(R)是Armendariz环。并推广了弱Armendariz环的两个结果。
简介:Generalizingthenotionofstronglynilcleanrings,weintroducestronglyquasinilcleanrings.Somefundamentalpropertiesandequivalentcharacterizationsofthisclassofringsareprovided.Bymeansofg-Drazininverses,Cline'sformulaandJacobson'slemmaforstronglyquasi-nilcleanelementsareinvestigated.
简介:LadiesandGentlemen:Todiscussthedevelopmentorientationoftheoilindustryundernewcircumstances,JCCPhasdecidedthetopicofthisyear'sIntemationalSymposiumas"TheDevelopment&Har-monyoftheOilindustryontheGlobalView".Thistopicreflectsthecommonwishbytheglobaloilcommunitythatenvironmentimprovementandsocialresponsibilityshouldgohandinhandwiththedevelopmentofoilindustry.
简介:在自反、严格凸、光滑的Banach空间中,设计了一种修正的混合投影迭代算法用来构造平衡问题与拟φ-渐近非扩张映像的不动点问题的公共元,并利用广义投影算子和K-K性质证明了此迭代算法生成的序列强收敛于这两个问题的公共元.所得结果是近期相关结果的改进和推广.
简介:AccordingtoLorenz,chaoticdynamicsystemshavesensitivedependenceoninitialconditions(SDIC),i.e.,thebutterfly-effect:atinydifferenceoninitialconditionsmightleadtohugedifferenceofcomputer-generatedsimulationsafteralongtime.Thus,computer-generatedchaoticresultsgivenbytraditionalalgorithmsindoubleprecisionareakindofmixtureof'true'(convergent)solutionandnumericalnoisesatthesamelevel.Today,thisdefectcanbeovercomebymeansofthe'cleannumericalsimulation'(CNS)withnegligiblenumericalnoisesinalongenoughintervaloftime.TheCNSisbasedontheTaylorseriesmethodathighenoughorderanddatainthemultipleprecisionwithlargeenoughnumberofdigits,plusaconvergencecheckusinganadditionalsimulationwithevensmallernumericalnoises.Intheory,convergent(reliable)chaoticsolutionscanbeobtainedinanarbitrarylong(butfinite)intervaloftimebymeansoftheCNS.TheCNScanreducenumericalnoisestosuchalevelevenmuchsmallerthanmicro-leveluncertaintyofphysicalquantitiesthatpropagationofthesephysicalmicro-leveluncertaintiescanbepreciselyinvestigated.Inthispaper,webrieflyintroducethebasicideasoftheCNS,anditsapplicationsinlong-termreliablesimulationsofLorenzequation,three-bodyproblemandRayleigh-Bénardturbulentflows.UsingtheCNS,itisfoundthatachaoticthree-bodysystemwithsymmetrymightdisruptwithoutanyexternaldisturbance,say,itssymmetry-breakingandsystem-disruptionare'self-excited',i.e.,out-of-nothing.Inaddition,bymeansoftheCNS,wecanprovidearigoroustheoreticalevidencethatthemicro-levelthermalfluctuationistheoriginofmacroscopicrandomnessofturbulentflows.Naturally,muchmoreprecisethantraditionalalgorithmsindoubleprecision,theCNScanprovideusanewwaytomoreaccuratelyinvestigatechaoticdynamicsystems.