简介：Inthispaper,westudythequotientofhypergeometricfunctionsμ_a(r)inthetheoryofRamanujan’sgeneralizedmodularequationfora∈(0,1/2].Severalnewinequalitiesaregivenforthisandrelatedfunctions.Ourmainresultscomplementandgeneralizesomeknownresultsintheliterature.

简介：Howtoefficientlymeasurethedistancebetweentwobasicprobabilityassignments(BPAs)isanopenissue.Inthispaper,anewmethodtomeasurethedistancebetweentwoBPAsisproposed,basedontwoexistingmeasuresofevidencedistance.Thenewproposedmethodiscomprehensiveandgeneralized.Numericalexamplesareusedtoillustratetheeffectivenessoftheproposedmethod.

简介：Anr-acyclicedgechromaticnumberofagraphG,denotedbyα’_r(G),istheminimumnumberofcolorsusedtoproduceanedgecoloringofthegraphsuchthatadjacentedgesreceivedifferentcolorsandeverycycleChasatleastmin{|C|,r}colors.Weprovethatα’_r(G)≤(4r+1)△(G),whenthegirthofthegraphGequalstomax{50,△A(G)}and4≤r≤7.Ifwerelaxtherestrictionofthegirthtomax{220,A(G)},theupperboundofa’_r(G)isnotlargerthan(2r+5)△(G)with4≤r≤10.

简介：Supposeb=(b_1,···,b_m)∈(BMO)~m,I_(α,m)~(Πb)istheiteratedcommutatorofbandthem-linearmultilinearfractionalintegraloperatorI_(α,m).ThepurposeofthispaperistodiscusstheboundednesspropertiesofI_(α,m)andI_(α,m)~(Πb)ongeneralizedHerzspaceswithgeneralMuckenhouptweights.

简介：在这篇论文，我们考虑在双线性的模型减小产生的一个概括Lyapunov方程的低等级近似答案。由使用变化原则，低等级近似答案问题被转变成一个非强迫的优化问题，然后我们使用非线性与准确的线搜索结合坡度方法解决相等的非强迫的优化问题。最后，一些数字例子被举说明建议方法的有效性。[从作者抽象]

简介：DenotebyQmthegeneralizedquaterniongroupoforder4m.LetR（Qm）beitscomplexrepresentationring,andΔ（Qm）itsaugmentationideal.Inthispaper,theauthorgivesanexplicitZ-basisfortheΔn（Qm）anddeterminestheisomorphismclassofthen-thaugmentationquotientΔn（Qm）/(Δn+1（Qm）)foreachpositiveintegern.

简介：UsingtheaveragingtheoryoffirstandsecondorderwestudythemaximumnumberoflimitcyclesofgeneralizedLinarddifferentialsystems{x=y+εhl1（x）+ε2hl2（x）,y=-x-ε(fn1（x）y2p+1+gm1（x）)+∈2(fn2（x）y2p+1+gm2（x）),whichbifurcatefromtheperiodicorbitsofthelinearcenterx=y,y=-x,whereεisasmallparameter.Thepolynomialshl1andhl2havedegreel;fn1andfn2havedegreen;andgm1,gm2havedegreem.p∈Nand[·]denotestheintegerpartfunction.

简介：Ageneralversionoftheinvertedexponentialdistributionisintroduced,studiedandanalyzed.ThisgeneralizationdependsonthemethodofMarshall-Olkintoextendafamilyofdistributions.Somestatisticalandreliabilitypropertiesofthisfamilyarestudied.Inaddition,numericalestimationofthemaximumlikelihoodestimate(MLE)parametersarediscussedindetails.Asanapplication,somerealdatasetsareanalyzedanditisobservedthatthepresentedfamilyprovidesabetterfitthansomeotherknowndistributions.

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简介：这份报纸学习nonconvex的一个班的系统稳定性问题微分包括。起初，基本稳定性结果被优点获得局部地，Lipschitz连续Lyapunov工作。而且，一个概括不变性原则和相关吸引力条件被建议并且证明了由于凸状的缺席克服技术困难。在技术分析，新奇珍视集合的衍生物被建议处理nonsmooth系统和nonsmoothLyapunov功能。另外，获得的结果与在有常规Lyapunov功能的凸的微分包括的情况中的存在的一致。最后，解说性的例子被给显示出方法的有效性。

简介：Thedetailsofthespecialthree-dimensionalmicro-nanoscalerippleswithaperiodofhundredsofmicronsonthesurfacesofaZr-basedandaLa-basedmetallicglassirradiatedseparatelybysinglelaserpulseareinvestigated.Weusethesmall-amplitudecapillarywavetheorytounveiltherippleformationmechanismthroughconsideringeachofthemoltenmetallicglassesasanincompressibleviscousfluid.Ageneralizedmodelispresentedtodescribethespecialmorphology,whichfitstheexperimentalresultwell.Itisalsorevealedthattheviscositybringsaboutthebiggesteffectonthemonotonedecreasingnatureoftheamplitudeandthewavelengthofthesurfaceripples.Thegreatertheviscosityis,theshortertheamplitudeandthewavelengthare.

简介：ThepreviouspaperreportedanewderivativeintheEuleriandescriptioninflatspace—thegeneralizedcovariantderivativeofgeneralizedEuleriancomponentwithrespecttotime.ThispaperextendsthethoughtfromtheEuleriandescriptiontotheLagrangiandescription:onthebasisofthepostulateofcovariantforminvariabilityintimefield,wedefineanewderivativeintheLagrangiandescriptioninflatspace—thegeneralizedcovariantderivativeofgeneralizedLagrangiancomponentwithrespecttotime.Besides,thecovariantdifferentialtransformationgroupissetup.ThecovariantforminvariabilityofLagrangianspace-timeisascertained.

简介：ThispaperreportsanewderivativeintheEuleriandescriptioninflatspace-thegeneralizedcovariantderivativewithrespecttotime.Thefollowingcontentsareincluded:(a)therestrictedcovariantderivativewithrespecttotimeforEuleriancomponentisdefined;(b)thepostulateofthecovariantforminvariabilityintimefieldissetup;(c)thegeneralizedcovariantderivativewithrespecttotimeforgeneralizedEuleriancomponentisdefined;(d)thealgebraicstructureofthegeneralizedcovariantderivativewithrespecttotimeismadeclear;(e)thecovariantdifferentialtransformationgroupintimefiledisderived.TheseprogressesrevealthecovariantforminvariabilityofEulerianspaceandtime.

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简介：Thepurposeofthispaperistointroduceasplitgeneralizedmixedequilibriumproblem(SGMEP)andconsidersomeiterativesequencestofindasolutionofthegeneralizedmixedequilibriumproblemsuchthatitsimageunderagivenboundedlinearoperatorisasolutionofanothergeneralizedmixedequilibriumproblem.Weobtainsomeweakandstrongconvergencetheorems.

简介：Inthispaper,wearedevotedtotheasymptoticbehaviorforanonlinearparabolictypeequationofhigherorderwithadditivewhitenoise.WefocusontheGinzburg-Landaupopulationequationperturbedwithadditivenoise.Firstly,weshowthatthestochasticGinzburg-Landauequationwithadditivenoisecanberecastasarandomdynamicalsystem.Andthen,itisprovedthatundersomegrowthconditionsonthenonlinearterm,thisstochasticequationhasacompactrandomattractor,whichhasafiniteHausdorffdimension.

简介：Background:Measurementsoftreeheightsanddiametersareessentialinforestassessmentandmodelling.Treeheightsareusedforestimatingtimbervolume,siteindexandotherimportantvariablesrelatedtoforestgrowthandyield,successionandcarbonbudgetmodels.However,thediameteratbreastheight(dbh)canbemoreaccuratelyobtainedandatlowercost,thantotaltreeheight.Hence,generalizedheight-diameter(h-d)modelsthatpredicttreeheightfromdbh,ageandothercovariatesareneeded.Foramoreflexiblebutbiologicallyplausibleestimationofcovariateeffectsweuseshapeconstrainedgeneralizedadditivemodelsasanextensionofexistingh-dmodelapproaches.Weusecausalsiteparameterssuchasindexofariditytoenhancethegeneralityandcausalityofthemodelsandtoenablepredictionsunderprojectedchangeableclimaticconditions.Methods:Wedevelopunconstrainedgeneralizedadditivemodels(GAM)andshapeconstrainedgeneralizedadditivemodels(SCAM)forinvestigatingthepossibleeffectsoftree-specificparameterssuchastreeage,relativediameteratbreastheight,andsite-specificparameterssuchasindexofaridityandsumofdailymeantemperatureduringvegetationperiod,ontheh-drelationshipofforestsinLowerSaxony,Germany.Results:Someofthederivedeffects,e.g.effectsofage,indexofaridityandsumofdailymeantemperaturehavesignificantlynon-linearpattern.TheneedforusingSCAMresultsfromthefactthatsomeofthemodeleffectsshowpartiallyimplausiblepatternsespeciallyattheboundariesofdataranges.Thederivedmodelpredictsmonotonicallyincreasinglevelsoftreeheightwithincreasingageandtemperaturesumanddecreasingaridityandsocialrankofatreewithinastand.ThedefinitionofconstraintsleadsonlytomarginalorminordeclineinthemodelstatisticslikeAlC.Anobservedstructuredspatialtrendintreeheightismodelledvia2-dimensionalsurfacefitting.Conclusions:WedemonstratethattheSCAMapproachallowsoptimalregressionmodellingflexibil

简介：Westudytheconsistencyconditionsofthegeneralizedf(R)gravitybyextendingf(R)gravitywithnon-minimalcouplingtothegeneralizedf(R)witharbitrarygeometry-mattercoupling.Specifically,wediscussthetwoparticularmodelsofgeneralizedf(R)bymeansofconsistencyconditions.Itisfoundthatthesecondmodelisnotphysicallyviablesoastoberuledout.Moreover,wefurtherconstrainthefirstmodelusingtheDolgovKawasakistabilitycriterion,andgivethevaluerangesoftheparametersinthefirstmodel.Itisworthstressingthatourresultsincludetheonesinf(R)gravitywithnon-minimalcouplingasthespecialcaseofQ(L_m)=L_m.

简介：Inthispaper,westudytheCauchyproblemforthe3DgeneralizedNavier-Stokes-Boussinesqequationswithfractionaldiffusion:{ut+（u·▽）u+v∧2αu=-▽p+θe（3）,e3=（0,0,1）T,θt+（u·▽）θ=0,Dicu=0.Withthehelpofthesmoothingeffectofthefractionaldiffusionoperatorandalogarithmicestimate,weprovetheglobalwell-posednessforthissystemwithα≥5/4.Moreover,theuniquenessandcontinuityofthesolutionwithweakerinitialdataisbasedonFourierlocalizationtechnique.Ourresultsextendonesonthe3DNavier-Stokesequationswithfractionaldiffusion.

简介：Invariantsubspacemethodisexploitedtoobtainexactsolutionsofthetwocomponentb-familysystem.Itisshownthatthetwo-componentb-familysystemadmitsthegeneralizedfunctionalseparablesolutions.Furthermore,blowupandbehaviorofthoseexactsolutionsarealsoinvestigated.