简介：WeproposethevariationaldescriptionofgeneratingfunctionapproachoffirstkindforHamil-tonianODEs,andextendtheapproachtothesemi-linearwaveequations.Inthisway,wecanconstructanyfiniteorderaccuracyscheme,andshowthattheresultingnumericalschemeismultisymplectic.Atlast,wepresentsomenumericalexperimentsbyusingderivednewscheme.

简介：Weproveconvergenceforameshfreefirst-ordersystemleastsquares(FOSLS)partitionofunityfiniteelementmethod(PUFEM).Essentially,byvirtueofthepartitionofunity,localapproximationgivesrisetoglobalapproximationinH(div)∩H(curl).TheFOSLSformulationyieldslocalaposteriorierrorestimatestoguidethejudiciousallotmentofnewdegreesoffreedomtoenrichtheinitialpointsetinameshfreedis-cretization.Preliminarynumericalresultsareprovidedandremainingchallengesarediscussed.

简介：ThispapergivesacharacterizationofaHuntprocesspathbythefirstexitleftlimitdistribution.Itisalsoshowedthatifthefirstexitleftlimitdistributionleavinganyballfromthecenterisauniformdistributiononthesphere,thentheL'evyProcessesareascaledBrownianmotion.

简介：ThispaperdevelopsaclaseofquadratureformulawithfirstderivativesItisdemonstratedthatitsdegreeofaccuracyisnotlessthan2k+1forasetofdistinctnodes{x0,x1,...,xn}overinterval[a,b],andjustonly2k+1forequallyspacednodes.FarovercomingtheshortcomingofinvolvingagreatnumberofmanualcomputationsfortheintegrationrulesoftheHermitianinterpolationformula,somesimpleformulasforcomputingautomaticallyβi,γiandE[f]bycomputeraregiven,especiallyforequallyspacednodes.

简介：在这份报纸，为有海森堡组上的重量的第一顺序插值不平等的足够、必要的条件被给。必要性被海森堡组的极的坐标变化讨论。由插值为功能和Hardy-Sobolev类型不平等经由一个新表示公式建立强壮的类型不平等的一个班，我们导出充足。最后，为强壮的类型不平等的锋利的常数是坚定的。

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简介：Abstract.Thepapergivestwoestimatesofthedistancebetweenadjacentzerosofsolutions

简介：§1.IntroductionItisknownthatthefollowingCauchyproblemforaparabolicpartialdifferentialequation(wherethevaluesattherightboundary,u.(1,t)=v(t)areunknownandsoughtfor)isill-posed:thesolution(v)doesnotdependcontinuouslyonthedata(g).Inordertotreattheill-posednessanddevelopthenumericalmethod,onereformulatestheproblemasaVolterraintegralequationofthefirstkindwishaconvolutiontypekernel(seeSneddon[1],CarslawandJaeger[2])

简介：1.IntroductionConsiderthefirstorderdifferentialequationwithdeviatingargUmelltTheoscillationofEq.(1)wasstudiedextensivelyinthelastthreedecades.See,forexamDleif--101andthereferencescitedtherein.In1972Ladas.LakshlnhanthamanddeceivedApril1,1997.Re~AugUBt...

简介：ByadoptinganiceauxiliarytransformofMarkovoperators,wederivenewboundsforthefirsteigenvalueofthegeneratorcorrespondingtosymmetricMarkovprocesses.Ourresultsnotonlyextendtherelatedtopicintheliterature,butalsoareefficientlyusedtostudythefirsteigenvalueofbirth-deathprocesseswithkillingandthatofellipticoperatorswithkillingonhalfline.Inparticular,weobtaintwoapproximationproceduresforthefirsteigenvalueofbirth-deathprocesseswithkilling,andpresentqualitativelysharpupperandlowerboundsforthefirsteigenvalueofellipticoperatorswithkillingonhalfline.

简介：TheauthorgivesanoptimumestimateofthefirsteigenvalueofacompactRiemannianmanifold.ItisshownthatletMbeacompactRiemannianmanifold,thenthefirsteigenvalueλ1oftheLaplaceoperatorofMsatisfiesα1+max{0,-（n-1）K}≥π2/d2wheredisthediameterofMand（n-1）KisthenegativelowerboundoftheRiccicurvatureofM.

简介：在这篇文章，我们学习在联合起来的范围在一个领域上弄弯问题的更高的顺序的开始的二个特征值。我们以第一个特征值在第二个特征值上获得估计。特别地，弄弯黄，李和Qi的问题的更高的顺序的开始的二个特征值上的估计[5]在我们的结果被包括。

简介：Inthispaper,thefirstboundaryvalueproblemforquasilinearequationoftheform△A(u,x)+m∑i=1(e)bi(u,x)/(e)xi+c(u,x)=0,Au(u,x)≥0isstudied.Byusingthecompensatedcompactnesstheory,someresultsontheexistenceofweaksolutionareestablished.Inaddition,undercertainconditiontheuniquenessofsolutionisproved.

简介：本文通过对工科院校科技英语专业高等数学采用美国耶鲁大学SergeLang编的“AFirstCourseinCalculus”原版教材的教学实践,对该教材的第四版和第五版的基本结构有了比较全面深入的了解,特别是分析研究了该书的突出待点,并对几个具体问题的处理进行了阐述。

简介：Thispaperconcernswithexistenceofgeneralizedsolutionsoffirstboundaryvalueproblemforakindofstronglydegeneratequasilinearparabolicequations.TheauthorassumesthatthecoefficientsintheequationsatisfystronglydegeneratemonotoneconditionandotherweakenedconditionscomparingwiththoseofLadyzenskaja’s.Anexistencetheoremisgivenandproved.

简介：Inthispapertheexistenceresultsofpositiveω-periodicsolutionsareobtainedforsecondorderordinarydifferentialequation-u″(t)=f(t,u(t))(t∈R),andalsoforfirstorderordinarydifferentialequationu′(t)=f(t,u(t))(t∈R),wheref:R×R+→Risacontinuousfunctionwhichisω-periodicint.Thediscussionisbasedonthefixedpointindextheoryincones.

简介：Thispaperstudiesfirstordersemilinearhyperbolicsystemsinn(n≥2)spacedimensions.Underthehypothesisthatthesystemsatisfiessocalled‘nullcondition',thelocalwell-posednessforitsCauchyproblemwithinitialdatainH^(n-1)/2isproved.

简介：Theinitialvalueproblemsandthefirstboundaryproblemsforthequasilinearwaveequationutt-[a0+na1（ux）n-1]uxx-a2uxxtt=0areconsidered,wherea0,a2>0areconstants,a1isanarbitraryrealnumber,nisanaturalnumber.Theexistenceanduniquenessoftheclassicalsolutionsfortheinitialvalueproblemsandthefirstboundaryproblemsoftheequation（1）areprovedbytheGalerkinmethod.

简介：WestudythestructureofBernstein’sfirstsummableoperatorsandshowthattheycon-vergeuniformlytocontinuonsfunctionsonthespecialrealorthogonalgroupSO(n)inthispaper.Inaddition,wehavealsodiscussedtheapproximationdegreetoaclassoffunctionLipα(0<α≤1)onSO(n).

简介：Inthispaper,wenotonlyconstructtheconfidenceregionforparametersinamixedinteger-valuedautoregressiveprocessusingtheempiricallikelihoodmethod,butalsoestablishtheempiricallog-likelihoodratiostatisticandobtainitslimitingdistribution.Andthen,viasimulationstudieswegivecoverageprobabilitiesfortheparametersofinterest.Theresultsshowthattheempiricallikelihoodmethodperformsverywell.