简介：ThecommutatorsofsingularintegraloperatorswithhomogeneouskernelΩ(x)/|x|^narestudied,whereΩishomogeneousofdegreezero,andhasmeanvaluezeroontheunitsphere.ItisprovedthatΩ∈L(logL)^(k+1)(S^(n-1))isasufficientconditionsuchthatthek-thordercommutatorisboundedonL^2(R^n).

简介：Inthiswork,wewillprovetheexistenceofboundedsolutionsinW_0~(1,p)(Ω)∩L~∞(Ω)fornonlinearellipticequations-div(a(x,u,▽u))+g(x,u,▽u)+H(x,▽u)=f,wherea,gandHareCaratheodoryfunctionswhichsatisfysomeconditions,andtherighthandside/belongstoW~(-1,q)(Ω).

简介：

简介：引入了L-空间和L-空间上的KKM类映射，建立了关于该类映射的一些不动点定理，其中包括Schauder型和Fan-Browder型不动点定理．得到了L-空间中的KyFan匹配定理和叠合点定理．

简介：

简介：在Tikhonov正则化方法的基础上将其转化为一类l1极小化问题进行求解,并基于Bregman迭代正则化构建了Bregman迭代算法,实现了l1极小化问题的快速求解.数值实验结果表明,Bregman迭代算法在快速求解算子方程的同时,有着比最小二乘法和Tikhonov正则化方法更高的求解精度.

简介：设G是局部紧群，f是G上的右一致连续函数，本文讨论L^∞（G）中一个闭凸不变集的关系式/Co{Lxf:x∈G}^11·11^∞=/{￠*f:￠∈P’（G）}^11·11^∞（f∈RUC（G））。由此式易得出RUC（G）上的左不变平均与拓扑左不变平均的等价关系。

简介：一个图G的L(2,1)-标号是给图G上的顶点分配非负整数标号,使得G上相邻的两个点的标号至少相差2,距离为2的两个点的标号则不同.G的L(2,1)-标号数λ(G)是所有能使图G正常标号的最小标号.如果一个图的任何两个圈不含有公共边,则称这个图为仙人掌图.显然树是它的一个子图类.对于任何树T,有△(T)+1≤λ(T)≤△(T)+2.本文中我们证明了在一些条件下,这个界也适用于仙人掌图.

简介：考虑了两类有理插值型算子的Jackson型估计.当p>1时,建立了Dilzian-Totik型定理,当p=1时,利用通常连续模给出了Jackson型估计.

简介：ByusingtheperturbationresultsofsumsofrangesofaccretivemappingsofCalvertandGupta(1978),theabstractresultsontheexistenceofsolutionsofafamilyofnonlinearboundaryvalueproblemsinL^2(Ω)arestudied.TheequationdiscussedinthispaperandthemethodsusedhereareextensionandcomplementtothecorrespondingresultsofWeiLiandHeZhen'spreviouspapers.Especially,somenewtechniquesareusedinthispaper.

简介：

简介：我们为Davey-Stewartson系统学习发作答案(D-S系统，为短)在L<潜水艇class=“a-plus-plus”>x<啜class=“a-plus-plus”>2(<啜class=“a-plus-plus”>2)。首先，我们给D-S系统的解决方案的非线性的侧面分解。然后，我们证明最小的集体发作答案的存在。由使用最小的集体发作答案的特征，最后，我们获得限制侧面和L的精确集体的集中<啜class=“a-plus-plus”>D-S系统的2个发作解决方案。

简介：设T（t)是L^q(1＜q＜∞）空间上的Co-半群，A为其元穷小生成元。本文证明若T（t)是弱L^p稳定的，则其生成元的谱界是负的。由LotzWeis最近得到的关于L^q(Ω）空间中正Co半群的增长界等于生成元的谱界这一结果得出，L^q(Ω）空间中正Co半群弱L^p稳定与与指数稳定等价。

简介：Nonlineardynamicalsystemsaresometimesundertheinfluenceofrandomfluctuations.Itisdesirabletoexaminepossiblebifurcationsforstochasticdynamicalsystemswhenaparametervaries.Acomputationalanalysisisconductedtoinvestigatebifurcationsofasimpledynamicalsystemundernon-Gaussianα-stableLévymotions,byexaminingthechangesinstationaryprobabilitydensityfunctionsforthesolutionorbitsofthisstochasticsystem.ThestationaryprobabilitydensityfunctionsareobtainedbysolvinganonlocalFokker-Planckequationnumerically.Thisallowsnumericallyinvestigatingphenomenologicalbifurcation,orP-bifurcation,forstochasticdifferentialequationswithnon-GaussianLévynoises.

简介：Linearsystemsarisingfromimplicittimediscretizationsandfinitedifferencespacediscretizationsofsecond-orderhyperbolicequationsonL-shapedregionareconsidered.Weanalysetheuseofdomaindeocmposilionpreconditioner.sforthesolutionoflinearsystemsviathepreconditionedconjugategradientmethod.Fortheconstant-coefficientsecond-orderhyperbolicequaionswithinitialandDirichletboundaryconditions,weprovethattheconditionnumberofthepreconditionedinterfacesystemisboundedby2+x22+0.46x2wherexisthequo-tientbetweenthelimeandspacesteps.Suchconditionnumberproducesaconvergenceralethatisindependentofgridsizeandaspectratios.Theresultscouldbeextendedtoparabolicequations.

简介：LetL~2([0,1],x)bethespaceoftherealvalued,measurable,squaresummablefunctionson[0,1]withweightx,andlet■_nbethesubspaceofL~2([0,1],x)definedbyalinearcombinationofJ_0(μ_kx),whereJ_0istheBesselfunctionoforder0and{μ_k}isthestrictlyincreasingsequenceofallpositivezerosofJ_0.Forf∈L~2([0,1],x),letE(f,■_n)betheerrorofthebestL~2([0,1],x),i.e.,approximationoffbyelementsof■_n.Theshiftoperatoroffatpointx∈[0,1]withstept∈[0,1]isdefinedbyT(t)f(x)=(1/π)∫_0~πf((x~2+t~2-2xtcosθ)~(1/2))dθ.Thedifferences(1-T(t))~(r/2)f=∑_(j=0)~∞(-1)~j(_j~(r/2))T~j(t)foforderr∈(0,∞)andtheL~2([0,1],x)-modulusofcontinuityω_r(f,τ)=sup{||(I-T(t))~(r/2)f||:0≤t≤τ}oforderraredefinedinthestandardway,whereT~0(t)=Iistheidentityoperator.Inthispaper,weestablishthesharpJacksoninequalitybetweenE(f,■_n)andω_r(f,τ)forsomecasesofrandτ.Moreprecisely,wewillfindthesmallestconstant■_n(τ,r)whichdependsonlyonn,r,andτ,suchthattheinequalityE(f,■_n)≤■_n(τ,r)ω_r(f,τ)isvalid.

简介：Basedontherangespaceproperty(RSP),theequivalentconditionsbetweennonnegativesolutionstothepartialsparseandthecorrespondingweightedl_1-normminimizationproblemarestudiedinthispaper.Differentfromotherconditionsbasedonthesparkproperty,themutualcoherence,thenullspaceproperty(NSP)andtherestrictedisometryproperty(RIP),theRSPbasedconditionsareeasiertobeverified.Moreover,theproposedconditionsguaranteenotonlythestrongequivalence,butalsotheequivalencebetweenthetwoproblems.First,accordingtothefoundationofthestrictcomplementaritytheoremoflinearprogramming,asufficientandnecessarycondition,satisfyingtheRSPofthesensingmatrixandthefullcolumnrankpropertyofthecorrespondingsub-matrix,ispresentedfortheuniquenonnegativesolutiontotheweightedl_1-normminimizationproblem.Then,basedonthiscondition,theequivalenceconditionsbetweenthetwoproblemsareproposed.Finally,thispapershowsthatthematrixwiththeRSPoforderkcanguaranteethestrongequivalenceofthetwoproblems.

简介：本文在Lp（1≤P〈＋∞）空间上，研究了种群细胞增生中一类具扰动项的L—R模型，证明了这类模型相应的迁移算子生成半群的Dyson—Phillips展式的9阶余项R9（t）在L1空间上是弱紧和在Lp（1〈P〈＋∞）空间上是紧的，从而获得了该迁移算子的谱在右半平面上仅由有限个具有限代数重数的离散本征值组成及该迁移方程解的渐近稳定性等结果．

简介：

简介：