简介:让f(z)是为完整的模块化的组的重量k的holomorphicHeckeeigencuspform。让f(n)是f(z)的第n个规范的Fourier系数。建议那L(sym2f,s)对称的方形的L功能与f(z)被联系,并且$\lambda_{sym^2f}(n)$(n)表示第n系数L(sym2f,s)。在这份报纸,它被证明那$$\sum\limits_{n\leqslantx}{\lambda_{sym^2f}^4(n)}=xP2(\logx)+O(x^{\frac{{79}}{{81}}+\varepsilon}),$$,在P2(t)是在度2的t的一个多项式的地方。同样,它被获得那$$\sum\limits_{n\leqslantx}{\lambda_f^4(n^2)}=x\tildeP2(\logx)+O(x^{\frac{{79}}{{81}}+\varepsilon}),$$,在哪儿$\tildeP_2(t)$是在度2的t的一个多项式。
简介:LetAbead×drealexpansivematrix.AnA-dilationParsevalframewaveletisafunctionψ∈L2(Rd),suchthattheset{|detA|n/2ψ(Ant-l):n∈Z,l∈Zd}formsaParsevalframeforL2(R~d).AmeasurablefunctionfiscalledanA-dilationParsevalframewaveletmultiplieriftheinverseFouriertransformoff■isanA-dilationParsevalframewaveletwheneverψisanA-dilationParsevalframewavelet,where■denotestheFouriertransformofψ.Inthispaper,theauthorscompletelycharacterizeallA-dilationParsevalframewaveletmultipliersforanyintegralexpansivematrixAwith|det(A)|=2.Asanapplication,thepath-connectivityofthesetofallA-dilationParsevalframewaveletswithaframeMRAinL2(Rd)isdiscussed.
简介:Inthisarticle,weshowthatifXisanexcellentsurfacewithrationalsingularities,theconstantsheafQeisadualizingcomplex.IncoefficientZe,wealsoprovethattheobstructionforZetobecomeadualizingcomplex,liesonthedivisorclassgroupsatsingularpoints.Asapplications,westudytheperversesheavesandtheweightsof-adiccohomologygroupsonsuchsurfaces.
简介:Inthispaperwewillshowthatifanapproximationprocess{Ln}n∈Nisshapepreservingrelativetotheconeofallk-timesdifferentiablefunctionswithnon-negativek-thderivativeon[0,1],andtheoperatorsLnareassumedtobeoffiniterankn,thentheorderofconvergenceofDkLnftoDkfcannotbebetterthann2evenforthefunctionsxk,xk+1,xk+2onanysubsetof[0,1]withpositivemeasure.Takingintoaccountthisfact,wewillbeabletofindsomeasymptoticestimatesoflinearrelativen-widthofsetsofdifferentiablefunctionsinthespaceLp[0,1],p∈N.
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:Nonlineardynamicalsystemsaresometimesundertheinfluenceofrandomfluctuations.Itisdesirabletoexaminepossiblebifurcationsforstochasticdynamicalsystemswhenaparametervaries.Acomputationalanalysisisconductedtoinvestigatebifurcationsofasimpledynamicalsystemundernon-Gaussianα-stableLévymotions,byexaminingthechangesinstationaryprobabilitydensityfunctionsforthesolutionorbitsofthisstochasticsystem.ThestationaryprobabilitydensityfunctionsareobtainedbysolvinganonlocalFokker-Planckequationnumerically.Thisallowsnumericallyinvestigatingphenomenologicalbifurcation,orP-bifurcation,forstochasticdifferentialequationswithnon-GaussianLévynoises.
简介:Aseriesofnovel1H-benzimidazol-1-ylacetatesand1H-benzimidazol-1-ylpropionatescontaining1H-1,2,4-triazolemoietyweresynthesizedundermicrowaveirradiationbymulti-stepreactions,inyieldsof87-94%.TheirinvitroantifungalactivitiesagainstBotrytiscinereaandSclerotiniasclerotiorumwereevaluatedbymycelialgrowthratemethod.AllthetargetcompoundsexhibithighactivitiesagainstB.cinereawiththeEC50valuesof7.96-21.74μg/mL,higherthanthatofcarbendazim.
简介:Poly(4-vinylpyridine)supportednanoparticleofcopper(Ⅰ)iodideisreportedasagreenandrecyclablecatalystfortheregioselectivesynthesisof1,4-disubstituted-1H-1,2,3-triazolesfrombenzylhalides,sodiumazideandterminalalkynesinwater.Thiscatalystcanberecoveredbysimplefiltrationandrecycledupto8consecutiverunswithoutanylossofitsefficiency.