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关于Littlewood的一个问题 总被引:1,自引:0,他引:1
本文证明了: (1)如果{a_n}_n~N=1是非负不减序列,p>0,q>0,0≤r≤1,且p(q+r)≥q+p,则sum from n=1 to N(a_n~pA_n~q)(sum from m=n to N(a_n~(1+p/q)~r≤1·sum from n=1 to N(a_n~pA_n~q)~(1+p/q),其中A_n=sum from m=n to n (a_m).上述不等式在0≤r≤1时完全解决了H.Alzer~([4])在1996年提出的一个问题,且1是最佳常数; (2)如果{a_n}_n~N=1是非负序列,p,p≥1,r>0,r(p-1)≤2(q-1),令α=((p-1)(q+r)+p~2+1)/(p+1) β=(2p+2r+p-1)/(q+1),σ=(q+r-1)/(p+q+r)则sum from n=1 to N (a_n~p)sum from i=1 to n (a_i~qA_i~r)≤2~σsum from n=1 to N(a_n~αA_n~β)(0.2)(0.2)式改进了G.Be(?)et~([2,3])在1987年对Littlewood一个问题的结果,常数因子的3/2降为2~(3/2)=1.2598… 相似文献
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IntroductionManyproblemsencounteredinengineeringpracticeandotherdisciplinescanbesummarizedintoPDEssuchasosmosis,diffusion,heatconduction,wavepropagation,etc.ItisthenofvitalsignificancehowtosolvePDEsbothrapidlyandefficiently,ThenumericalsolutionsofPDEsarecustomarilyobtainedbythefiniteelementmethod(FEM),thefinitedifferencemethod(FDM)!and.the,,[l'2).Thesemethods,however,showtheirdemeritsforlargercomputationaldomains.AsforFEM,thevastnumberofunknownscausedbyspacecoordinatediscretizationlead… 相似文献
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