简介：InthispaperL^p-L^qestimatesforthesolutionu(x,t)tothefollowingperturbedhigh-erorderhyperbolicequationareconsidered,(ρπ--a△)(ρπ--b△)u+V(x)u=O,x∈R^n,n≥6,ρ1eu(x,O)=O,ρ^3eu(x,O)=f(x),(j=O,1,2).WeassumethattheotentialV(x)andtheinitialdataf(x)arecompactlysupported,andV(x)issufficientlysmall,thenthesolutionu(x,t)oftheaboveproblemsatisfiesthesameL^p-L^qestimatesasthatoftheunperturbedproblem.

简介：<正>InthispaperitisprovedthatforallcompletelydistributivelatticesL.thecategoryofL-fuzzifyingtopologicalspacescanbewmbeddedinthecategoryofL-topologicalspaces(stratifiedChang-Goguenspaces)asasimultaneouslybireflectiveandbicoreflectivefullsubcategory.

简介：WeconstructaclassofintegrablegeneralizationofTodamechanicswithlong-rangeinteractions.ThesesystemsareassociatedwiththeloopalgebrasL(Cr)andL(Dr)inthesensethattheirLaxmatricescanberealizedintermsofthec=0representationsoftheaffineLiealgebrasCr(1)andDr(1)andtheinteractionspatterninvolvedbearsthetypicalcharactersofthecorrespondingrootsystems.WepresenttheequationsofmotionandtheHamiltonianstructure.Thesegeneralizedsystemscanbeidentifiedunambiguouslybyspecifyingtheunderlyingloopalgebratogetherwithanorderedpairofintegers(n,m).Itturnsoutthatdifferentsystemsassociatedwiththesameunderlyingloopalgebrabutwithdifferentpairsofintegers(n1,m1)and(n2,m2)withn2＜n1andm2＜m1canberelatedbyanestedHamiltonianreductionprocedure.Forallnontrivialgeneralizations,theextracoordinatesbesidesthestandardTodavariablesarePoissonnon-commute,andwheneithernorm≥3,thePoissonstructurefortheextracoordinatevariablesbecomessomeLiealgebra(i.e.theextravariablesappearlinearlyontheright-handsideofthePoissonbrackets).Inthequantumcase,suchgeneralizationswillbecomesystemswithnoncommutativevariableswithoutspoilingtheintegrability.

简介：TwocharacterizationtheoremsofcontinuousL-domainaregiven.ThenaproblemraisedbyJ.D.LawsonandM.Misloveissolved.

简介：1.IntroductionInthispaperweconsiderCauchyproblemforaclassofnonhomogeneousNavier-Stokesequationsintheinfinitecylinderwith.Givensatisfyinginthedistributionsensediv,weseekasolutionvectorandapressurefunctionP(t,x)suchthatwhereisanonlinearvector-valuedfun...

简介：Inthispaper,asimplebutinherentrelationbetweentheL-integralandtheBueeknerworkconjugateintegralisprovedforcrackproblemsinisotropic,anisotropic,anddissimilarmateri-als,respectively.Itisfoundthat,intheabove-mentionedthreecases,theL-integral,fromthemath-ematicalpointofviewaswellasinprinciple,arisesfromBetti’sreciprocaltheorem.ThismeansthattheBuecknerworkconjugateintegralisamoregeneralpath-independentintegralthantheotherssinceanyotherpath-independentintegralscouldbederivedbyusin8theBuecknerintegralwhilechoosingadifferentsubsidiarystress-displacementfield.

简介：We’llstudytheFEMforamodelforcompressiblemiscibledisplacementinporousmediawhichincludesmoleculardiffusionandmechanicaldispersioninone-dimensionalspace.Aclassofvertices-edges-elementsinterpolationoperatorinkisintroduced.Withthehelpofink(notellipticprojection),theoptimalerrorestimateinL∞(J;L2(Ω))normofFEMisproved.

简介：Inthispaper,theLp-convergenceofGrünwaldinterpolationGn（f,x）basedonthezerosofJacobipolynomialsJ（α,β）n（x）（-1<α,β<1）isconsidered.Lp-convergence（00）ofGn（f,x）isobtainedfor-1<α,β≤0.Therefore,theresultsof[1]and[3-5]areimproved.

简介：Inthisnote,theauthorprovesthattheinverseproblemofsubmodularfunctionondigraphswithl∞objectivefunctioncanbesolvedbystronglypolynomialalgorithm.Theresultshowsthatmostinversenetworkoptimizationproblemswithl∞objectivefunctioncanbesolvedinthepolynomialtime.

简介：ThepaperisasurveyontheactionofBergmantypeprojectionsonvariousLpspaces.Thefocusisonthreetypesofholomorphicfunctionspaces:weightedBergmanspaces,theBlochspace,anddiagonalBesovspaces.

简介：InthispaperitturnsoutthataBanachlatticeXisorderisomorphictol~1(Γ)forsomenonemptysetΓiffitisaSchurspaceandalltheinfinitelydimensional,separableandclosedidealsofXareorderisomorphic.

简介：NineteenL-N-2-hydroxyethylaminoacidsandL-N,N-bis(2-hydroxyethyl)aminoacidswerepreparedfromthereactionofchlorohydrinwithL-alanine,L-valine,L-leucine,L-isoleucine,L-phenylalanine,L-serine,L-thrcunine,L-glutamicacid,L-asparticacidandglycine.L-N,N,N’,N’-tetra(2-hydroxyethyl)cystinewaspreparedbythereactionofL-cystinewithchlorohydrin.

简介：令Vn=span{1,2,…,n},设函数f∈Lp[E,μ],1≤p<∞,在点p处定义一个最佳Lp逼近算子τ∫（p）。记Nf（p）=∥f-τ∫（p）∥p=inf/Q∈Vn∥f-Q∥po本文证明了Nf（p）/[μ（E）]l/p是p的单调增加且有界的函数。如果f∈L∞[E,μ],则存在τ∫（∞）∈Vn,使得∥f-τ∫（∞）∥∞=inf/Q∈Vn∥f-Q∥∞,并且给出了最佳逼近值。

简介：GivenacontinuousfunctionfdefinedontheunitcubeofRnandaconvexfunctiont,t（0）-0,t（x）>0,forx>0,weprovethatthesetofbestLt-approximationsbymonotonefunctionshasexactlyoneelementft,whichisalsoacontinuousfunction.Moreoverifthefamilyofconvexfunctions{t}t>0convergesuniformlyoncompactsetstoafunction0,thenthebestapproximationft→f0uniformly,ast→0,wherefoisthebestapproximationoffwithintheOrliczspaceL0Thebestapproxima-tions{ft}areobtainedaswellasminimizingintegralsortheLuxemburgnorm

简介：AcharacteristicoftheextendedCarlesonmeasureexpressedbythederivativesofLpfunctionsinRn+1+isobtained.

简介：让Sq-1，q≥2，联合起来的范围的表面在欧几里德几何学的spaceRq，f(x)∈Lp(Sq-1)，f(x)≥0，f吗？0，1≤p≤+∞。然后，它在现在的纸被证明有顺序≤N和经常的C>的球形的泛音PN(x)0以便‖f-1/P_N‖L_p≤Cω(f,N~(-1))Lp,在哪儿ω(f，吗δ)Lp=sup_(0

简介：

简介：证明了双诱导映射下L-Fuzzy子格群的像与逆像仍为L-Fuzzy子格群,基于L-Fuzzy集的层次结构特征,研究L-Fuzzy子格群的同态,给出了它们的性质.

简介：Letf（x）∈C[-1,1],pn*（x）bethebestapproximationpolynomialofdegreentof（x）.G.Iorentzconjecturedthatifforalln,p2n*（x）=p2n+1*（x）,thenfiseven;andifp2n+1*（x）=p2n+2*（x）,po*（z）=0,thenfisodd.Inthispaper,itisprovedthat,undertheL1-norm,theLorentzconjectureisvalidconditionally,i.e.if（i）（1-x2）f（x）canbeextendedtoanabsolutelyconvergentTehebyshevsories;（ii）foreveryn,f（x）-p2n+1*（x）hasexactly2n+2zeros(or,inthearcondsituation,f（x）-p2n+2*（x）hasexaetly2n+3zeros),thenLorentzconjectureisvalid.

简介：ConsiderL2-projectionuhofuton-degreefiniteelementspaceonone-dimensionaluniformgrids.TwodifferentclassesoftheorthogonalexpansioninanelementforconstructingasuperclosetofunctionuhareproposedandthensuperconvergenceforbothuhandDuhareproved.Whennisoddandnoboundaryconditionsareprescribed,thenuhisofsuperconvergenceatn+1orderGausspointsGn+1ineachelement.Whennisevenandfunctionvaluesontheboundaryareprescribed,thenuhisofsuperconvergenceatn+1orderpointsZn+1ineachelement.Iftheotherboundaryconditionsaregiven,thentheconclusionsarevalidinallelementsthatitsdistancefromtheboundary≥ch|lnh|.Theaboveconclusionsarealsovalid.forn-dergreerectangularelementQ1（n）.