简介：Inthispaper,wedevelopGaussianquadratureformulasfortheHadamardfi-nitepartintegrals.Inourformulas,theclassicalorthogonalpolynomialssuchasLegendreandChebyshevpolynomialsareusedtoapproximatethedensityfunctionf(x)sothattheGaussianquadratureformulashavedegreen-1.Theerrorestimatesoftheformulasareobtained.Itisfoundfromthenumericalexamplesthattheconvergencerateandtheaccu-racyoftheapproximationresultsaresatisfactory.Moreover,therateandtheaccuracycanbeimprovedbychoosingappropriateweightfunctions.

简介：Theaimofthispaperistoprovethefollowingtheoremconcerningthetermbytermdifferentiationthe-oremofWalsh-Kaczmarzseries.Let(ck)beadecreasingrealsequencewithck＝o(1/(logk)r)γ)forsomeγ＞1.Theng(x)＝∞∑k=1ckκk(x),f(x)＝∞∑k=1ck/kkk(x)areintegrablefunctionsandf(x)isa.e.dyadic(orButzerandWagner)differentiablewithf[1](x)＝g(x)fora.e.x∈[0,1).ThefunctionκkmeansthekthWalsh-Kaczmarzfunction.

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简介：FinitepartintegralsintroducedbyHadamardinconnectionwithhyperbolicpartialdifferentialequations,havebeenusefulinanumberofengineeringapplications.Inthispaperweinvestigatesomenumericalmethodsforcomputingfinite-partintegrals.

简介：本文讨论了Walsh函数的Walsh序、Paley序与Hadamard序相应的变换核矩阵的相互转化关系，给出了三类序的Walsh变换核矩阵的生成算法，且生成算法简单，还给出了Matlab生成该类矩阵的Matlab程序，并将几类矩阵的转换置换矩阵应用到图像信息的加密置乱中，置乱效果很好。

简介：用较初等简捷的方法给出Hadamard不等式的改进的一个新证明,得出相关定理、引理和推论.

简介：1IntroductionForann×nmatrixAwhichisaninverseM-matrix,M.Neumannin[1]conjecturedthattheHadamardproductA·AisaninverseofanM-matrix.TheyhavecheckedhisconjecturewithoutfailureonUltrametricmatricesandinverseofMMA-matrices,Uni-pathicmatricesandtheWillongbyinverseM-matrices.Bo-YingWangetal.in[2]haveinvestigatedTriangularinverseM-matriceswhichareclosedundertheHadamardmultipli-cation.LuLinzheng,SunWeiweiandLiWenin[3]presentedamoregeneralconjecture

简介：

简介：The(Nrlund)logarithmicmeansoftheFourierseriesoftheintegrablefunctionfis:1/l_nsumfromk=1ton-1S_k(f)/(n-k),wherel_n:=sumfromk=1ton-11/kInthispaperwediscusssomeconvergenceanddivergencepropertiesofthislogarithmicmeansoftheWalsh-Fourierseriesoffunctionsintheuniform,andintheL~1Lebesguenorm.Amongothers,asanapplicationofourdivergenceresultswegiveanegativeanswertoaquestionofMóriczconcerningtheconvergenceoflogarithmicmeansinnorm.

简介：ForaCarnotgroupG,weestablishtherelationshipbetweenextendedmeanvaluesandr-convexfunctionswhichisintroducedinthispaper,whichisaclassofinequalitiesofHadamardtypeforr-convexfunctiononG.

简介：对于任意的n阶实矩阵A,给出了A°(A*)T与A的奇异性间的关系,指出了A°(A*)T的行和与列和为矩阵A的行列式|A|,最后给出了矩阵类A°(A*)T与n阶方阵的一个等价类的一一对应关系.

简介：Anewapproach,basedonthewaveformrelaxationtechniqueandfastWalshtrans-form,ispresentedtoanalyzethecoupledloosytransmissionlines(CLTL)witharbitraryterminalnetworks.Thesimulationaccuracyofthenewmethodcanbegreatlyimproved,thedisadvantagewhichalwaysexistsinpreviousmethodscanbeavoidedandaconsiderablesavingintimeandmemoryofCPUisobtained.

简介：我们熟知著名的Hadamard（哈达玛）不等式│|A|│

简介：ForthelowerboundaboutthedeterminantofHadamardproductofAandB,whereAisan×nrealpositivedefinitematrixandBisan×nM-matrix,JianzhouLiu[SLAMJ.MatrixAnal.Appl.,18(2)(1997):305-311]obtainedtheestimatedinequalityasfollowsdet(AoB)≥a11b11nⅡk=2(bkkdetAk/detAk-1+detBk/detBk-1(k-1Ei=1aikaki/aii))=Ln(A,B),whereAkiskthordersequentialprincipalsub-matrixofA.WeestablishanimprovedlowerboundoftheformYn(A,B)=a11baanⅡk=2(bkkdetAk/detAk-1+akkdetBk/detBk-1-detAdetBk/detak-1detBk-1)≥Ln(A,B).Formoreweakerandpracticallowerbound,Liugiventhatdet(AoB)≥(nⅡi=1bii)detA+(nⅡi=1aii)detB(nⅡk=2k-1Ei=1aikaki/aiiakk)=(L)n(A,B).WefurtherimproveitasYn(A,B)=(nⅡi=1bii)detA+(nⅡi=1aii)detB-(detA)(detB)+max1≤k≤nwn(A,B,k)≥(nⅡi=1bii)detA+(nⅡi=1aii)detB-(detA)(detB)≥(L)n(A,B).

简介：讨论了稳定矩阵Keroncker积与Hadamard积的一些性质,得到了某些类型稳定矩阵的Ker-onecker积与Hadamard积是稳定矩阵的一些条件。

简介：Earlyin1904,Hadamard[1]showedthescaleimplicitfunctiontheoremoffinitedimensions.Thenitwasgeneralizedtoinfinitedimensions.Inthispaperanewproofofthistheoremisgivenandtheuniqueexistenceoftheperiodicsolutionforaclassofordinarydifferentialequationsystemsatresonanceisobtained.