简介：Alongwithnecessariesappliedandthegoingdeeplyintotheresearch,thattheuni-tarymatrixandHermitematrixarepopularizedinmanykinds,andinthispaperuni-versalunitarymatrixanduniversal（oblique）Hermitematrixarestudiedfurther,andthismustbeusefulformatrixtheoryandapplications（likeoptimizationtheory,symplecticgeometryandphysicsetc）.Inthepaper,Cm×nshowsm×ncompoundmatrixset,Cnm×nshowsnstepcompoundinvertiblematrixset,A*showsconjugatetransposematrixofA,

简介：在这份报纸，积极明确的矩阵functionals在一套方形的integrable矩阵上定义珍视的功能被介绍并且学习。最好的近似问题以矩阵Fourier系列被解决。Riemann-Lebesgue矩阵性质和Bessel-Parseval矩阵不平等被给。

简介：Inthispapertheconceptofpositivedefinitebilinearmatrixmomentfunctional.actingonthespaceofallthematrixvaluedcontinuousfunctionsdefinedonaboundedinterval[a,b],isintroduced.ThebestapproximationmatrixproblemwithrespecttosuchafunctionalissolvedintermsofmatrixFourierseries.BasicpropertiesofmatrixFourierseriessuchastheKiemann-Lebesguematrixpropertyandthebessel-parsevalmatrixinequalityareproved.Theconceptoftotalsetvjithrespecttoapositivedefinitematrixfunctionalisintroduced,andthetotallityofanorthonormalsequenceofmatrixpolynomialswithrespecttothefunctional,isestablished.

简介：InthispaperweintroducetheclassofHermite’smatrixpolynomialswhichappearasfiniteseriessolutionsofsecondordermatrixdifferentialequationsY"-xAY’+BY=0.AnexplicitexpressionfortheHermitematrixpolynomials,theorthogonalitypropertyandaRodrigues’formulaaregiven.

简介：LetA=M-NbearegularsplittingofanM-matrix.WestudythespectralpropertiesoftheinerationmatrixM-1N.UnderamildassumptiononM-1N.somenecessaryandsufficentconditionssuchthatp(M-1N)=1areobtainedandthealgebraicmultiplicityandtheindexassociatedwitheigenvalue1inM-1Nareconsidered.

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简介：Inthispaperbasicresultsforatheoryoforthogonalmatrixpolynomialswithrespecttoaconjugatebilinearmatrixmomentfunctionalareproposed.Propertiesoforthogonalmatrixpolynomialsequencesincludingathreetermmatrixrelationshiparegiven.PositivedefiniteconjugatebilinearmatrixmomentfunctionalsareintroducedandacharacterizationofpositivedefinitenessintermsofablockHaenkelmomentmatrixisestablished.Foreachpositivedefiniteconjugatebilinearmatrixmomentfunctionalanassociatedmatrixinnerproductisdefined.

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简介：TheconceptofFiedlermatriceswasintroducedin[1]byL.StuartandR.Weaver.In[1],theyinvestigatedthefactorizationofFiedlermatrixintoFiedlermatricesandpre-sentedsomeopenquestionsi.e.WhenisaFiedlermatrixfactorizableasaproductofFiedlermatrices?Arethereusefulsufficientconditions?IfaFiedlermatrixisfactorizable,arethefactorsunique?Ifnot,arethedimensionsofthefactorsunique?Inthispaper,we

简介：ThispaperdiscussesthesolvabilityofquaternionmatrixequationA^*X^*B^*±BXA=Dandobtainsit'sgeneralexplicitsolutionsintermsofA,B,DandtheirMoore-Penroseinverses.

简介：Thenonchromatinproteinousresidueofthecellnucleuswasrevealedinourlaboratoryasearlyasin1948andthenidentifiedbylightandelectronmicroscopyasresidualnucleoli,intranuclearnetworkandnuclearenvelopebefore1960,Thisstructuretermedafterwardsas'nuclearresidue','nuclearskeleton','nuclearcage','nuclearcarcass'etc.,wasmuchlater(in1974)isolated,studiedandentitledas'nuclearmatrix'byBerezneyandCoffey,towhomthediscoveryofthisresidualstructureisoftenwronlyascribed.Therealhistoryofnuclearmatrixmanifestationisreportedinthispaper.

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：Anewmethodfortheconstructionofbivariatematrixvaluedrationalinterpolants(BGIRI)onarectangulargridispresentedin[6].TherationalinterpolantsareofThiele-typecontinuedfractionformwithscalardenominator.Thegeneralizedinverseintroducedby[3]isgen-eralizedtorectangularmatrixcaseinthispaper.Anexacterrorformulaforinterpolationisob-tained,whichisanextensioninmatrixformofbivariatescalarandvectorvaluedrationalinterpola-tiondiscussedbySiemaszko[l2]andbyGuChuangqing[7]respectively.Bydefiningrowandcol-umn-transformationinthesenseofthepartialinverteddifferencesformatrices,twotypematrixalgorithmsareestablishedtoconstructcorrespondingtwodifferentBGIRI,whichholdforthevec-torcaseandthescalarcase.

简介：Inthispaper,someinequalitiesforsequencerearrangementandmatrixproductareestablished.Theauthorsextendandimprovesomeknownresults,andshowthattherearesomeerrorsinreferenceoninequalitiesforsequencerearrangementbyexamples,

简介：1IntroductionLetA∈Cn×n,B∈Cn×n.WesayBisasquarerootofAifA=B×Bi.e.A=B2.Itiswell-knownthatanysymmetricpositivedefinitematrixexistsoneandonlyonesquarerootwhichisasymmetricpositivedefinitematrix,too（e.g.see[5]）.Higham[4]studiedcarefullytherelationofarealnonsingularmatrixbetweenitsrealsquarerootsanditseigenvalues.AlefeldandSchneider[1]pointedoutthatforanynonsingularM-ma-trixthereisoneandonlyoneM-matrixasitssquareroot.Inthispaper,westudyona

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简介：Microstructuresofmatrixesofaseriesofhightechnologycastableshavebeenanalyzed.Intheselowcement,ultra-lowcementandnon-cementcastablematrixes,whichweresinteredrespectivelyat1350℃and1500℃，silicaulrtafineandα-Al2O3ultrafinewereadded,Theresultsshowthatthenon-cementcastablehadthebestpropertiesathightemerature;addingα-Al2O3ultrafinewashelpfultocalcium-feldspardeveopingandgrowing;andhighlypurifiedsilicaultrafinestiumulatedmullitecrystaldevelopingwhilethecommononestimulateditsgrowing.

简介：Inthispaper,wefirstintroduceaconceptofcompanionvector,andstudytheJordancanonicalformsofquaternionmatricesbyusingthemethodsofcomplexrepresentationandcompanionvector,notonlygiveoutapracticalalgorithmforJordancanonicalformJofaquaternionmatrixA,butalsoprovideapracticalalgorithmforcorrespondingnonsingularmatrixPwithP-1AP=J.

简介：Thematrixmetalloproteinases(MMPs)areafamilyofzine-dependentendopeptidasesthatplayakeyroleinbothnormalandpathologicalprocessesinvolvingtissueremodelingevents.Theexpressionoftheseproteolyticenzymesishighlyregulatedbyabalancebetweenextracellularmatrix(ECM)depositionanditsdegradation,andiscontrolledbygrowthfactors,cytokines,hormones,aswellasinteractionswiththeECMmacromolecules.Furthermore,theactivityoftheMMPsisregulatedbytheirnaturalendogenousinhibitors,whicharemembersofthetissueinhibitorofmetalloproteinases(TIMP)family.Inthenormalmammarygland,MMPsareexpressedduringductaldevelopment,lobulo-alveolardevelopmentinpregnancyandinvolutionafterlactation.Underpathologicalconditions,suchastumorigenesis,thedysregulatedexpressionofMMPsplayaroleintumorinitiation,progressionandmalignantconversionaswellasfacilitatinginvasionandmetastasisofmalignantcellsthroughdegradationoftheECMandbasementmembranes.