简介：Toenhancetheexpressivepowerandthedeclarativeabilityofadeductivedatabase,variousCWA(ClosedWorldAssumption)formalizationsincludingthenaiveCWA,thegeneralizedCWAandthecarefulCWAareextendedtomulti-valuedlogics.Thebasicideaistoembedlogicformulasintosomepolynomialring.Theextensionscanbeappliedinauniformmannertoanyfinitelymulti-valuedlogics.Thereforetheyarealsoofcomputationalsignificance.

简介：Theset-valuedoptimizationproblemwithconstraintsisconsideredinthesenseofsuperefficiencyinlocallyconvexlineartopologicalspaces.Undertheassumptionofic-cone-convexlikeness,byapplyingtheseperationtheorem,Kuhn-Tucker's,Lagrange'sandsaddlepointsoptimalityconditions,thenecessaryconditionsareobtainedfortheset-valuedoptimizationproblemtoattainitssupereffcientsolutions.Also,thesufficientconditionsforKuhn-Tucker's,Lagrange'sandsaddlepointsoptimalityconditionsarederived.

简介：Inthispaper,weintroducematrix-valuedmultiresolutionanalysisandmatrix-valuedwaveletpackets.Aprocedurefortheconstructionoftheorthogonalmatrix-valuedwaveletpacketsispresented.Thepropertiesofthematrix-valuedwaveletpacketsareinvestigated.Inparticular,aneworthonormalbasisofL2(R,Cs×s)isobtainedfromthematrix-valuedwaveletpackets.

简介：Efficientalgorithmsareestablishedforthecomputationofbivariatelacunaryvectorvaluedrationalinterpolantsbasedonthebranchedcontinuedfractionsandanumericalexampleisgiventoshowhowthealgorithmsareimplemented,

简介：In[3],akindofmatrix-valuedrationalinterpolants(MRIs)intheformofRn(x)=M(x)/D(x)withthedivisibilityconditionD(x)|‖M(x)‖2,wasdefined,andthecharacterizationtheoremanduniquenesstheoremforMRIswereproved.Howeverthisdivisibilityconditionisfoundnotnecessaryinsomecases.Inthispaper,weremovethisrestrictedcondition,definethegeneralizedmatrix-valuedrationalinterpolants(GMRIs)andestablishthecharacterizationtheoremanduniquenesstheoremforGMRIs.OnecanseethatthecharacterizationtheoremanduniquenesstheoremforMRIsarethespecialcasesofthoseforGMRIs.Moreover,bydefiningakindofinnerproduct,wesucceedinunifyingtheSamelsoninversesforavectorandamatrix.

简介：Avarietyofmatrixrationalinterpolationproblemsincludethepartialrealizationproblemformatrixpowerseriesandtheminimalrationalinterpolationproblemforgeneralmatrixfunctions.Severalproblemsincircuittheoryanddigitalfilterdesigncanalsobere-ducedtothesolutionofmatrixrationalinterpolationproblems[1—4].Bymeansofthereachabilityandtheobservabilityindicesofdefinedpairsofmatrices,Antoulas,Ball,KangandWillemssolvedtheminimalmatrixrationalinterpolationproblemin[1].Onthe

简介：ApeaknormisdefinedforLpspacesofE-valuedBochnerintegrablefunctions,whereEisaBanachspace,andbestapproximationsfromasuntoelementsofthespacearecharacterized.Applicationsaregiventosomefamiliesofsimultaneousbestapproximationproblems.

简介：AnewkindofvectorvaluedrationalinterpolantsisestablishedbymeansofSamelsoninverse,withscalarnumeratorandvectorvalueddenominator.ItisessentiallydifferentfromthatofGraves-Morris(1983),wheretheinterpolantsareconstructedbyThiele-typecontinuedfractionswithvectorvaluednumeratorandscalardenominator.Thenewapproachismoresuitabletocalculatethevalueofavectorvaluedfunctionforagivenpoint.Andanerrorformulaisalsogivenandproven.

简介：有四值的沃尔什系列的布尔功能的三个班被介绍，他们的沃尔什光谱分布是坚定的。他们从Maiorana-McFarland和DillonPS的弄弯的函数被导出<潜水艇class=“a-plus-plus”>ap类型并且单项的形式\Tr_1^{2m}\lambdax^{r2^m-1}由在二点补充弄弯的函数的值的\指。

简介：Somenonlinearapproximants,i.e.,exponential-suminterpolationwithequaldistanceoratorigin,(0,1)-type,(0,2)-typeand(1,2)-typefraction-sumapproximations,formatrixvaluedfunctionsareintroduced.Alltheseapproximationproblemsleadtoasameformsystemofnonlinearequations.Solvingmethodsforthenonlinearsystemarediscussed.Conclusionsonuniquenessandconvergenceoftheapproximantsforcertainclassoffunctionsaregiven.

简介：在这份报纸，我们考虑Banach空间的一个班珍视单个积分。这些操作员的Lp固定已经被获得了。我们将从BMO讨论他们的固定到BMO。作为应用，我们为经典g功能和Marcinkiewicz积分得到BMO固定。一些已知的结果被改进。

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简介：Thecomputationalproblemsoftwospecialdeterminantsareinvestigated.Thosedeterminantsappearintheconstructionofthefunction-valuedPade-typeapproximationforcomputingFredholmintegralequationofthesecondkind.Themaintooltobeusedinthispaperisthewell-knownSchurcomplementtheorem.

简介：Let{Xk(t),t≥0},k=1,2,...,beasequenceofindependentGaussianprocesseswithaσ^2k(h)=E(Xk(t+h)--Xk(t))^2.Putσ(p,h)=(∞/∑/k=1σ^pk(h))^1/p,p≥1.Theauthorestablishesthelargeincrementresultsforboundedσ(p,h).

简介：BymakinguseofThiele-typebivariatebranchedcontinuedfractionsandSumelsoninverse,weconstructafewkindsofbivariatevectorvaluedrationalinterpolonts(BVRIs)overrectangulargridsandfindoutcertainrelationsamongtheseBVRIssuchasboundaryidentityandduality.

简介：Triplebranchedcontinuedfractions(TBCFs)areconstructedbymeansofwell-defineThiele-typepartialinverteddifferences.Thecharacterizatioontheorem,uniquenesstheoremandsomeprojectionidentitypropertiesareobtainedforvectorvaluedrationalinterpolantshyTBCFs.

简介：Inthisarticleweintroducethevectorvaluedsequencespacem(Eκ,φ,A),associatedwiththemultipliersequenceA=(λκ)ofnon-zerocomplexnumbers,andthetermsofthesequencearechosenfromtheseminormedspacesEκ,seminormedbyfκforallkεN.Thisgeneralizesthesequencespacere(φ)introducedandstudiedbySargent.Westudysomeofitspropertieslikesolidity,completeness,andobtainsomeinclusionresults.Wealsocharacterizethemultiplierproblemandobtainthecorrespondingspacesdualtom(Eκ,φ,A).Weprovesomegeneralresultstoo.

简介：1IutroductionManykindsofmatrix-valuedrationalinterpolationorapproximationproblemshaveappearedinrecentyears([1-7]).MotivatedbyGraves-Morris’Thiele-typevector-val-uedrationalinterpolants[6],GuChuanqingandChenZhibing[7]discussedthematrix-valuedrationalinterpolantsinThiele-typecontinuedfractionform,withmatrix-valuednu-

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