简介：Abstract.LetGbeasimplegraph.ThecyclicbandwidthsumproblemistodeterminealabelingofgraphGinacyclesuchthatthetotallengthofedgesisassmallaspossible.Inthispaper,someupperandlowerboundsoncyclicbandwidthsumofgraphsarestudied.

简介：LetRbeafinitechainringwithmaximalidealγandresiduefieldF,andletγbeofnilpotencyindext.ToeverycodeCoflengthnoverR,atowerofcodesC=(C:γ0)(C:γ)(C:γi)(C:γt-1)canbeassociatedwithC,whereforanyr∈R,(C:r)={e∈Rn|re∈C}.UsinggeneratorelementsoftheprojectionofsuchatowerofcodestotheresiduefieldF,wecharacterizecycliccodesoverR.ThischaracterizationturnstheconditionforcodesoverRtobecyclicintooneforcodesovertheresiduefieldF.Furthermore,weobtainacharacterizationofcycliccodesovertheformalpowerseriesringofafinitechainring.

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简介：Assumethatm≥2,pisaprimenumber,(m,p(p-1))=1,-1(Z/mZ)~*and[(Z/mZ)~*:]=4.Inthispaper,wecalculatethevalueofGausssumG(X)=Σ_(x∈F_q~*)x(x)ζ_p~(T(x))overF_q,whereq=p~f,f=((m))/4xisamultiplicativecharacterofF_qandTisthetracemapfromF_qtoF_p.Underourassumptions,G(x)belongstothedecompositionfieldKofpinQ(ζm)andKisanimaginaryquarticabeliannumberfield.WhentheGaloisgroupGal(K/Q)iscyclic,wehavestudiedthiscycliceaseinanotherpaper:'Gausssumsofindexfour:(1)cycliccase'(acceptedbyActaMathematicaSinica,2003).Inthispaperwedealwiththenon-cycliccase.

简介：Basedontheblockstylespectraldecomposition,thispaperdealswiththeoptimalbackwardperturbationanalysisforthelinearsystemwithblockcycliccoefficientmatrix.

简介：Inthispaper,wegivesomedecompositionsoftriplesofZpnorZ3pnintocyclictriplesystems.Newconstructionsofdiferencefamiliesaregiven.Someinfniteclassesofsimplecyclictriplesystemsareobtainedfromthesedecompositions.

简介：Inthispaper,weintroducegeneralizedcyclicC-contractionsthroughpnumberofsubsetsofaprobabilisticmetricspaceandestablishtwofixedpointresultsforsuchcontractions.InourfirsttheoremweusetheHadzictypet-norm.InournexttheoremweuseLukasiewiczt-norm.OurresultsgeneralizetheresultsofChoudhuryandBhandari[11].Acontrolfunction[3]hasbeenutilizedinoursecondtheorem.Theresultsareillustratedwithsomeexamples.