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简介：InthispaperwestudythesolutionsandstabilityofthegeneralizedWilson’sfunctionalequation∫_Gf(xty)dμ(t)+∫_Gf(xtσ(y))dμ(t)=2f(x)g(y),x,y∈G,whereGisalocallycompactgroup,σisacontinuousinvolutionofGandμisanidempotentcomplexmeasurewithcompactsupportandwhichisσ-invariant.Weshowthat∫_Gg(xty)dμ(t)+∫_Gg(xtσ(y))dμ(t)=2g(x)g(y)iff≠0and∫_Gf(t.)dμ(t)≠0,where[∫_Gf(t.)dμ(t)](x)=∫_Gf(tx)dμ(t).WealsostudysomestabilitytheoremsofthatequationandweestablishthestabilityonnoncommutativegroupsoftheclassicalWilson’sfunctionalequationf(xy)+χ(y)f(xσ(y))=2f(x)g(y)x,y∈G,whereχisaunitarycharacterofG.

简介：TheConwaypotentialfunction(CPF)forcoloredlinksisaconvenientversionofthemultivariableAlexander–Conwaypolynomial.WegiveaskeincharacterizationofCPF,muchsimplerthantheonebyMurakami.Inparticular,Conway’s"smoothingofcrossings"isnotintheaxioms.Theproofusesareductionschemeinatwistedgroup-algebraP_nB_n,whereB_nisabraidgroupandP_nisadomainofmulti-variablerationalfractions.Theproofdoesnotusecomputeralgebratools.Aninterestingby-productisacharacterizationoftheAlexander–Conwaypolynomialofknots.

简介：FranklandFürediin[1]conjecturedthatther-graphwithmedgesformedbytakingthefirstmsetsinthecolexorderingofN（r）hasthelargestLagrangianofallr-graphswithmedges.Denotethisr-graphbyCr,mandtheLagrangianofahypergraphbyλ（G）.Inthispaper,wefirstshowthatif(3t-1)≤m<（3t）,Gisaleft-compressed3-graphwithmedgesandonvertexset[t],thetriplewithminimumcolexorderinginGcis（t—2—i）（t—2）t,thenλ（G）≤λ(C3,m).Asanimplication,theconjectureofFranklandFiirediistruefor（3t）-6≤m≤（3t）.

简介：InthisnoteweconsiderWente’stypeinequalityontheLorentz-Sobolevspace.If▽f∈Lp1,q1（Rn）,G∈Lp2,q2（Rn）anddivG≡0inthesenseofdistributionwhere（1/p1）+（1/P2）=（1/q1）+（1/q2）=1,1

简介：Inthispaper,anewclassofsolutionsofthevacuumEinstein'sfieldequationswithcosmologicalconstantisobtained.Thisclassofsolutionspossessesthenakedphysicalsingularity.ThenormoftheRiemanncurvaturetensorofthisclassofsolutionstakesinfinityatsomepointsandthesolutionsdonothaveanyeventhorizonaroundthesingularity.

简介：Inordertoimprovethecarsalesservice4Sshopmanagementlevel,improvetheeconomicandsocialbenefitsofenterprises,incentivesareusedtoencouragetheirown4sshops.Inthispaper,throughouttherelatedanalysisofthequarterlyandannualawardsincentiveprograminlarge-scaledomesticautomobileenterprises,entropymethodwithMATLABsoftwareisappliedtoestablishthedimensionalfitfunction.Inthedataprocessing,themultiplelinearregressionfunctionintoLingosoftwareisemployedtogetthebestsolution;andClanguageisusedtorunthescreeningdataprogramthroughtheconsistencytestprograminthesensitivityanderroranalysis.Firstofall,considerthecompanytomaximizeprofitsandmaximizetheamountofcomplaintsinthestoretomaintainalowtarget;intermsofstaff,weshouldconsiderprovidingmoreincentivesforemployees;inthecustomer,theoverallsatisfaction,serviceAttitude,vehiclecleanlinessbasedshouldbeimproved.Andtwoprogramsforthemonthlyprofitandexcessprofitsofprogressiveincentivesshouldalsobeimproved.

简介：Inthispaper,thefuzzyreliabilityfunctionZ=X+Yhasbeenderived.InthecaseofthatX,YsubjectstoMarshall-Olkinbivariateexponentialdistribution,assumingμ=μ1μ2.

简介：Inthispaper,theauthorsstudytheCohen-Fischman-Westreich’sdoublecentralizertheoremfortriangularHopfalgebrasinthesettingofalmost-triangularHopfalgebras.

简介：Klapper(1994)showedthatthereexistsaclassofgeometricsequenceswiththemaximalpossiblelinearcomplexitywhenconsideredassequencesoverGF(2),butthesesequenceshaveverylowlinearcomplexitieswhenconsideredassequencesoverGF(p)(pisanoddprime).ThislinearcomplexityofabinarysequencewhenconsideredasasequenceoverGF(p)iscalledGF(p)complexity.ThisindicatesthatthebinarysequenceswithhighGF(2)linearcomplexitiesareinadequateforsecurityinthepracticalapplication,while,theirGF(p)linearcomplexitiesarealsoequallyimportant,evenwhentheonlyconcerniswithattacksusingtheBerlekamp-Masseyalgorithm[Massey,J.L.,Shift-registersynthesisandbchdecoding,IEEETransactionsonInformationTheory,15(1),1969,122–127].Fromthisperspective,inthispapertheauthorsstudytheGF(p)linearcomplexityofHall’ssexticresiduesequencesandsomeknowncyclotomic-set-basedsequences.

简介：ThispaperconsidersthereliablecontroldesignforT-Sfuzzysystemswithprobabilisticactuatorsfaultsandrandomtime-varyingdelays.Thefaultsofeachactuatoroccursrandomlyanditsfailureratesaregovernedbyasetofunrelatedrandomvariablessatisfyingcertainprobabilisticdistribution.Intermsoftheprobabilisticfailuresofeachactuatorandtime-varyingrandomdelays,newfaultmodelisproposed.Basedonthenewfuzzymodel,reliablecontrollerisdesignedandsufficientconditionsfortheexponentiallymeansquarestability(EMSS)ofT-SfuzzysystemsarederivedbyusingLyapunovfunctionalmethodandlinearmatrixinequality(LMI)technique.Itshouldbenotedthattheobtainedcriteriadependonnotonlythesizeofthedelay,butalsotheprobabilitydistributionofit.Finally,anumericalexampleisgiventoshowtheeffectivenessoftheproposedmethod.