简介:TheauthorsconsidertheextendedHeckegroupsH(λq)generatedbyT(z)=-1/z,S(z)=-1/(z+λq)andR(z)=1/-zwithλq=2cos(π/q)forq≥3aninteger.Inthispaper,theevensubgroupHe(λq),thesecondcommutatorsubgroupH"(λq)andtheprincipalcongruencesubgroupsHp(λq)oftheextendedHeckegroupsH(λq)arestudied.Also,relationsbetweenthemaregiven.
简介:ThispapereonsidersanARIMA(p,d,q)medel.Amethodforestimatingtheorderdandtestingthehypothesis:d=d0isgiven.Theasymptoticpropertiesoftheestimatorhavebeendiscussed.
简介:LetAbearealsquarematrixandVTAV=GbeanupperHessenbergmatrixwithpositivesubdiagonalentries,whereVisanorthogonalmatrix.ThentheimplicitQ-theoremstatesthatoncethefirstcolumnofVisgiventhenVandGareuniquelydetermined.Inthispaper,threeresultsareestablished.First,itholdsareverseorderimplicitQ-theorem:oncethelastcolumnofVisgiven,thenVandGareuniquelydeterminedtoo.Second,itisprovedthatforaKrylovsubspacetwoformulationsoftheArnoldiprocessareequivalentandinonetoonecorrespondence.Finally,bytheequivalencerelationandthereverseorderimplicitQ-theorem,itisprovedthatfortheKrylovsubspace,ifthelastvectorofvectorsequencegeneratedbytheArnoldiprocessisgiven,thenthevectorsequenceandresultingHessenbergmatrixareuniquelydetermined.
简介:ForagraphG,P(G,λ)denotesthechromaticpolynomialofG.TwographsGandHaresaidtobechromaticallyequivalent,denotedbyG-H,ifP(G,λ)=p(H,λ).Let[G]={H|H-G}.If[G]={G},thenGissaidtobechromaticallyunique.Foracomplete5-partitegraphGwith5nvertices,defineθ(G)=(a(G,6)-2^n+1-2^n-1+5)/2n-2,wherea(G,6)denotesthenumberof6-independentpartitionsofG.Inthispaper,theauthorsshowthatθ(G)≥0anddetermineallgraphswithθ(G)=0,1,2,5/2,7/2,4,17/4.Byusingtheseresultsthechromaticityof5-partitegraphsoftheformG-Swithθ(G)=0,1,2,5/2,7/2,4,17/4isinvestigated,whereSisasetofedgesofG.Manynewchromaticallyunique5-partitegraphsareobtained.
简介:InthispaperL^p-L^qestimatesforthesolutionu(x,t)tothefollowingperturbedhigh-erorderhyperbolicequationareconsidered,(ρπ--a△)(ρπ--b△)u+V(x)u=O,x∈R^n,n≥6,ρ1eu(x,O)=O,ρ^3eu(x,O)=f(x),(j=O,1,2).WeassumethattheotentialV(x)andtheinitialdataf(x)arecompactlysupported,andV(x)issufficientlysmall,thenthesolutionu(x,t)oftheaboveproblemsatisfiesthesameL^p-L^qestimatesasthatoftheunperturbedproblem.
简介:ThispaperconstructsasetofconfidenceregionsofparametersintermsofstatisticalcurvaturesforAR(q)nonlinearregressionmodels.Thegeometricframeworksareproposedforthemodel.Thenseveralconfidenceregionsforparametersandparametersubsetsintermsofstatisticalcurvaturesaregivenbasedonthelikelihoodratiostatisticsandscorestatistics.Severalpreviousresults,,suchas[1]and[2]areextendedtoAR(q)nonlinearregressionmodels.
简介:TheIncompleteOrthogonalizationMethod(IOM(q)),atruncatedversionoftheFullOrthogonalizationMethod(FOM)proposedbySaad,hasbeenusedforsolvinglargeunsymmetriclinearsystmes.However,theIOM(q)exhibitesirregularconvergencebehaviorwithwildoscillationintheresidualnormsthoughittendstodecreaseinaveryslowmanner,whichisowingtothelackofminimizationpropertyovertheKrylovsubspace.QMRmethodproposedbyFreund,GutknechtandNachtigal,owingtoitsabilitytoavoidbreakdownsandsmoothconvergencebehavior,isarobustiterativesolverforgeneralnonsingularunsymmetriclinearsystems.Inthispaper,weproposeanovelquasi-minimalresidual(QMR)variantoftheIncompleteOrthogonalizationMethod(IOM(q)).Numericalexpermentsshowthatithassmoothconvergencebehaviorandismoreeffective,especiallywhenusingitsrestartedversion.