简介:LetP(z)beapolynomialofdegreenandforanycomplexnumbera,letDaP(z)=nP(z)+(a-z)P′(z)denotethepolarderivativeofthepolynomialP(z)withrespecttoa.Inthispaper,weobtaininequalitiesforthepolarderivativeofapolynomialhavingallzerosinsideacircle.Ourresultsshallgeneralizeandsharpensomewell-knownresultsofTuran,Govil,Dewanetal.andothers.
简介:theAlternatingSegmentCrank-Nicolsonschemeforone-dimensionaldiffusionequationhasbeendevelopedin[1],andtheAlternatingBlockCrank-Nicolsonmethodfortwo-dimensionalproblemin[2].Themethodshavetheadvantagesofparallelcomputing,stabilityandgoodaccuracy.Inthispaperforthetwo-dimensionaldiffusionequation,thenetregionisdividedintobands,aspecialkindofblock.ThismethodiscalledthealternatingBandCrank-Nicolsonmethod.
简介:Bystudyingmodularinvariancepropertiesofsomecharacteristicforms,wegetsomegen-eralizedanomalycancellationformulason(4r-1)-dimensionalmanifoldswithnoassumptionthatthe3rdde-Rhamcohomologyofmanifoldsvanishes.Theseanomalycancellationformulasgeneralizeourpreviousanomalycancellationformulason(4r-1)-dimensionalmanifolds.Wealsogeneralizeourpreviousanomalycancellationformulason(4r-1)-dimensionalmanifoldsandtheHauYurigiditytheoremtothe(a,b)case.
简介:WepresentaparalleliterativealgorithmtofindtheshortestdistanceprojectionofagivenpointontotheintersectionofafinitenumberofclosedconvexsetsinarealHilbertspace;thenumberofsetsusedateachiterationsteptcorrespondingtothenumberofavailableprocessors,maybesmallerthanthetotalnumberofsets.TherelaxationcoefficientateachiterationstepisdeterminedbyageometricalconditioninanassociatedHilbertspace,whilefortheweightsmildconditionsaregiventoassurenormconvergenceoftheresultingsequence.Thesemildconditionsleaveenoughflexibilitytodeterminetheweightsmorespecificallyinordertoimprovethespeedofconvergence.
简介:LetP(G,λ)bethechromaticpolynomialofagraphG.TwographsGandHaresaidtobechromaticallyequivalent,denotedG~H,ifP(G,λ)=P(H,λ).Wewrite[G]={H|H~G}.If[G]={G},thenGissaidtobechromaticallyunique.Inthispaper,wefirstcharacterizecertaincomplete6-partitegraphswith6n+1verticesaccordingtothenumberof7-independentpartitionsofG.Usingtheseresults,weinvestigatethechromaticityofGwithcertainstarormatchingdeleted.Asaby-product,manynewfamiliesofchromaticallyuniquecomplete6-partitegraphswithcertainstarormatchingdeletedareobtained.
简介:Modelinglog-mortalityratesonO-UtypeprocessesandforecastinglifeexpectanciesareexploredusingU.S.data.IntheclassicLee-Cartermodelofmortality,thetimetrendandtheage-specificpatternofmortalityoveragegrouparelinear,thisisnotthefeatureofmortalitmodel.Toavoidthisdisadvantage,O-Utypeprocesseswillbeusedtomodelthelog-mortalityinthispaper.Infact,thismodelisanAR(1)process,butwithanonlineartimedriftterm.BasedonthemortalitydataofAmericafromHumanMortalitydatabase(HMD),mortalityprojectionconsistentlyindicatesapreferenceformortalitywithO-UtypeprocessesoverthosewiththeclassicalLee-Cartermodel.Bymeansofthismodel,thelowboundsofmortalityratesateveryagearegiven.Therefore,lengtheningofmaximumlifeexpectanciesspanisestimatedinthispaper.