RESEARCH ARTICLES

InternationalJournalofMathematicsandMathematicalSciencesISSN0161-1712,Volume2004,Numbers69–72FoundingManagingEditor:LokenathDebnathHindawiPublishingCorporation,Volume2004,Numbers69–72FoundingManagingEditor:LokenathDebnathHindawiPublishingCorporation,Number69,11November2004RESEARCHARTICLESRationaltoralranksincertainalgebras,YasusukeKotaniandToshihiroYamaguchi..........................................3765Thesecond-orderKlein-Gordonfieldequation,D.GomesandE.CapelasdeOliveira.................................................3775Relatedfixedpointsforset-valuedmappingsontwouniformspaces,DuranTürko˘gluandBrianFisher....................................................3783Asummabilityfactortheoremforabsolutesummabilityinvolvingalmostincreasingsequences,B.E.RhoadesandEkremSava¸s..............................3793ConstructingBanaschewskicompactificationwithoutDedekindcompletenessaxiom,S.K.Acharyya,K.C.Chattopadhyay,andParthaPratimGhosh............3799RESEARCHNOTESOntheLagrangeresolventsofadihedralquinticpolynomial,BlairK.SpearmanandKennethS.Williams..........................................3817JustificationoftheexistenceofagroupofasymptoticsofthegeneralfifthPainlevétranscendent,YouminLuandZhoudeShao.........................................3821Volume2004,Number70,16December2004RESEARCHARTICLESATychonofftheoreminintuitionisticfuzzytopologicalspaces,Do˘ganÇoker,A.HaydarE¸s,andNeclaTuranli......................................3829MultiplicityandstructuresfortravelingwavesolutionsoftheKuramoto-Sivashinskyequation,Bao-FengFeng.............................3839Convergenceandstabilityofthethree-stepiterativeschemesforaclassofgeneralquasivariational-likeinequalities,ZeqingLiu,ZhefuAn,ShinMinKang,andJeongSheokUme.......................3849Onderivationsandcommutativityinprimerings,VincenzoDeFilippis............3859MeasuresofconcordancedeterminedbyD4-invariantcopulas,H.H.Edwards,P.Mikusi´nski,andM.D.Taylor......................................3867Boundsfortotalantieigenvalueofanormaloperator,SK.M.Hossein,K.C.Das,L.Debnath,andK.Paul...................................3877RESEARCHNOTESRadicalapproachinBCH-algebras,EunHwanRoh..................................3885AgeneralizationofanecessaryandsufficientconditionforprimalityduetoVantieghem,L.J.P.Kilford....................................................3889Volume2004,Number71,21December2004RESEARCHARTICLESOscillationpropertiesofnonlinearneutraldifferentialequationsofnthorder,T.CandanandR.S.Dahiya...........................................................3893ProjectivestructureandintegrablegeodesicflowsontheextensionofBott-Virasorogroup,ParthaGuha.................................................3901MagnetoelasticplanewavesinrotatingmediainthermoelasticityoftypeII(G-Nmodel),S.K.RoychoudhuriandManidipaBanerjee(Chattopadhyay).........3917Ontheuniquenessofthe(2,2)-dimensionalsupertorusassociatedtoanontrivialrepresentationofitsunderlying2-torus,andhavingnontrivialoddbrackets,R.Peniche,O.A.Sánchez-Valenzuela,andF.Thompson............................3931RESEARCHNOTESEssentialnormofweightedcompositionoperatorbetweenα-Blochspaceandβ-Blochspaceinpolydiscs,LiSongxiaoandZhuXiangling.........................3941OnsimultaneousapproximationforsomemodifiedBernstein-typeoperators,VijayGuptaandNurhayatIspir......................................................3951Volume2004,Number72,26December2004RESEARCHARTICLESOnahigher-orderevolutionequationwithaStepanov-boundedsolution,AribindiSatyanarayanRao...........................................................3959Finiteelementleast-squaresmethodsforacompressibleStokessystem,KeehwanKim,SangdongKim,andSangsikShin....................................3965RESEARCHNOTESNumericalsolutionofStokesproblemforfreeconvectioneffectsindissipativedustymedium,V.VenkataramanandK.Kannan...................................3975Propertiesofsome∗-dense-in-itselfsubsets,V.RenukaDevi,D.Sivaraj,andT.TamizhChelvam................................3989Marcinkiewiczintegralsalongsubvarietiesonproductdomains,AhmadAl-Salman.....................................................................4001IJMMS2004:69,3765–3774PII.S0161171204403421©HindawiPublishingCorp.RATIONALTORALRANKSINCERTAINALGEBRASYASUSUKEKOTANIandTOSHIHIROYAMAGUCHIReceived24March2004andinrevisedform17September2004Wecalculatetherationaltoralranksoftwospaceswhosecohomologiesareisomorphicandnotethatrationaltoralrankisarationalhomotopyinvariantbutnotacohomologyinvariant.2000MathematicsSubjectClassification:55P62,57S99.1.Introduction.Letrk0(Y)betherationaltoralrankofasimplyconnectedspaceY,thatis,thelargestintegerrsuchthatanr-torusTr=S1×···×S1(r-factors)canactcontinuouslyonaCW-complexwhichhastherationalhomotopytypeofYwithallitsisotropysubgroupsfinite.Forexample,rk0(Y)=1ifYhastherationalhomotopytypeofanodd-dimensionalsphereS2n+1.LetQbethefieldoftherat