简介：Asanresearchexampleofthewidelyexistingcooperation-competitionsystems,theauthorspresentanempiricalinvestigationonafruitnutritivefactornetwork.Itisdescribedbyanode-weightedbipartitegraph.Thefruitnutritivefactorsaredefinedasthenodes,andtwonodesareconnectedbyanedgeifatleastonefruitcontainsthesetwonutritivefactors.Thefruitsaredefinedasthecollaborationacts.Thenode-weightW_(nt),whichsignifiesthe'importancedegree'ofeachactornode,isdefinedasthecontentofanutritivefactorinafruit.Theempiricalinvestigationresultsshowsomeuniquefeatures.Thenode-weightdistributionstakeso-called'shiftedpowerlaw'functionforms,buttheact-weightdistributiontakesanormalform.Thedegreeandact-degreedistributionsshowimpulsive-spectrumlikeforms.Theseobservationsmaybehelpfulforthestudyoffruits.Thenetworkdescriptionmethodproposedinthisarticlemaybeuniversalforakindofcooperation-competitionsystems.

简介：AHamiltoniank-factorisak-factorcontainingaHamiltoniancycle.Ann/2-criticalgraphGisasimplegraphofordernwhichsatisfiesδ(G)≥n/2andδ(G-e)

简介：Inthispaper,rankfactorizationsandfactorleftprimefactorizationsarestudied.Theauthorsprovethatanypolynomialmatrixwithfullrowrankhasfactorleftprimefactorizations.Andforaclassofpolynomialmatrices,theauthorsgiveanalgorithmtodecidewhethertheyhaverankfactorizationsorfactorleftprimefactorizationsandcomputethesefactorizationsiftheyexist.