简介:Aroutingtreeforasetoftasksisadecisiontreewhichassignsthetaskstotheirdestinationsaccordingtothefeaturesofthetasks.Aweightedroutingtreeisonewithcostsattachedtoeachlinkofthetree.Linksofthesamefeaturehavethesamecost.Itisprovedthattheproblemoffinding?routingtreeoftheminimumcostforagivensetoftasksoftwofeaturesisNP-complete.
简介:<正>Foranyintegersa1,a2,a3,a4andcwitha1a2a3a40(modp),thispapershowsthatthereexistsasolutionX=(x1,x2,x3,x4)∈Z4ofthecongruencea1x12+a2x22+a3x32+a4x42≡c(modp)suchthat‖X‖=max{|x1|,|x2|,|x3|,|x4|}《p1/2logp.
简介:At-hyperwheel(t≥3)oflengthl(orW(t)lforbrevity)isat-uniformhypergraph(V,E),whereE={e1,e2,...,el}andv1,v2,...,vlaredistinctverticesofV=∪eii=1lsuchthatfori=1,...,l,vi,vi+1∈eiandei∩ej=P,j∈/{i1,i,i+1},wheretheoperationonthesubscriptsismodulolandPisavertexofVwhichisdifferentfromvi,1≤i≤l.Inthispaper,theminimumcoveringproblemofMCλ(3,W(3)4,v)isinvestigated.DirectandrecursiveconstructionsonMCλ(3,W(3)4,v)arepresented.Thecoveringnumbercλ(3,W(3)4,v)isfinallydeterminedforanypositiveintegersv≥5andλ.
简介:BytheSchauder-Tychonofffixed-pointtheorem,weinvestigatetheexistenceandasymptoticbehaviorofpositiveradialsolutionsoffullynonlinearellipticequationsinR^n.WegivesomesufficientconditionstoguaranteetheexistenceofboundedandunboundedradialsolutionsandconsiderthenonexistenceofpositivesolutioninR^n.
简介:Inthispaper,weconsiderthen-widthsandaveragewidthsofBesovclassesintheusualSobolevspaces.TheweakasymptoticresultsconcerningtheKolmogorovn-widths,thelinearn-widths,theGel'fandn-widths,intheSobolevspacesonT~d,andtheinfinite-dimensionalwidthsandtheaveragewidthsintheSobolevspacesonR~dareobtained,respectively.
简介:AnexampleofcompletsRiemannianmetricofpositive(ornonnagative)curvatureonR^nsuchasds^2=a(x)dx^2isobtainedbydirectcaculations.Furthermore,byusingageodesicconvexconditionandatheoremforcompletenoncompactRiemannianmanifold,anexistenceresultofperiodicsulutionofprescribedenergyforasingularHamiltoniansystemisalsoobtained.
简介:ForsomeclassesofperiodicfunctionswithboundaryconditionsthestrongasymptoticsoftheKolmogorov’s,theGelfand’s,andlinearN-widthsareobtained.
简介:在N-解析函数类中,对于无穷直线上的Riemann-Hilbert边值问题,通过轴的对称扩张法将其转化为在附加条件下相应的Riemann边值问题,从而建立了其齐次和非齐次问题的可解性理论。
简介:LongtimebehaviorofdegenerateequationswiththenonlinearityofpolynomialgrowthofarbitraryorderonthewholespaceRNisconsidered.Byusing-trajectoriesmethods,weprovedthatweaksolutionsgeneratedbydegenerateequationspossessan(L2U(RN),L2loc(RN))-globalattractor.Moreover,theupperboundsoftheKolmogorovε-entropyforsuchglobalattractorarealsoobtained.
简介:ThepaperdefinesanextendedCesàrooperatorTgwithholomorphicsymbolgintheunitballBofCnasWhereg(z)=∑j=1∑nzjg/zjistheradialderivativeofg.Inthispaper,theauthorcharacterizesgforwhichTgisbounded(orcompact)ontheBlochspaceBandthelittleBlochspaceB0.