简介:Thispaperstudiesonlineschedulingofjobswithkindreleasetimesonasinglemachine.Here“kindreleasetime”meansthatinonlinesetting,nojobscanbereleasedwhenthemachineisbusy.EachjobJhasakindreleasetimer(J)≥0,aprocessingtimep(J)>0andadeadlined(J)>0.Thegoalistodetermineaschedulewhichmaximizestotalprocessingtime(∑p(J)E(J))ortotalnumber(∑E(J))oftheacceptedjobs.Forthefirstobjectivefunction∑p(J)E(J),wefirstpresentalowerbound√2,andthenprovideanonlinealgorithmLEJwithacompetitiveratioof3.Thisisthefirstdeterministicalgorithmfortheproblemwithaconstantcompetitiveratio.Whenp(J)∈{1,k},k>1isarealnumber,wefirstpresentalowerboundminf(1+k)/k,2k/(1+k)g,andthenweshowthatLEJhasacompetitiveratioof1+┌k┐=k.Inparticular,whenalltheklengthjobshavetightdeadlines,wefirstpresentalowerboundmax{4=(2+k),1}(for∑p(J)E(J))and4/3(for∑E(J)).ThenweprovethatLEJis┌k┐/k-competitivefor∑p(J)E(J)andweprovideanonlinealgorithmHwithacompetitiveratioof2┌k┐/(┌k┐+1)forthesecondobjectivefunction∑E(J).
简介:Thispaperusesthegeometricsingularperturbationtheorytoinvestigatedynamicalbehaviorsandsingularitiesinafundamentalpowersystempresentedinasingle-machineinfinite-busformulation.ThepowersystemcanbeapproximatedbytwosimplifiedsystemsSandF,whichcorrespondrespectivelytoslowandfastsubsystems.Thesingularities,includingHopfbifurcation(HB),saddle-nodebifurcation(SNB)andsingularityinducedbifurcation(SIB),arecharacterized.WeshowthatSNBoccursatPTc=3.4382,SIBatPTO=2.8653andHBatPTh=2.802forthesingularperturbationsystem.ItmeansthatthepowersystemwillcollapsenearSIBwhichprecedesSNBandthatthepowersystemwilloscillatenearHBwhichprecedesSIB.Inotherwords,thepowersystemwillloseitsstabilitybymeansofoscillationneartheHBwhichprecedesSIBandSNBasPTisincreasingtoacriticalvalue.Theboundaryofthestabilityregionofthesystemcanbedescribedapproximatelybyacombinationofboundariesofthestabilityregionsofthefastsubsystemandslowsubsystem.
简介:students'mathematicalunderstanding,theyarenotableyettomastertothenextdegree.Thedecreasingofstudents'MathqualitycanbeseenonthesurveydataonProgramforInternationalStudentAssessment(PISA)thatconductedeachofthreeyears.On2003,Indonesiawasinthe38^thfrom40stateswiththescore360.On2006,itwasin50thfrom57stateswiththescore391.