简介:Yangetalgavesomecriteriaofprequasi-invexfunctions,semistrictlyprequasi-invexfunctionsandstrictlyprequasi-invexfunctionsin2001,underacertainsetofconditions.Inthisnote,someoftheseconditionscanbeweakenedtogetthesameresults,andanothersimplifiedproofforacriterionofprequasi-invexfunctionsestablishedundertheconditionoflowersemicontinuityisgiven.
简介:Anewadaptivecontrolschemeisproposedformultivariablemodelreferenceadaptivecontrol(MRAC)systemsbasedonthenonlinearbacksteppingapproachwithvectorform.Theassumptiononaprioriknowledgeofthehighfrequencygainmatrixinexistingresultsisrelaxedandthenewrequiredconditionforthehighfrequencygainmatrixcanbeeasilycheckedforcertainplantssothattheproposedmethodiswidelyapplicable.Thiscontrolschemeguaranteestheglobalstabilityoftheclosed-loopsystemsandthetrackingerrorcanbearbitrarysmall.Thesimulationresultforanapplicationexampleshowsthevalidityoftheproposednonlinearadaptivescheme.
简介:根据Rumyantsev提出的Poincaré—Chetaev变量下的广义Routh方程.用无限小变换的方法研究它的对称性与守恒量,得到守恒量存在的条件和形式.该结果比以往的Poincaré—Chetaev方程的相关结论更一般.最后.举例说明结果的应用。
简介:在解一元二次方程根与系数的各类题中.要有一个前提,就是当一元二次方程的根存在时才有这样的关系.在研究这类题型时必须要考虑一元二次方程的根是否存在,即考虑到判别式△≥0,保证根的存在.现举例如下: