简介：ThispaperisdevotedtoclarifyingtherelationshipbetweentheclassicalMorsetheoryandtheMountainPassLemmaviathelocallinkingconcept.ItisshownthatforaC~1-functionfwithalocallinking,them-thcriticalgroupisnontrivial,wheremistheMorseindex.Combinedwiththebehavioroffatinfinity,thisresultcanbeusedtooffertheexistenceofnontrivialcriticalpoints.

简介：It’swell-knownthatchange-pointproblemisanimportantpartofmodelstatisticalanalysis.Mostoftheexistingmethodsarenotrobusttocriteriaoftheevaluationofchange-pointproblem.Inthisarticle,weconsider'mean-shift'probleminchange-pointstudies.Aquantiletestofsinglequantileisproposedbasedonsaddlepointapproximationmethod.Inordertoutilizetheinformationatdifferentquantileofthesequence,wefurtherconstructa'compositequantiletest'tocalculatetheprobabilityofeverylocationofthesequencetobeachange-point.Thelocationofchange-pointcanbepinpointedratherthanestimatedwithinainterval.Theproposedtestsmakenoassumptionsaboutthefunctionalformsofthesequencedistributionandworksensitivelyonbothlargeandsmallsizesamples,thecaseofchange-pointinthetails,andmultiplechange-pointssituation.Thegoodperformancesofthetestsareconfirmedbysimulationsandrealdataanalysis.Thesaddlepointapproximationbaseddistributionoftheteststatisticthatisdevelopedinthepaperisofindependentinterestandappealing.Thisfindingmaybeofindependentinteresttothereadersinthisresearcharea.

简介：处于PnP问题，成像设备遵循观点规则，成像光线通过一个普通的点。然而，有许多新成像设备，为机器视觉在成像技术与进展为机器人航行或另外的地被开发。这些设计未必被设计遵循观点规则以便满足某设计标准，因此，成像光线不能通过一个普通的点。Suchgeneralized成像设备不能是观点，因此，他们的姿势不能与传统的观点技术被估计。用Wu-Ritt的零个分解方法，为nonperspective-three-point问题的主要部件被给。我们证明有至多在一般盒子中的八个答案并且为NP3P问题给答案分类。

简介：Thispaperconsiderstwodimensionalsystemswhichhavepurelyimaginaryeigenvalues.Inordertoobtainmorepropositionsofinvariantcurves,theauthorstransformtherealsystemsintocomplexdifferentialsystemsbyusingasuitablelineartransformation.Theauthorsalsoproposeanalgorithmtocomputeexponentialfactors.Animprovedmethodofconstructingintegratingfactorbyusingallinvariantcurvesispresentedandcanbeusedindeterminingthetypeoftheequilibriumpoints.

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简介：Byusinganalyticgeometricmethod,anewalgorithmisadvancedonquicklocatingforturningpointsindiscretepointsetofplanecurve.Thealgorithmissimpleinstructureandhashighcomputationefficiency,andcanquicklylocateforturningpointsindiscretepointsetofplaneparametercurveaswell.

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简介：perspective-three-point(P3P)的一个完全的答案分类问题被使用Gr给?bner基础方法。P3P问题推出的多项式系统的解决方案空格的结构能被计算全面Gr获得?bner系统。与概括判别式的性质结合定序，作者给明确的条件决定P3P问题的不同真实积极答案的数字。几个例子被提供说明建议条件的有效性。

简介：这份报纸认为nonsmooth是半无限的得最高分的战略局部地包含Lipschitzinvex的部分编程问题(SIMFP)工作。作者为SIMFP建立必要optimality条件。作者建立在SIMFP的SIMFP的一个最佳的解决方案和分级的Lagrange功能的僵绳点之间的关系。进一步，作者学习为SIMFP定义的向量Lagrange功能的僵绳点标准。

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