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

简介：作为绝对错误方法的一种选择，例如最不方形、最少的绝对偏差评价，一个产品亲戚错误评价为一个趋于增加的单个索引回归模型被建议。在模型的回归系数经由一个二阶段的过程被估计，他们象一致性和规度那样的统计性质被学习。包括模拟和一个身体脂肪例子的数字研究证明建议方法表现很好。

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简介：Journalevaluationisacompliatedengineeringsystem,howtoevaluateacademicjournalsmorescientificallyinscientificmethodshavebecomesaproblemofgreatconcerns.Thispaperpresentsattributemathematicalmodelforcomprehensiveindexsystem'qualityevaluationfornaturalscienceacademicjournals,aimingtomakecomprehensiveindexsystem'qualityevaluationforacademicjournalsmoreobjectiveandreasonablecomparedwithotherquantitativeevaluationways.

简介：High-frequencystocktrendpredictionusingmachinelearnershasraisedsubstantialinterestinliterature.Nevertheless,thereisnogoldstandardtoselecttheinputsforthelearners.Thispaperinvestigatestheapproachofadaptiveinputselection(AIS)forthetrendpredictionofhigh-frequencystockindexpriceandcomparesitwiththecommonlyuseddeterministicinputsetting(DIS)approach.TheDISapproachisimplementedthroughcomputationoftechnicalindicatorvaluesondeterministicperiodparameters.TheAISapproachselectsthemostsuitableindicatorsandtheirparametersforthetime-varyingdatasetusingfeatureselectionmethods.Twostate-of-the-artmachinelearners,supportvectormachine(SVM)andartificialneuralnetwork(ANN),areadoptedaslearningmodels.AccuracyandF-measureofSVMandANNmodelswithboththeapproachesarecomputedbasedonthehigh-frequencydataofCSI300index.TheresultssuggestthattheAISapproachusingt-statistics,informationgainandROCmethodscanachievebetterpredictionperformancethantheDISapproach.Also,theinvestmentperformanceevaluationshowsthattheAISapproachwiththesamethreefeatureselectionmethodsprovidessignificantlyhigherreturnsthantheDISapproach.