简介：Assetallocationisanimportantissueinfinance,andbothriskandreturnareitsfundamentalingredients.Ratherthanthereturn,themeasureoftheriskiscomplicatedandofcontroversy.Inthispaper,weproposeanappropriateriskmeasurewhichispreciselyaconvexcombinationofmeansemi-deviationandconditionalvalue-at-risk.Basedonthisriskmeasure,investorscantrade-offflexiblybetweenthevolatilityandthelosstotackletheincurringriskbychoosingdifferentconvexcoefficients.Asthepresentedriskmeasurecontainsnonsmoothterm,theassetallocationmodelbasedonitisnonsmooth.Toemploytraditionalgradientalgorithms,wedevelopauniformsmoothapproximationoftheplusfunctionandconvertthemodelintoasmoothone.Finally,anillustrativeempiricalstudyisgiven.Theresultsindicatethatinvestorscancontrolriskefficientlybyadjustingtheconvexcoefficientandtheconfidencelevelsimultaneouslyaccordingtotheirperceptions.Moreover,theeffectivenessofthesmoothingfunctionproposedinthepaperisverified.

简介：Anewefficientcouplingrelationshipdescriptionmethodhasbeendevelopedtoprovideanautomatedandvisualizedwaytomultidisciplinarydesignoptimization(MDO)modelingandsolving.Thedisciplinaryrelationmatrix(DRM)isproposedtodescribethecouplingrelationshipaccordingtodisciplinaryinput/outputvariables,andtheMDOdefinitionhasbeenreformulatedtoadoptthenewinterfaces.Basedonthese,auniversalMDOsolvingprocedureisproposedtoestablishanautomatedandefficientwayforMDOmodelingandsolving.Throughasimpleandconvenientinitialconfiguration,MDOproblemscanbesolvedusinganyofavailableMDOarchitectureswithnofurthereffort.SeveralexamplesareusedtoverifytheproposedMDOmodelingandsolvingprocess.ResultshowsthattheDRMmethodhastheabilitytosimplifyandautomatetheMDOprocedure,andtherelatedMDOframeworkcanevaluatetheMDOproblemautomaticallyandefficiently.

简介：Themainobjectiveforthisresearchwastheanalyticalexplorationofthedynamicsofplanarsatelliterotationduringthemotionofanellipticalorbitaroundaplanet.First,werevisittheresultsofJ.Wisdometal.(1984),inwhich,bytheelegantchangeofvariables(consideringthetrueanomalyfastheindependentvariable),thegoverningequationofsatelliterotationtakestheformofanAbelordinarydifferentialequation(ODE)ofthesecondkind,asortofgeneralizationoftheRiccatiODE.WenotethatduetothespecialcharacterofsolutionsofaRiccati-typeODE,thereexiststhepossibilityofsuddenjumpinginthemagnitudeofthesolutionatsomemomentoftime.Inthephysicalsense,thisjumpingoftheRiccati-typesolutionsofthegoverningODEcouldbeassociatedwiththeeffectofsuddenacceleration/decelerationinthesatelliterotationaroundthechosenprincipleaxisatadefinitemomentofparametrictime.Thismeansthatthereexistsnotonlyachaoticsatelliterotationregime(aspertheresultsofJ.Wisdometal.(1984)),butakindofgradientcatastrophe(Arnold,1992)couldoccurduringthesatelliterotationprocess.Weespeciallynotethatifagradientcatastrophecouldoccur,thisdoesnotmeanthatitmustoccur:suchapossibilitydependsontheinitialconditions.Inaddition,weobtainedasymptoticalsolutionsthatmanifestaquasi-periodiccharacterevenwiththestrongsimplifyngassumptionse→0,p=1,whichreducethegoverningequationofJ.Wisdometal.(1984)toakindofBeletskii'sequation.

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