简介：Inthispaper,westudytherelaxedsmoothingproblemswithgeneralclosedconvexconstraints.Itispointedoutthatsuchproblemscanbeconvertedtoaconvexquadraticminimizationproblemforwhichtherearegoodprogramsinsoftwarelibraries.

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简介：Thispaperdiscussestherobustquadraticstabilizationcontrolproblemforstochasticuncertainsystems,wheretheuncertainmatrixisnormbounded,andtheexternaldisturbanceisastochasticprocess.Twokindsofcontrollersaredesigned,whichincludestatefeedbackcaseandoutputfeedbackcase.Theconditionsfortherobustquadraticstabilizationofstochasticuncertainsystemsaregivenvialinearmatrixinequalities.Thedetaileddesignmethodsarepresented.Numericalexamplesshowtheeffectivenessofourresults.

简介：<正>Inthispaperwegivethenecessaryandsufficientconditionsforallfinitecriticalpointsofquadraticdifferentialsystemstobeweakfoci,andsolveanopenproblemproposedbyYanqianYe.

简介：BasedonthesemidefiniteprogrammingrelaxationoftheCDMAmaximumlikelihoodmultiuserdetectionproblem,adetectionstrategybythesuccessivequadraticprogrammingalgorithmispresented.Coupledwiththerandomizedcutgenerationscheme,thesuboptimalsolutionofthemultiuserdetectionprobleminobtained.Comparedtotheinteriorpointmethodspreviouslyreportedbasedonsemidefiniteprogramming,simulationsdemonstratethatthesuccessivequadraticprogrammingalgorithmoftenyieldsthesimilarBERperformancesofthemultiuserdetectionproblem.ButtheaverageCPUtimeofthisapproachissignificantlyreduced.

简介：Inthispaper,wegivealowerboundexp(2.2×10~8)forthosediscriminantsofrealquadraticfieldsQ(√d)withd=N~2-4andh(d)=1.

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简介：Thispaperrepresentsaninexactsequentialquadraticprogramming(SQP)algorithmwhichcansolvenonlinearprogramming(NLP)problems.Aninexactsolutionofthequadraticprogrammingsubproblemisdeterminedbyaprojectionandcontractionmethodsuchthatonlymatrix-vectorproductisrequired.SometruncatedcriteriaarechosensuchthatthealgorithmissuitabletolargescaleNLPproblem.Theglobalconvergenceofthealgorithmisproved.

简介：Derivativesofeigenvaluesandeigenvectorswithrespecttoparametersinsymmetricquadraticeigenvalueproblemarestudied.Thefirstandsecondorderderivativesofeigenpairsaregiven.Thederivativesarecalculatedintermsoftheeigenvaluesandeigenvectorsofthequadraticeigenvalueproblem,andtheuseofstatespacerepresentationisavoided,hencethecostofcomputationisgreatlyreduced.Theefficiencyofthepresentedmethodisdemonstratedbyconsideringaspring-mass-dampersystem.

简介：Itisprovedthatthequadraticsystemwithaweakfocusandastrongfocushasauniquelimitcyclearoundoneofthetwofoci,ifthereexistssimultaneouslylimitcyclesaroundeachofthetwofociforthesystem.

简介：Thebilevelprogrammingisappliedtosolvehierarchicalintelligencecontrolproblemsinsuchfieldsasindustry,agriculture,transportation,military,andsoon.Thispaperpresentsaquadraticobjectivepenaltyfunctionwithtwopenaltyparametersforinequalityconstrainedbilevelprogramming.Undersomeconditions,theoptimalsolutiontothebilevelprogrammingdefinedbythequadraticobjectivepenaltyfunctionisprovedtobeanoptimalsolutiontotheoriginalbilevelprogramming.Moreover,basedonthequadraticobjectivepenaltyfunction,analgorithmisdevelopedtofindanoptimalsolutiontotheoriginalbilevelprogramming,anditsconvergenceprovedundersomeconditions.Furthermore,undertheassumptionofconvexityatlowerlevelproblems,aquadraticobjectivepenaltyfunctionwithoutlowerlevelproblemsisdefinedandisprovedequaltotheoriginalbilevelprogramming.

简介：Thispaperstudiesthedynamicsoftheanalyticfamilyz+1/z+banddescribesthetopologyoftheparameterspace,structuralstabilityandJ-stability.Themappingclassgroupofalmostallmapsoftheabovefamilyisdetermined.

简介：<正>Inthispaper,wemakeacompletestudyoftheunfoldingofaquadraticintegrablesystemwithahomoclinicloop.MakingaPoincaretransformationandusingsomenewtechniquestoestimatethenumberofzerosofAbelianintegrals,weobtainthecompletebifurcationdiagramandallphaseportraitsofsystemscorrespondingtodifferentregionsintheparameterspace.Inparticular,weprovethattwoisthemaximalnumberoflimitcyclesbifurcatingfromthesystemunderquadraticnon-conservativeperturbations.

简介：Inordertoslovethelarge-scalenonlinearprogramming(NLP)problemsefficiently,anefficientoptimizationalgorithmbasedonreducedsequentialquadraticprogramming(rSQP)andautomaticdifferentiation(AD)ispresentedinthispaper.Withthecharacteristicsofsparseness,relativelylowdegreesoffreedomandequalityconstraintsutilized,thenonlinearprogrammingproblemissolvedbyimprovedrSQPsolver.Inthesolvingprocess,ADtechnologyisusedtoobtainaccurategradientinformation.Thenumericalresultsshowthatthecombinedalgorithm,whichissuitableforlarge-scaleprocessoptimizationproblems,cancalculatemoreefficientlythanrSQPitself.

简介：这份报纸为可逆二次的系统的一个类被奉献给时期函数的学习$\begin{聚在一起}\dotx=-2xy，\hfill\\\doty=k-1-2kx+\left({k+1}\right)x^2-\tfrac{1}{2}y^2。\hfill\\\end{聚在一起}$\begin{聚在一起}\dotx=-2xy，\hfill\\\doty=k-1-2kx+\left({k+1}\right)x^2-\tfrac{1}{2}y^2。\hfill\\\end{聚在一起}

简介：ＲＯＷ－ＡＣＴＩＯＮＭＥＴＨＯＤＳＦＯＲＣＯＮＶＥＸＱＵＡＤＲＡＴＩＣＰＲＯＧＲＡＭＭＩＮＧＧＵＯＴｉａｎｄｅ（ＭａｔｈｅｍａｔｉｃｓＤｅｐａｒｔｍｅｎｔｏｆＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ，Ｓｈａｎｄｏｎｇ２７３１６５，Ｃｈｉｎａ...

简介：Thequadratictransformationmethodisproposedtoestimatethetrabecularspacing(Tb.Sp),animportantindexforosteoporosisdiagnosis.Theperformanceofthisalgorithmwasinvestigatedbyscattermodel,two-dimensionfinitedifferencetimedomain(2D-FDTD)simulationandinvitroexperimentsofbovinecancellousbonespecimens.Comparingwiththeotherfourmethods—autoregressivecepstrum(AR),adaptivefilter-autoregressivecepstral(AFAR),inversefilter-autoregressivecepstrum(InvAR),andsimplifiedinversefiltertracking(SIFT),quadratictransformationismuchmorestableandaccurate.TheresultsdemonstratedthatquadratictransformationisagreatalgorithmforTb.Spestimation.

简介：InthispaperweanalyzetheoptimalcontrolproblemforaclassofaffinenonlinearsystemsundertheassumptionthattheassociatedLiealgebraisnilpotent.TheLiebracketsgeneratedbythevectorfieldswhichdefinethenonlinearsystemrepresentaremarkablemathematicalinstrumentforthecontrolofaffinesystems.Wedeterminetheoptimalcontrolwhichcorrespondstothenilpotentoperatorofthefirstorder.Inparticular,weobtainthecontrolthatminimizestheenergyofthegivennonlinearsystem.Applicationsofthiscontroltobilinearsystemswithfirstordernilpotentoperatorareconsidered.

简介：WeproposethegenerationofphotonicEPRstatefromquadraticwaveguidearray.Boththepropagationconstantandthenonlinearityinthearrayaredesignedtopossessaperiodicalmodulationalongthepropagationdirection.Thisensuresthatthephotonpairscanbegeneratedefficientlythroughthequasi-phase-matchingspontaneousparametricdownconversionbyholdingthespatialEPRentanglementinthefashionofcorrelatedpositionandanticorrelatedmomentum.TheSchmidtnumberwhichdenotesthedegreeofEPRentanglementiscalculatedanditcanapproachahighvaluewhenthenumberofilluminatedwaveguidechannelsandthelengthofthewaveguidearrayareproperlychosen.Theseresultssuggestthequadraticwaveguidearrayasacompactplatformforengineeringphotonicquantumstatesinahigh-dimensionalHilbertspace.

简介：Thepaperpresentsaneuralnetworkforsolvingaclassofquadraticprogrammingproblems.Theneuralnetworkiscompletelystabletoexactsolutionsandtherearenoparameterstoset.Moreover,noanaloguemultipliersanddividersarerequired,incontrasttoexistingneuralnetwork[3]whichneedsplentyofanaloguemultipliers.