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简介：Singularityanalysisinanimportantsubjectofthegeometricconstraintsatisfactionproblem.Inthispaper,threekindsofsingularitiesaredescribedandcorrespondingidentifcationmethodsarepresentedforbothunder0constrainedsystemsandover-constrainedsystems,Anotherspecialbutcommonsingularityforunder-constrainedgeometricsystems,pseudo-singularity,isanalyzed.Pseudo-singularityiscausedbyavarietyofconstraintmathchingofunder-constrainedsystemsandcanberemovedbyimprovingconstraintdistribution.Toavoidpseudo-singularityanddecideredundantconstraintsadaptively,adifferentiaitonalgorithmisproposedinthepaper.Itscorrctnessandeffciencyhavebeenvalidatedthroughitspracticalapplicationsina2D/3DgeometricconstraintsolverCBA.

简介：Inthisnotewecharacterizethegeometricfactureofa(μ,r,k)-FES.Namely,foraC~μtriangularin-terpolationschcmewithC~rvertexdata,anyangleofthemacrotrianglemustbedividedintoatleast(μ+1)/(r+1-μ)parts.

简介：A.D的古典结果。Alexandrov说那一个连接协议smoothn维没有边界歧管，在R~(n+1)嵌入，并且以便它的吝啬的弯曲是不变的，是一个范围。这里，我们在一个亢奋的飞机X_(n+1)=常数学习M的对称的问题以防M满足：为任何二个点(X“，X_(n+1))，(X”，X_(n+1))与X_(n+1)>X_(n+1)，在M上，在第一点的吝啬的弯曲不在第二点比那大。对称不必总是认为我们在一些另外的条件下面建立它，但是在这糊。theHopf词根的一些变化也被介绍。几个开的问题被描述。部分Ⅰ处理了相应的维的问题。

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简介：YagerpresentedtheOrderedWeightedAveraging(OWA)operatortoprovideamethodforaggregatinginformationofdecision-making.YagerandFilevfurtherpresentedtheInducedOrderedWeightedAveraging(IOWA)operator.Inthispaper,weproposeaGeneralizedInducedOrderedWeightedGeometric(GIOWG)operatorandestablishasimpleobjective-programmingmodeltolearntheassociatedweightingvectorfromobservationaldata.EachobjectprocessedbytheGIOWGoperatorconsistsofthreecomponents,wherethefirstcomponentrepresentstheimportancedegreeorcharacterofthesecondcomponent,andthesecondcomponentisusedtoinduceanordering,throughthefirstcomponent,overthethirdcomponentswhicharethenaggregated.Thedesirableproperties,suchascommutativity,idempotencyandmonotonicity,etc.,associatedwlththeGIOWGoperatorarestudiedindetail,andsomenumericalexamplesaregiventoshowthepracticalityandeffectivenessofthedevelopedoperator.

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简介：Theauthorsdefinethesceneryflowofthetorus.Theflowspaceistheunionofallflat2-dimensionaltoriofarea1withamarkeddirection(orequivalently,theunionofalltoriwithaquadraticdifferentialofnorm1).Thisisa5-dimensionalspace,andtheflowactsbyfollowingindividualpointsunderanextremaldeformationofthequadraticdifferential.Theauthorsdefineassociatedhorocycleandtranslationflows;thelatterpreserveeachtorusandarethehorizontalandverticalflowsofthecorrespondingquadraticdifferential.Thesceneryflowprojectstothegeodesicflowonthemodularsurface,andadmits,foreachorientationpreservinghyperbolictoralautomorphism,aninvariant3-dimensionalsubsetonwhichitisthesuspensionflowofthatmap.Theauthorsfirstgiveasimplealgebraicdefinitionintermsofthegroupofaffinemapsoftheplane,andprovethattheflowisAnosov.Theygiveanexplicitformulaforthefirst-returnmapoftheflowonconvenientcross-sections.Then,inthemainpartofthepaper,theauthorsgiveseveraldifferentmodelsfortheflowanditscross-sections,intermsof:●stackingandrescalingperiodictilingsoftheplane;●symbolicdynamics:thenaturalextensionoftherecodingofSturmiansequences,ortheS-adicsystemgeneratedbytwosubstitutions;●zoomingandsubdividingquasi-periodictilingsoftherealline,oraperiodicquasicrystalsofminimalcomplexity;●thenaturalextensionoftwo-dimensionalcontinuedfractions;●inductiononexchangesofthreeintervals;●rescalingonpairsoftransversemeasurefoliationsonthetorus,ortheTeichmiillerflowonthetwice-puncturedtorus.

简介：ThemodeloftheuniversalTeichmullerspacebythederivativesoflogarithmistheunionofinfinitedisconnectedcomponents.Inthispaper,thefactthateachcomponentisnotstarlikewithrespecttoitscenterisproved,andtheouterradiusofthespacewithrespecttoeachcenterisobtained.

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简介：InthispaperwepresentatransformationpathalgorithmforUnconstrainedSignomialGeometricProgramming(USGP).ThealgorithmisproposedfromanewpointofviewbasedonexploringthecharacteristicsofUSGPproblem.Firstlybysomestabletransformations,aparticularsubproblemisderivedwhichisveryeasytosolve.Secondly,aspecialpathisformedconveniently.Andthenthestepofthealgorithmconsistsinfindinga"good"pointtothecurrentiteratebychoosingitalongthespecialpathandwithinatrustregion.Itisprovedthatthealgorithmisgloballyconvergent.

简介：Let{X(t),t≥0}beBrownianmotiononSierpinskigasket,TheHausdorffandpackingdimensionsoftheimageofaompactsetarestudied,TheuniformHausdorffandpackingdimensionsoftheinverseimagearealsodiscussed.

简介：<正>ThedifferentiabilityofanormofaBanachspacemaybecharacterizedbyitsunitsphere.Thispapergeneralizesthesegeometricconditionsofnorm’sdifferentiabilitytothecaseofaregularlocallyLipschitzfunction.

简介：Theexploitationofdifferentnon-rigorousmathematicalmodelsasopposedtothesatelliterigorousmodelsisdiscussedforgeometriccorrectionsandtopographic/thematicmapsproductionofhigh-resolutionsatelliteimagery(HRSI).Furthermore,thispaperfocusesontheeffectsofthenumberofGCPsandtheterrainelevationdifferencewithintheareacoveredbytheimagesontheobtainedgroundpointsaccuracy.Fromtheresearch,itisobviouslyfoundthatnon-rigorousorientationandtriangulationmodelscanbeusedsuccessfullyinmostcasesfor2Drectificationand3Dgroundpointsdeterminationwithoutacameramodelorthesatelliteephemerisdata.Inaddition,theaccuracyuptothesub-pixellevelinplaneandaboutonepixelinelevationcanbeachievedwithamodestnumberofGCPs.

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简介：GeometricprocesswasfirstintroducedbyLam^[10,11].Astochasticprocess{Xi,i=1,2,...}iscalledageometricprocess(GP)if,forsomeα>0,{a^i-1Xi,i=1,2,...}formsarenewalprocess.Inthispaper,theGPisusedtoanalyzethedatafromaseriesofevents.AnonparametricmethodisintroducedfortheestimationofthethreeparametersintheGP.Thelimitingdistributionsofthethreeestimatorsarestudied.Throughtheanalysisofsomerealdatasets,theGPmodeliscomparedwithotherthreehomogeneousandnonhomogeneousPoissonmodels.ItseemsthatonaveragetheGPmodelisthebestmodelamongthesefourmodelsinanalyzingthedatafromaseriesofevents.

简介：Inthispaper,thequadraticprogramproblmandminimumdiscrimiationinformation(MDI)problemwithasetofquadraticinequalityconstraintsandentropyconstraintsofdensityareconsidered.Basedonthepropertiesofthegeneralizedgeometricprogramming,thedualprogramsofthsestwoproblemsarederived.Furthermore,thedualitytheormsandrelatedKuhn-Tuckerconditionsfortwopairsoftheprime-dualprogramsarealsoestablishedbythedualitytheory.

简介：In1980'sdifferentialgeometricmethodsaresuccessfullyusedtostudycurvedexpomentialfamiliesandnormalnonlinearregressionmodels.Thispaperpresentsanewgeometricstructuretostudymultinomialdistributionmodelswhichcontainasetofnonlinearparameters.Basedonthisgeometricstructure,thesuthorsstudyseveralasymptoticpropertiesforsequentialestimation.Thebias,thevarianceandtheinformationlossofthesequentialestimatesaregivenfromgeomentricviewpoint,andalimittheoremconnectedwiththeobservedandexpectedFisherinformationisobtainedintermsofcurvatvremeasures.Theresultsshowthatthesequentialestimationprocedncehassomebetterpropertieswhicharegenerallyimpossiblefornonsequentialestimationprocedures.

简介：TheeccentricityofthecentreofmassfromthegeometriccentreofasphericalattractingmassindeterminingtheNewtoniangravitationalconstantGistestedbymeansofanelectronicbalance.Theexperimentalresultshowsthattheeccentricityofthesampleisabout0.31μmwithuncertaintyof0.05μm.TwodensitydistributionmodelsarediscussedtoestimatetheuncertaintytoGbytheeccentricitiesoftheattractingmasses.

简介：GivenastablematrixA∈Cn×n,therearesomesimplesimultaneousinequalitieswhosecoefficientsrelyonA.For（?）PH=P∈Cn×n,ifPsatisfiestheseinequlities,thenPA+AHP<0.Asanapplicationofthemainresults,thestabilityofthematrixfamilyistreated.Besides,somegeometricpropertiesofthesetofalltheLyapunovmatricesofagivenstablematrixareconsidered.