简介：Geometriccomputingisanimportanttoolindesignandmanufacturingandinarts.Conventionally,geometriccomputingistakenbyalgebraiccomputing.Thevividintuitionofobjectsinvisualizationislostinnumericfunctions,whichishoweververyusefultohumancognitionaswellasemotion.Inthispaper,weproposedaconceptandtheoryofgeometricbasis(GB)asthesolvingcellforgeometriccomputing.EachGBrepresentsabasicgeometricoperation.GBworksasbothexpressingandsolvingcelljustliketheconceptofbasisinlinearalgebrabywhicheveryelementofthevectorspacecanbeexpressed.For3Dproblems,withaprocedureofaprojectionsreduction,theproblemcanbereducedtoplaneandthereductionfunctioncanbedesignedasaGB.AsequenceofGBcanconstructahigherlayerGB.Then,bythetraversaloftree,asequenceofGBisgotandthissequenceisjusttheconstructionprocessandalsothesolutionofthisgeometricproblem.

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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：Theemergenceofalargequantityofdigitalresourcesingeometry,variousgeometricautomatedtheoremprovingsystems,andkindsofdynamicgeometrysoftwaresystemshasmadegeometriccomputation,reasoning,drawing,andknowledgemanagementdynamic,automaticorinteractiveoncomputer.Integrationofelectroniccontentsanddifferentsystemsisdesiredtoenhancetheiraccessibilityandexploitability.Thispaperproposesanequivalenttransformationframeworkformanipulatinggeometricstatementsavailableintheliteraturebyusinggeometrysoftwaresystems.Suchaframeworkworksbasedonanewlydesignedgeometrydescriptionlanguage(GDL),inwhichgeometricstatementscanberepresentednaturallyandeasily.TheauthordiscussesandpresentskeyproceduresofautomaticallytransformingGDLstatementsintotargetsystem-nativerepresentationsformanipulation.Theauthoralsodemonstratestheframeworkbyillustratingequivalenttransformationprocessesandinterfacesforcompilingthetransformationresultsintoexecutableformatsthatcanbeinterpretedbythetargetgeometrysoftwaresystemsforautomatedtheoremprovinganddynamicdiagramdrawing.

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。

简介：让B(R~n)是所有nxn的集合真实矩阵，S_r有等级r，0鈮?r鈮?n，和S_r~#的所有矩阵的集合弧的数字S_r的明智的连接部件。它知道iswell那S_n=GL(R~n)是一个谎言组并且另外在有尺寸nxn的B(R~n)的光滑的亢奋的表面。但是我们还没单个矩阵S_r的几何建设怎么样知道那，0

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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：Polygonalmodelsarepopularrepresentationsof3Dobjects.Theuseofpolygonalmodelsincomputationalapplicationsoftenrequiresamodeltoproperlybounda3Dsolid.Thatis,thepolygonalmodelneedstobeclosed,manifold,andfreeofself-intersections.Thispapersurveysasizeableliteratureforrepairingmodelsthatdonotsatisfythiscriteria,focusingoncategorizingthembytheirmethodologyandcapability.Wehopetoofferpointerstofurtherreadingsforresearchersandpractitioners,andsuggestionsofpromisingdirectionsforfutureresearchendeavors.

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：Hybridmodelsderivedfromrotationalsolidslikecylinders,conesandsphereswereimplementedonCATIAsoftware.Firstly,maketheisoscelestriangularprism,cuboid,cylinder,cone,sphere,andtheprismwithtangentconicandcurvedtriangleends,thecuboidwithtangentcylindricalandcurvedrectangleends,thecylinderwithtangentsphericalandcurvedcircularendsasthebasicBooleandeferenceunitstotheprimarycylinders,conesandspheresonsymmetricalandsomecriticalgeometricconditions,formingaseriesofvariantsolidmodels.Secondly,makethedeferenceunitsaboveasthebasicunionunitstothemaincylinders,cones,andspheresaccordingly,forminganothersetofsolidmodels.Thirdly,makethetangentendsofunionunitsintoobliqueconic,cylindrical,orwithrevolvedtriangularpyramid,quarterlycylinderandannulusendsonsketchbasedfeaturestothemaincylinders,cones,andspheresrepeatedly,thusformingstillanothersetofsolidmodels.Itisexpectedthatthesederivativemodelsbebeneficialbothinthestructuredesign,hybridmodeling,andfiniteelementanalysisofengineeringcomponentsandincomprehensivetrainingofspatialconfigurationofengineeringgraphics.

简介：ThemodeloftheuniversalTeichmullerspacebythederivativesoflogarithmistheunionofinfinitedisconnectedcomponents.Inthispaper,thefactthateachcomponentisnotstarlikewithrespecttoitscenterisproved,andtheouterradiusofthespacewithrespecttoeachcenterisobtained.

简介：BasedonexactGreenstrainofspatialcurvedbeam,thenonlinearstrain-displacementrelationforplanecurvedbeamwithvaryingcurvatureisderived.Insteadofusingthepreviousstraightbeamelements,curvedbeamelementsareusedtoapproximatethecurvedbeamwithvaryingcurvature.Basedonvirtualworkprinciple,rigid-flexiblecouplingdynamicequationsareobtained.Physicalexperimentswerecarriedouttocapturethelargeoverallmotionandthestrainofcurvedbeamtoverifythepresentrigid-flexiblecouplingformulationforcurvedbeambasedoncurvedbeamelement.Numericalresultsobtainedfromsimulationswerecomparedwiththoseresultsfromthephysicalexperiments.Inordertoillustratetheeffectivenessofthecurvedbeamelementmethodology,thesimulationresultsofpresentcurvedbeamelementsarecomparedwiththoseobtainedbypreviousstraightbeamelements.Thedynamicbehaviorofaslider-crankmechanismwithaninitiallycurvedelasticconnectingrodisinvestigated.Theadvantageofemployinggeneralized-αmethodispointedoutandthespecialnonlineardynamiccharacteristicsofthecurvedbeamareconcluded.

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简介：Thegeometricshapesofspecimensareimportantinimpacttensiletestsbecausegeometricshapesdeterminethestressstatesofthespecimens,andprecisegeometricshapescanobtainpropermaterialpropertieswithoutnon-materialfactors.Theaimofthisstudywastoinvestigatethe1Dformofthestressbychangingthelength-to-diameter(L/D)ratiosofspecimens.TheexperimentswerecarriedoutonasplitHopkinsontensilebar(SHTB)-rotatingdiskindirectbar-bartensileimpactapparatus.TheL/DratiosoftheLY12CZspecimensusedinthetestrangedfrom1to5.ResultsshowthatthespecimenscanbeusedtoobtainexactparametersofmaterialsundertheproposedconditionswhentheL/Dratioisgreaterthan2.Thisisbecausethelongerlengthwillreduceoreliminatetheeffectsoftheinterfaces.

简介：三个最佳的线性态度评估者用一条几何途径为太空船态度的单个点的即时评价被建议。最后的最佳的态度被修改Rodrigues参数(MRP)代表。在为每测量价值介绍偶然的右边的直角的坐标以后，三错误向量被点或/并且生气产品的使用获得。相应optimality标准严厉地二次、非强迫，它不与Wahbas与抑制标准一致。奇特，当主要角度接近时，发生，能被一合适的旋转容易避免。数字模拟证明建议三个最佳的线性评估者能提供与遵循Wahbaoptimality定义的那些可比较的精确，并且比著名四元数评估者(探索)有更快的计算速度。

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

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