简介：Inthispaper,wepresenttwonewunifiedmathematicsmodelsofconicsandpolynomialcurves,calledalgebraichyperbolictrigonometric(AHT)Béziercurvesandnon-uniformalgebraichyperbolictrigonometric(NUAHT)B-splinecurvesofordern,whicharegeneratedoverthespacespan{sint,cost,sinht,cosht,1,t,...,t~(n-5)},n≥5.ThetwokindsofcurvessharemostofthepropertiesasthoseoftheBéziercurvesandB-splinecurvesinpolynomialspace.Inparticular,theycanrepresentexactlysomeremarkabletranscendentalcurvessuchasthehelix,thecycloidandthecatenary.Thesubdivisionformulaeofthesenewkindsofcurvesarealsogiven.Thegenerationsofthetensorproductsurfacesarestraightforward.Usingthenewmathematicsmodels,wepresentthecontrolmeshrepresentationsoftwoclassesofminimalsurfaces.

简介：Ancientpeoplesfromaroundtheworldknewaboutthespecialrelationshipbetweenacircle'scircumferenceanditsdiameter.π,thenumberrepresentingtheresultwhenacircle'scircumferenceisdividedbyitsdiameter,hadbeenknownandusedonproblemsforthousandsofyears.Consequently,inordertocalculatetheareaofacircle,πisalsoused,area=πr2.

简介：ＯＮＴＨＥＩＳＯＭＯＲＰＨＩＳＭＳＯＦＳＭＯＯＴＨＡＬＧＥＢＲＡＩＣＣＵＲＶＥＳ（Ⅰ）ＤＵＨｏｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉ...

简介：WedefinethenotionofevolutesofcurvesinahyperbolicplaneandestablishtherelationshipsbetweensingularitiesofthesesubjectsandgeometricinvariantsofcurvesundertheactionoftheLorentzgroup.WealsodescribehowwecandrawthepictureofanevoluteofahyperbolicplanecurveinthePoincarédisk.

简介：<正>WegiveatreatmentoftheWeiertrasspointsofcurveswhichisalittledifferentfromthetreatmentbyLaksov.Weintroducethenotionoftheithweightwhichmakesthetreatmenteasierandgivesanalgorithmforcomputingthegapsequenceofaneffectivedivisorandtheweightatapoint.

简介：Weconsidertheclassofparametriccurvesthatcanberepresentedbycombinationofcontrolpointsandbasisfunc-tions.Acontrolpointisletvarywhiletherestisheldfixed.It’sshownthatthelocusofthemovingcontrolpointthatyieldspointsofzerotorsionistheosculatingplaneofthecorrespondingdiscriminantcurveatitspointofthesameparametervalue.Thespecialcaseisstudiedwhenthebasisfunctionssumtoone.

简介：ＡＰＰＲＯＸＩＭＡＴＥＭＥＲＧＩＮＧＯＦＢｅＺＩＥＲＣＵＲＶＥＳＴｏｎｇＲｕｏｆｅｎｇ；ＨｕＳｈｉｍｉｎ；ＷａｎｇＧｕｏｚｈａｏＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ａｓｉｍｐｌｅｍｅｔｈｏｄｆｏｒｍｅｒｇｉｎｇｏｆＢｅｚｉｅｒｃｕｒｖｅｓｉｓｐ...

简介：ＲＡＴＩＯＮＡＬＩＴＹＯＦＴＨＥＯＦＦＳＥＴＳＴＯＡＬＧＥＢＲＡＩＣＣＵＲＶＥＳＡＮＤＳＵＲＦＡＣＥＳ￥ＬＵＷＥＩ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ３１００２７）Ａｂ...

简介：ＣＯＭＰＵＴＩＮＧＡＲＥＡＳＢＯＵＮＤＥＤＢＹＲＡＴＩＯＮＡＬＢＥＺＩＥＲＣＵＲＶＥＳＧｕｏｊｉｎＷａｎｇ；ＴｈｏｍａｓＷ．ＳｅｄｅｒｂｅｒｇＣＯＭＰＵＴＩＮＧＡＲＥＡＳＢＯＵＮＤＥＤＢＹＲＡＴＩＯＮＡＬＢＥＺＩＥＲＣＵＲＶＥＳ￥ＧｕｏｊｉｎＷａｎｇ...

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简介：AsolutiontothereparametrizationofBéziercurvesbysinetransformationofBernsteinbasisispresented.Theneweffectivereparametrizationmethodisgiventhroughthefollowingprocedures:educingSineBernstein-BézierClass-SBBCfunction,definingSBBCcurveanddiscussingtherelationbetweenSBBCandBéziercurve.

简介：Theappriximationpropertiesofgeneralizedconiccurvesarestudiedinthispaper.Ageneralizedconiccurveisdefinedasoneofthefollowingcurvesortheiraffineandtranslatione-quivalentcurves:(i)coniccurvesiincludingparabolas,hyperbolasandellipses;(ii)generalizedmonomialcurves,includingcurvesoftheformx=yr,.rR.r=0,1,inthex-yCartesiancoordinatesystem;(iii)exponentialspiralcurvesoftheformp=Apolarcoordinatesystem.Thistypeofcurveshasmanyimportantpropertiessuchasconvexity,approximationproperty,effectivenumericalcomputationpropertyandthesubdivisionpropertyetc.Applicationsofthesecurvesinbothinterpolationandapproximationsusingpiecewisegeneralizedconicsegmentarealsodeveloped.Itisshownthatthesegeneralizedconicsplinesareverysimilartothecubicpolynomialsplinesandthebesterrorofapproximationisoratleastingeneralprovidedappropriateproceduresareused.Finallysomenumericalexamplesofinterpolationandappro

简介：当错误当模特儿在GIS描述曲线的错误，曲线的一个随机的错误过程被建议。以随机的进程，有关曲线的本地错误的四个特征也就是，意味着错误的错误功能，标准错误函数，绝对误差函数，和相关函数，被提出。一条曲线的全部的错误被随机的错误过程的吝啬的方形的积分表示。概率的意思和上面提及的特征的几何意思也被讨论。一个scandigitization实验被设计检查模型的效率。在实验，一条等高线被数字化因为超过100次和大量样品功能从实验被导出。最后，所有错误特征根据样品功能被估计。实验结果证明在数字化的地图数据的系统的错误不是可以忽略的，并且曲线上的点的错误主要依赖于弯曲和曲线的凹度。

简介：Thispapeerpresentsamethodforcreatingmodificablequarticandquinticcurveswithshape-parameters.ThecuroescanachieveC2evenC3continuityandunifybothinterpolationandapproximationtothecontrolpointswithoutsolvingasystemofequationsorinsertingadditionalcontrolpoints.TheyhavethelocalpropertieslikethecubicB-spline.Besides,thequinticcurvewouldbeablegloballytotendthecontrolpolygon.

简介：Seedgerminationprocesshascloselyrelationwithmaterialtransformationandenergyexchangewithintheseed.Studyonitsthermaleffectisimportantforunderstandingthemechanismandtheinfluencingfactorsoftheseedgermination.ThethermogeneticcurvesofseedgerminationofRobiniapseudoacaciawasmeasuredbyanew-typeconductivemicrocalo-rimetermadeinWuhanUniversity.Therelationshipwasanalyzedbetweenthegerminationthermogeneticregulationandseedgerminationphysiology.ThethermogenticcurveswerefurtheranalyzedbythermokinetictheorytoobtainthedynamicparametersandthethermokineticmodelonseedgerminationofRobiniapseudoacacia.Therelationshipofthethermogeneticpower(μw)andthegerminationtime(h)ofthegerminationprocessof20grainsRobiniapseudocaciaseedsat25℃wasP=208.77/[0.1937+0.8063exp(-0.06563t)]

简介：ＴｈｅＡｐｐｌｉｃａｔｉｏｎｓｏｆＷａｖｅｌｅｔｓｉｎＨｉｅｒａｒｃｈｉｃａｌＲｅｐｒｅｓｅｎｔａｔｉｏｎｓａｎｄＳｍｏｏｔｈｉｎｇｏｆＣｕｒｖｅｓａｎｄＳｕｒｆａｃｅｓ①ＳｕｎＹａｎｋｕｉＺｈｕＸｉｎｘｉｏｎｇＭａＬｉｎｇＢｅｉｊｉｎｇＵｎｖｉｅｒ...

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简介：Thispaperstudiestheadsorptionisothermcurvesoffouraminoacids(glycine,asparticacid,glutamicacidandlysine)andtheeffectsofexistencesofdifferentconcentrationsotCu(Ⅱ)onthem.BoththeadsorptionisothermoftheaminoacidsonthekaoliniteandthatwhenthecopperionCu(Ⅱ)existsbelongtotheLangmuirtype.TheslopesoftheseadsorptionisothermincreasewiththeincreasingconcentrationsofCu(Ⅱ)added.Itcanbeexplainedintermsofformationofthetype(Ⅰ)ternarysurfacecomplexesinthesesystems.TheregularpatternoftheeffectsofcopperionCu(Ⅱ)ontheadsorptionisothermofaminoacidsonthekaoliniteisidenticalwiththatofitseffectsontheexchangeandadsorptionpercentageE(%)-pHonthekaoliniteinthesamesystem.

简介：Thispaperconsiderstwodimensionalsystemswhichhavepurelyimaginaryeigenvalues.Inordertoobtainmorepropositionsofinvariantcurves,theauthorstransformtherealsystemsintocomplexdifferentialsystemsbyusingasuitablelineartransformation.Theauthorsalsoproposeanalgorithmtocomputeexponentialfactors.Animprovedmethodofconstructingintegratingfactorbyusingallinvariantcurvesispresentedandcanbeusedindeterminingthetypeoftheequilibriumpoints.