参数曲线

For fitting ROC curves and getting the area under the ROC curve, we applied the parametric methods of binormal models and ordinal regression models, the semiparametric method of Cox proportional hazards model, the nonparametric methods of Hanley, Delong.

本文采用双正态模型、有序回归模型等参数法，Cox比例风险模型半参数法，Hanley、Delong非参数法拟合了ROC曲线；文中也考虑了样本量的估计、协变量的混杂效应、再抽样技术计算ROC曲线下面积的标准误与可信区间等问题；并研究了SROC分析方法。

In order to overcome shortcomings that the circular arc and ellipse could not be accurately represented by CE-Bézier curves, this method used the continuity condition of CE-Bézier curves and C-Bézier curves to resolve the representation of circular arc and ellipse in CE-Bézier curve modeling.

该方法首先构造了一种具有优良形状可调性和更好逼近性的带3个形状参数α，β，γ的三次扩展Bézier曲线(CE-Bézier曲线)；并针对CE-Bézier曲线无法精确表示圆弧和椭圆弧等二次曲线的缺点，利用CE-Bézier曲线与C-Bézier曲线间的拼接技术，解决了CE-Bézier曲线造型中圆弧和椭圆弧的表示问题。

The advantage of this measure is that the optimum rational reparameterization's parametric speed satisfies that the maximum deviation from unity is the minimum in this family.

利用该方法求得的最优参数化在曲线的重新参数化曲线族中，参数速度偏离单位速度的最大值达到最小。

In this paper,a rational approximation method of the norm of parametric speed is given,which is more effective than the polynomial approximation.

文章根据等距曲线逼近的关键在于对其参数速度模的逼近，提出了对参数速度模有理逼近的2种形式，在此基础上给出了平面Bézier曲线等距曲线的逼近函数和误差估计函数，并导出了保持法矢平移方向的代数方式的等距有理逼近算法。

Objective To elucidate and compare the parametric method and non-parametricmethod in estimation of the area under ROC curve, so as to provide a basis fortheir application in diagnosis assessment.

中文摘要：目的本研究旨在以ROC曲线分析的理论与实例相结合的方式，阐述Hanley和McNeil非参数法、双正态模型参数法估计ROC曲线下面积，以及通过两个小样本(每组例数均＜100)实例探讨两种估计方法结果的差异，为医务工作者选择适宜的ROC曲线下面积的估计方法提供参考。

The first class of curve contains the quartic Wang-Ball and Said-Ball curve and many curves locating between them. The second class of curve contains the quartic Said-Ball and Bézier curve and many curves locating between them. By analyzing the relation between the new curves and the quartic B6zier curve, the geometric meaning of the shape parameters is obtained, and the geometrical drawing method of the new curves is given.

第一种曲线包含了四次Wang-Ball和Said-Ball曲线以及介于它们之间的无数曲线；第二种曲线包含了四次Said-Ball和Bézier曲线以及介于它们之闻的无数曲线；通过分析新曲线与四次Bézier曲线之问的关系，得出了形状参数的几何意义，并给出了它们的几何作图法。

The study of the mineralogy indicates:(1)Few impurity and poor sulfur in thestibnite of Shalagang antimony.(2)From the stibnite's cell parameter, it finds that thecell parameter of Shalagang antimony's stibnite approachs the standard value. And iteduces the forming temperature of the stibnite is between 150℃～200℃.(3)Thequartz in different period have different thermoluminescence curve, and thethermoluminescence curves of the quartz in rich ore havethe characters of gently curve, unconspicuous peak and the luminous intensity has therelationship of positive correlation with the temperature.

矿物学研究发现：(1)沙拉岗锑矿床辉锑矿以所含杂质少，贫硫为主要特征；(2)利用晶胞参数测定得出，沙拉岗锑矿床辉锑矿晶胞参数接近于标准值，推算形成温度在150℃～200℃之间；(3)不同期次石英具有明显不同的热释光曲线，其中主成矿期石英的热释光曲线以发光曲线平缓，峰位不明显，发光强度随温度升高而增强为特征。

Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values.

通过调整形状参数来修改曲线形状是计算机辅助几何设计中一个非常活跃的研究课题，研究形状参数的变化对样条曲线形状的影响，对于增加曲线造型的灵活性是非常必要的。

A necessary and sufficient condition for the curve being torsion curve in every sub-interval is given.

当张力参数趋于零或趋于无穷大时的极限曲线，分别是等距节点的有理三次B样条曲线和其控制多边形，故张力参数可用于调节曲线的光顺性。

Soil water characteristic curve was measured with a sand column for both drying and wetting processes, and the data were used to fit the van Genuchten model. The fitted curve is in good agreement with the actual measurements, residual water content and other factors used in the van Genuchten model were obtained. For the sand studied,. The results from this study may provide reference for research of water and solute movement in unsaturated soil.

利用Van Genuchten模型对用砂性漏斗测量中砂的吸湿过程和脱湿过程土壤水分特征曲线进行拟合，结果表明实测曲线和拟合曲线吻合很好，并得出Van Genuchten模型中的残余含水量、特性参数α和n，模拟计算表明，中砂有α=1.69α的关系，为研究水分和污染物在非饱和土壤中运移问题提供土壤水分运动键参数。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。