查询词典 parametric curve

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。

Rational planar curve; rational space curve; rational ruled surface; moving curve/surface;μ-bases; singularity; self-intersection curve; moving curve/moving surface ideal; ideal-theoretic/set-theoretic generators

基础科学，数学，几何、拓扑平面有理曲线；空间有理曲线；有理直纹面；动曲线/曲面；μ基；奇点；自交线；动曲线/动曲面理想；集论/理想论生成元

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ)，这两类序列具有&优&的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

The polarization curve is not sufficient for a reliable and unique validation of a PEMFC model since different parameters can lead to an identical polarization curve. A three-step validation approach is proposed for a complete and unique validation. These three steps are:(1) validated by the global polarization curve,(2) validated by the local current density distribution curve, and (3) validated by the cathode over-potential and anode over-potential versus current density curve. The results from the comparison of four flow-fields show that the PEMFC performance of the flow-fields decreases in order by interdigitated, metal foam, pin-type and parallel.

通过PEMFC参数敏感性研究发现，PEMFC性能受多种参数的影响，这些参数可分为非敏感性参数、敏感性参数和高敏感性参数；与阳极侧参数相比，PEMFC性能对阴极侧的参数更敏感；不同参数值的组合可以得到几乎完全相同的极化曲线，因此电池的极化曲线不足以用于验证数学模型的唯一性与可靠性；为验证PEMFC数学模型的唯一性与可靠性，提出了模型验证的三步法：极化曲线验证、局部电流密度验证和阳极总过电位与阴极总过电位验证。

Based on vector expression of parametric equation of a third－order Bezier curve, Bezier curve interpolation algorithm is proposed in order to imitate tabulation curve.

为了描述列表曲线，本文从三次Bezier曲线参数方程的矢量表达式出发，推导出CNC系统三次Bezier曲线插补法。

Methods The program algorithm was based on non-parametric and parametric ROC curve analysis theory.

但是这些指标受主观选定分界点的影响，难以准确反映诊断方法的优劣。

Based on the parametric design of fair curve,the parametric design method of hull form is presented in the paper.

基于光顺曲线的参数化设计，提出了参数化的船型设计方法。

According to the feature of case design method, first characteristic parametric curve laws about case is studied, and by classifying parametric curves the solving accuracy is improved.

按实例化设计方法的特点，首先研究了实例特征参数曲线规律，并将其分类组织提高实例的搜索速度和问题的求解精度。

Area under ROC curve ; parametric method ; non-parametric method

ROC曲线下面积；参数法；非参数法

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。