查询词典 theoretical 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 the theories of rheology, Non-Newtonian Fluid Mechanics, petroleum chemistry, crystallography and pipeline technology etc. and sampling Huabei crudes, experimental indexes and programmes are drew out, integrating the oil properties and parameter analysis; in terms of the macro analysis of continuum mechanics, substantial experiments are conducted with HAAKE RS600 rotational rheometer and the rheological equation as well as the viscosity-temperature equation are further developed with tested rhrogramme and viscosity-temperature curve, respectively. Beased on the researches on thixotropic mechanism and thixotropy fluid property, hysteresis loop curve, structure failure and viscosity build-up curve as well as shear stress decrement curve for one type oil are first present in this paper. According to the theoretical researches and testing results, a novel thixotropy equation with τ=τ_∞e~ pattern, which is of hi-accuracy, few parameter and simplicity, is developed. Considering the influence of various parameters on rheological behaviour, depressant adding condition is optimized and experimental evaluation on BEM-5P is conducted, which further unrip its mechanism on the Huabei crude. A corresponding viable pipe transportion programmel is also recommended.

本文基于原油流变学、非牛顿流体力学、石油化学、结晶学、原油管输工艺学等理论，以华北原油为研究对象，结合原油物性及实验影响因素分析，制定出实验研究的评价指标及实验方案；从连续介质力学宏观分析的角度，利用HAAKE RS600高端旋转流变仪开展了大量的室内实验，并运用微观研究方法，测定了油样的流变曲线和粘温曲线，建立了流变方程和粘温方程；通过对触变性机理和触变性流体特征的研究，首次对华北原油测定出滞回环曲线、结构破坏与恢复粘时曲线、剪切应力裂降过程曲线，并在理论研究和实验结果的基础之上，建立了能定量描述含蜡原油剪切应力裂降过程的新型三参数触变模式τ=τ_∞e~b/(t+c，该模型具有精度高、参数少、实验简便且适用性强的特点；通过对含蜡原油流变性的影响因素理论研究，开展了加剂条件优选及BEM-5P降凝剂室内评价实验，进一步揭示了降凝剂对华北原油作用机理，在此基础之上，提出了华北原油管输的可行性方案。

Based on the theories of rheology, Non-Newtonian Fluid Mechanics, petroleum chemistry, crystallography and pipeline technology etc. and sampling Huabei crudes, experimental indexes and programmes are drew out, integrating the oil properties and parameter analysis; in terms of the macro analysis of continuum mechanics, substantial experiments are conducted with HAAKE RS600 rotational rheometer and the rheological equation as well as the viscosity-temperature equation are further developed with tested rhrogramme and viscosity-temperature curve, respectively. Beased on the researches on thixotropic mechanism and thixotropy fluid property, hysteresis loop curve, structure failure and viscosity build-up curve as well as shear stress decrement curve for one type oil are first present in this paper. According to the theoretical researches and testing results, a novel thixotropy equationwith τ=τ_∞e~ pattern, which is of hi-accuracy, few parameter and simplicity, is developed.Considering the influence of various parameters on rheological behaviour, depressant adding condition is optimized and experimental evaluation on BEM-5P is conducted, which further unrip its mechanism on the Huabei crude. A corresponding viable pipe transportion programmel is also recommended.

本文基于原油流变学、非牛顿流体力学、石油化学、结晶学、原油管输工艺学等理论，以华北原油为研究对象，结合原油物性及实验影响因素分析，制定出实验研究的评价指标及实验方案；从连续介质力学宏观分析的角度，利用HAAKE RS600高端旋转流变仪开展了大量的室内实验，并运用微观研究方法，测定了油样的流变曲线和粘温曲线，建立了流变方程和粘温方程；通过对触变性机理和触变性流体特征的研究，首次对华北原油测定出滞回环曲线、结构破坏与恢复粘时曲线、剪切应力裂降过程曲线，并在理论研究和实验结果的基础之上，建立了能定量描述含蜡原油剪切应力裂降过程的新型三参数触变模式τ=τ_∞e~b/(t+c，该模型具有精度高、参数少、实验简便且适用性强的特点；通过对含蜡原油流变性的影响因素理论研究，开展了加剂条件优选及BEM-5P降凝剂室内评价实验，进一步揭示了降凝剂对华北原油作用机理，在此基础之上，提出了华北原油管输的可行性方案。

Algebraic curve is commonly used in CAGD. Traditional curve interpolation is in various forms of spline fuction. Although better result can be obtained by spline curve, the former two of elliptic, hyperbolic and parabolic shapes can not be represented by spline curve. An exploring research in this aspect is made in this thesis.

代数曲线是CAGD中经常用到的曲线，以往的曲线插值基本上是采用样条函数的形式，采用这种形式虽然能够获得很好的效果，但样条函数所能表达的形状都是抛物线型，对椭圆型与双曲线型曲线的表示是无能为力的。

The cubic algebraic curves (the Bezier curve and B style curve, etc belong to the parameter curve) is apter to realize the curve transition and fitting to dispersed data than the cubic parametric curves.

比如参数曲面与平面的交线就是一条平面代数曲线；平面参数曲线的等距曲线也是一条代数曲线。

In the term of unloading and opposite side loading, let the stress-strain curve have the same form of skeleton curve, the curve uses the last unloading point as its starting point, and uses soil's ultimate stress level as its asymptote. Then the hysteretic curve is constructed.

在卸载和反向加载时，采用与骨架曲线相同的函数形式，并以前一次卸载开始点作为起点，以土体的极限应力水平作为渐近线，构造出土体动力本构模型的滞回曲线。

Hanna: That's over now, isn't it?

都结束了，对吗

You must be ill. You look so pale.

你一定是病了，你的脸色苍白。