参数曲线

The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly.

其基本思想是：首先构造带有形状可调参数的一类平面(-B样条插值曲线，再把其一阶导矢的两个分量分别转化为Bernstein多项式，从而利用Bernstein多项式的正性条件，得到此曲线为单调的充要条件，即形状参数的取值范围，简单、快捷地实现此参数样条曲线的保单调插值。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

On the basis of dual porosity theory,the well test interpretation model which considers the variation of krg versus the volume of liquid is also established and resolved by the implicit method numerically.

摘要通过分析凝析气藏的相图，建立了凝析液饱和度随压力降的变化规律，并回归得出了相应的公式；同时通过对气体压缩因子、黏度随压力、温度的变化，建立了这些参数和无因次压力的关系；在双重介质地层假设的基础上，建立了在试井过程中凝析气相对渗透率随凝析液饱和度变化的凝析气藏试井解释数学模型，采用隐式迭代的方法进行了求解并进行了参数敏感性分析；结果表明：凝析液的饱和度对凝析气藏试井的压力及压力导数曲线有着很大的影响，早期由于凝析液的析出，阻碍了气藏的流动，导致压力及压力导数曲线上升；在凝析液饱和度达到峰值之后，随着凝析液的挥发，凝析气的相对渗透率逐渐恢复，压力及压力导数曲线又回归到正常的径向流位置；由于裂缝和基岩之间的压力差，使得裂缝弹性储容比在测试过程中发生变化，进而影响了压力及压力导数；窜流系数和裂缝弹性储容比的变化决定了窜流段发生的早晚和程度；而基岩中气体黏度的变化使得窜流的发生稍微滞后。

In order to transfer the experimental JR curves from laboratory to real cracked components, a mathematical expression representing a family of the JR curves was constructed for steel 18G2A by using the test data of JR curves for the SENB specimens.

同时，为了将实验得到的18G2A钢的JR曲线应用于实际裂纹构件，建立了JR曲线与约束参数A2之间的关系，给出了与约束参数A2相关的JR曲线族的表达式。

Also the constructed curve is a shape-preserving curve for the original curve. We can also adjust the shape of curves by parameters of trigonometric uniform polynomial curve to approach the polygon closer. The general trigonometric polynomial curves with m degree and C(superscript 2m-1)(m=1, 2, 3) continuity are further presented.

除了通过切点参数，还可以通过三角均匀多项式曲线参数来调整曲线形状，使所得曲线更加逼近多边形，并可进一步、类似地可构造与给定多边形相切的C(上标 2m-1)(m=1， 2， 3)连续的m次三角多项式曲线。

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一，对其有效的表示是造型的基础，而特征参数化表示是其中一种包含语义信息的高层次表示，本文对空间自由曲线的特征参数化表示进行研究，建立了一种针织物线圈的特征参数化几何模型，采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系，并将该模型与能量极小化的方法相结合，得到了一种能较好地预测针织物缩水率的新模型，对随机选取的一些针织布缩水预测实验表明了算法的可行性。

In this chapter, three kinds of target recognition methods are performed, which are:①Target recognition method based on the description of polarization parameter plane. The echo polarization states of target are projected onto the polarization state plane described by the ellipticity ε and the tilt angle τ of the polarization ellipse, the change of parameter following ferquency becomes the chart. According to the changing trait of the chart, the multidimensional polarization feature space of target has been contructed. Furthermore, a series of polarization feature parameters used in designing the structure of target recognition device are extracted, and they are insensible to the posture of target.②Target recognition method based on the description of Poincare polarization sphere. The echo polarization states of target expressed by Stokes vector are projected onto the Poincare polarization sphere. The conception of polarization ferquency stability, which is used in describing the dynamic distribution characteristics of the target echo polarization states on Poincare polarization sphere, has been defined. A group of polarization feature parameters used in designing the structure of target recognition device are extracted, and they are insensible to the posture of target.③Target recognition method based on the description of frequency sensitivity. In accordance with the conception of the polarization state distance defined on Poincare polarization sphere, the frequency sensibility of the physical structure property of target has been investigated, the frequency distribution feature curves in PSD domain are obtained, and targets'features are extracted by means of the curve-fitting method with Least Square Criterion.

这章具体研究了基于三种极化散射特性描述的相应的目标识别方法：①基于极化参数平面描述的目标识别方法，将目标回波极化状态投影到以极化椭圆参数，即椭圆率角ε和倾角τ表征的极化状态平面上，参数随观测频率的变化就形成了图，根据图的变化特点构造了目标的多维极化特征空间，并提取了不敏感目标姿态变化的极化特征参数组来设计目标的识别器结构；②基于Poincare极化球面描述的目标识别方法，采用Stokes矢量表征目标回波的极化状态，并将其投影到描述极化状态的Poincare极化球面上，定义了极化频率稳定度的概念用以刻画目标回波极化状态在Poincare极化球面上的动态分布信息，提取了准方位不变性的目标极化特征，最后设计了目标的识别器结构；③基于频率敏感性描述的目标识别方法，通过在Poincare极化球面上所定义的极化状态距离的概念，研究的是复杂目标物理结构特性对探测信号频率的敏感程度问题，获得了在极化状态距离下的频率分布特性曲线，采用最小二乘估计曲线拟合方法，它既用于极化特征的降维，同时又直接将拟合参数作为目标的分类特征。

Through the new research methods, this thesis has made the following contributions in this field: 1. For the first time the curvature radii and relative angles of a planar continuous curve at discrete points are chosen as local parameters to represent the curve, which reflect clearly the local geometrical characteristics of the curve and are easy to be dealt with.

借助于新的研究方法，本文在这一领域作出如下贡献：（1）首次提出用曲线上离散点处曲率半径和相对转角作为局部参数表示平面连续曲线，直观地反映曲线各个局部的几何特征，且便于曲线的修改和变换，并通过机构运动分析，快速求出机构轨迹的这两个局部参数。

Calculating results show that variation of the propellant inlet pressure makes little impact on engine performance parameters, and the engine will transit to a new stable state. The parameter transition curves are smooth. When the engine thrust is adjusted in a small range within a short period, the parameter transition curves are also reposeful. But when the adjusting range becomes large, the parameter transition curves will fluctuate acutely. Thus, when large range adjusting is required, the time of adjusting should be lengthened or the adjusting should be divided into adequate steps.

计算结果表明，当发动机在某一个稳定工况工作时，发动机入口推进剂压强的变化对发动机性能参数的影响不大，发动机的参数都能比较平稳的过渡到一个新的稳定工况；当发动机在短时间内进行小范围的推力调节时，发动机参数的过渡过程的曲线也比较平稳，但是当在短时间内进行大范围推力调节时，参数的过渡过程的曲线振动比较剧烈，因此应当在进行大范围推力调节时，应当对调节时间进行适当延长，或者分级进行推力调节。

The relations of parametric equations with the route coordinates and the part coordinates are found out according to the curve model,the parametric equations of middle and side stakes in circular curve and easement curve are derived,thence the value of parameters is obtained,the solution procedure is got.

根据曲线模型，找出线路控制坐标系与局部坐标系坐标之间的参数方程关系，推出了缓和曲线及圆曲线中边桩坐标的参数方程，代入已知量求得参数的值，给出了求解步骤。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。