曲线

In this paper,We define the notions of lightcone Gauss maps ,Hghtcone pedal curves and lightcone height function of a spacelike curve in Minkowski 4-space, and established the relationships between singularities of these objects and geometric invariants of curves under the action Lorentz group ,and as an applications of standard techniques of singularity theory classified singularities of a spacelike curve in this space .

在本文中我们定义了四维Minkowski空间内类空曲线的光锥高斯映射，光锥垂足曲线，光锥高度函数的概念，建立了这些对象的奇点与在洛仑兹群作用下曲线的几何不变量之间的关系，并且运用奇点理论的标准工具对该空间中类空曲线的奇点进行分类。

The interpolation algorithm of introduced error compensation for complex parametric curve in space is proposed for the high precision interpolation of parametric curve on the basis of studying the first, second order taylor expression parametric curve interpolation algorithm and the plane parametric curves interpolation algorithm.

以一、二阶泰勒展开式参数曲线插补算法和平面参数曲线插补算法研究为基础，提出引入误差补偿值的复杂空间参数曲线高精度插补算法以实现空间曲线的高精度插补。

It is supposed that the initial normal stiffness of unloading and reloading curves is calculated from those of the previous loading and unloading curves, and then the cyclic loading constitutive equation for rock fracture is established.

假定卸载曲线和重加载曲线在法向的起始刚度由前一次加载曲线和卸载曲线决定，从而完全确定岩体节理循环加载本构方程。

An optical system with refraction and total internal reflection was proposed according to the luminous characteristic of LED and the law of energy conservation. The ordinary differential equations satisfying the spots on the contour curve of TIR refractive and reflective planes were established. The coordinates of points on profile curves were obtained by solving these ordinary differential equations using Runge-Kutta method. The profile curves were acquired by curve fitting of the coordinate spots with software UG, and then TIR model of the projector and data of the surface shape suitable for NC manufacture were obtained.

根据LED的发光特性以及能量守恒定律选择采用折射全反射光学系统，通过建立TIR折射面及全反射面轮廓曲线上的点所满足的常微分方程，利用RungeKutta求解常微分方程得到轮廓曲线上点的坐标，再在UG中对坐标点进行曲线拟合得到轮廓曲线，进而得到TIR模型及适合数控加工的面形数据。

The history and representative work of methods of the developable surface modeling and surface development in the field of CAGD are briefly reviewed.

二、推导出了三次C-B？zier曲线导矢计算的简洁公式，证明了B？zier曲线的速端曲线性质对C-B？zier曲线不成立。

The main task of this article contains:compares algorithm and encryption and decryption between the widely-used public key encryption system RSA and ECC;(2) directing against present elliptic curve attack algorithm, uses SEA algorithm to perform choosing of safe elliptic curve and to achieve based on prime field elliptic curve"s ELGamal encryption and decryption and digital signature;(3) discusses elliptic curve"s application on smart card and proposes two identification plans based on EEC.

2针对目前已有的椭圆曲线攻击算法，使用SEA算法实现了安全椭圆曲线的选取，实现了基于大素数域上的椭圆曲线的ELGamal加解密和数字签名。(3)讨论了椭圆曲线在智能卡上的应用，并提出了两种基于ECC的身份认证方案。

This paper introduces the real number domain and limited domain of the definition of Elliptic Curves, it introduces the basic principles of Diffie-Hellman key exchange in detail which bases on the definition of Elliptic Curve Cryptosystem, and the methods of implementation which makes use of Elliptic Curve. It analysis the advantages and disadvatages of the Diffie-Hellman key exchange technology , and gives a worthwhile improvement in the same time.

本文介绍了在实数域和有限域中椭圆曲线的基本定义，然后以椭圆曲线的基本定义为基础，详细论述了基于椭圆曲线密码的 Diffie-Hellman 密钥交换的基本原理及利用椭圆曲线实现密钥交换的方法，分析了Diffie-Hellman 密钥交换技术的优缺点，并给出了值得改进的地方。

This article first introduces the math foundation required by ECC,including the addition rule for elliptic curve point defined over finite field.Then , the principle of ECC is discussed and its security and efficiency of ECC are analyzed.Third, a cryptosystem is designed through analyzing the security requiration, choosing the elliptic curve domain parameters,denoting field element,elliptic curve and elliptic curve point,choosing associate primitves and schemes andpartitioning functional module.Forth, how to develop a crytosystem based on elliptic curve encryption algorithm is investigated.Fifth, a cryptosystem we have developed by us and the testing result is described.

本文首先介绍了ECC的数学基础，对有限域上椭圆曲线点的运算规则进行了详细描述；其次探讨了ECC的原理，分析了ECC的安全性和有效性；第三，设计了一个基于ECC的加密系统，包括系统的安全需求分析，域参数选择，域元、椭圆曲线、点的表示，原语和方案的选择，及整个系统的模块功能划分；第四，在设计的基础上，研究如何开发一个基于椭圆曲线的加密系统；第五，描述了一个我们已经设计与开发的基于椭圆曲线的加密系统，并给出了相应的测试结果。

But one major weakness of the empirical ROC curve estimator is its jagged form, since the true ROC curve is a smooth function.

在ROC 曲线的各种非参数估计中，经验ROC 曲线是最常用的方法，但经验ROC 曲线的函数值是跳跃的，往往与真实ROC 曲线的光滑性不符。

Methods Through the triaxial creep test, the triaxial creep curves and isochorounous stress-strain curves have been obtained, then the creep characteristics of mica-quartzose schist have been obtained by analyzing the triaxial creep curves, and the isochrounous stress-strain characteristics of mica-quartzose schist have been obtained by analyzing the isochorounous stress-strain curves. Finally, an empirical formula of creep curve is obtained by data fitting and the analysis of the relation between time and parameter of fitting formula.

通过三轴蠕变试验首先得到了云母石英片岩的蠕变曲线和应力应变等时曲线，然后对试验曲线进行分析得到云母石英片岩的蠕变特性和云母石英片岩的等时应力应变特性，最后拟合应力应变等时曲线，并分析时间和拟合公式中参数的关系，得出了蠕变经验公式。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。