椭圆的

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。

In 1976, the International Astronomical Union revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time.

但实际上地球绕日的轨道不是一个圆形，而是一个椭圆形：最初天文单位的定义就是上述椭圆的半长轴的长度。1976年，国际天文学联会把一天文单位定义为一颗质量可忽略、公转轨道不受干扰而且公转周期为365.2568983日的粒子与一个质量相等约一个太阳的物体的距离。

As illustrations of this alleged fact Ayer proceeds to cite perspective ('a coin which looks circular from one point of view may look elliptical from another'); refraction ('a stick which normally appears straight looks bent when it is seen in water'); changes in colour-vision produced by drugs ('such as mescal'); mirror-images; double vision; hallucination; apparent variations in tastes; variations in felt warmth 'according as the hand that is feeling it is itself

艾耶尔接下去援引下述内容作为这个所谓事实的示例：视点（"一枚硬币从一个视角看是圆的，从另外一个视角看则可能是椭圆的"）；折射（"一根小细棍在正常情况下显得是直的，在水中看上去却是弯屈的"）；由药物造成的"颜色视觉"的变化；镜象；复视觉；幻觉；味觉的明显变化；冷暖感的变化（根据感觉冷暖的手本身是

Carleman不等式及其在最优控制问题中的应用.Optimal control theory of distributed parameter systems mainly includes: Pontryagin's maximum principle; controllability; Hamilton-Jacobi equation (i.e., dynamic programming equation); time optimal control, etc.In this dissertation, we establish Pontryagin's maximum principle of optimal control problems governed by some nonlinear differential equations (parabolic differential equations, elliptic differential equations and 3-dimensional Navier-Stokes equations), which in particular could have local solut...

在这篇博士论文中，我们建立了非线性微分方程(包括抛物型微分方程，椭圆型微分方程以及3维Navier-Stokes方程)最优控制问题的庞特里雅金最大值原理，特别地，这些方程可能只有局部解或存在多解(我们称这样的系统为非适定系统，相应的最优控制问题为非适定最优控制问题)，以及适定的非线性发展方程最优控制问题的庞特里雅金最大值原理；我们研究了phase-field系统的时间最优控制问题以及Boussinesq系统的局部内可控性。

Firstly, the mapping of high level programming language to hardware description language is described, some principles of the conversion of algorithm to state machine are also proposed; Secondly, the basic raster graphics algorithms for drawing 2D primitives are introduced, including self-adaptive algorithm of singl...

首先讨论了高级语言描述到硬件描述语言的映射，提出了算法到算法状态机抽象的规律；然后，介绍了现有的基本图形生成算法，包括直线的自适应算法、三角形边相关扫描算法，宽直线线刷子算法及改进的圆形、椭圆的生成算法，同时讨论了加速算法的研究现状；接下来具体讨论了基本图形的硬件实现，给出了各算法的状态机流程图、接口定义和实现框架，并且从理论角度给出了二次曲线加速算法的证明；最后采用EDA工具对VHDL程序进行仿真、综合并实现。

The SeaRovers large oval cock pit for comfortable re-entry and is standard equipped with individually contained double day hatches , an exclusive Point 65 feature - as well as a newly designed super-comfy back rest, an ergonomically designed seat, a retractable skeg and innovative new foot braces. It is available with an optional, ingenious rudder and rudder control system.

SeaRovers 大而椭圆的驾驶室提供舒适的进仓环境，标准配置，包含个人2天的仓口，这是 Point65的独家特色，以及一个新的超轻松的背部休息设计，一个人体功率学设计的坐椅，可收回的 skeg ，创新的脚瞪带，可选择一个设计精巧的裹和舵控制系统。

The ellipse curre equation of circular image is derived based on the theory of spatial analytic geometry and rotation matrix s representation with unit quaternion then a mathematical model of the distortion error is established which relates the distortion error to the foca length of the used CCD camera,the radius as well as the position and the attitude of the inspected circle directly.

研究三维视觉检测中圆的中心经针孔摄像机成像后存在畸变误差的问题，首先基于空间解析几何理论和旋转矩阵的四元数表示法推导出像平面上投影椭圆的参数方程；然后根据参数方程建立圆中心成像畸变误差的数学模型；最后对影响畸变误差的主要因素进行分析。

A chosen vessel 上帝所选的人 the weaker vessel 较弱的人(指女性 lymph node Any of the small, oval or round bodies, located along the lymphatic vessels, that supply lymphocytes to the bloodstream and remove bacteria and foreign particles from the lymph.

淋巴结任一种长于淋巴管内的小的、呈椭圆或圆形的组织，它为血液输送淋巴细胞并清除淋巴液中的细菌和外部成分Also called： lymph gland filter n。滤纸，过滤器，滤波器 vt。

Artificial images with different levels of noise and nature images containing incomplete ellipses were employed to test this algorithm. Experimental results show that the improvements are notable.

通过对含有不同噪声的仿真图片和包括残缺椭圆的实际图片的实验表明，新算法的改进是有效的。

Panicle loose, elliptic to ovate in outline, 15–30 cm; branches 2–4 at each node, erect at first, spreading after anthesis, naked in lower half, scabrid.

轮廓的圆锥花序松散，椭圆的到卵形，15-30厘米；最初在每个节点，直立的分枝2-4，平展的在花后，裸露的在下半部，粗糙。

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。