椭圆的

In strictly, it is hard to make the light normal incident into the sphere, double refraction will take place in crystal sphere when a TEM〓 mode Gaussian beam oblique incident into the sphere, and the two orthogonal polarized beams are both elliptical Gaussian beam. The ellipticity and eccentricity of the elliptical Gaussian beam will change with the incident angle, and for a fixed incident angle, they will change with the shifting of incident beam waist position.

由于严格意义上的正入射较难实现，基模圆高斯光束斜入射晶体球后将在球内产生双折射，且球内偏振态正交的两束折射光都将是椭圆高斯光束，它们的椭圆度e和偏心度Δ随入射角的改变而改变，在入射角一定的情况下，入射光束束腰的移动也将改变这两束折射光的椭圆度e和偏心度Δ。

It briefly includes several following aspects: First, Jacobi elliptic function were introduced and some of its main characters were discussed simply.

本文首先简要介绍了Jacobi椭圆函数及其性质，然后介绍了非线性发展方程的Jacobi椭圆函数展开法和目前的一些演化和扩展情况，最后着重介绍本人对Jacobi椭圆函数在求解非线性发展方程中的应用方面所作的研究。

Taking into account the temperature effect ,the nonlinear vibration of elliptic paraboloid cable net using carbon fiber cables under foundation displacement excitation was studieded.Then the nonlinear vibration equation was presented,whose approximate solution was given with Galerkin principle and KBM method.

在考虑温度变化的基础上，研究椭圆平面双曲抛物面碳纤维索网在基础激励下的非线性振动问题，建立了椭圆平面双曲抛物面碳纤维索网在基础位移激励下的非线性振动方程，采用Galerkin原理及KBM法求得了椭圆平面双曲抛物面碳纤维索网非线性振动的近似解。

A new method of finding the points on an elliptic curve by Maple is supplied; Maple is applied to the addition operation, the scalar product operation and the method of seeking the order of a basic point on the elliptic curve are proposed; the applications of Maple on ECC including encryption and decryption are supplied.

利用Maple编程求出椭圆曲线上有理点，用Maple实现椭圆曲线上两点的加法、点的数乘运算及求某个基点阶数的算法，利用Maple实现椭圆曲线密码体制的加密及解密。相比C语言，Maple语言更接近于平时说话的语法。同时，Maple语言可以方便地转化成C语言。

I will present a feasible scheme for hardware implementation of elliptic curve cryptographic system.

本文结合椭圆曲线算法的数学基础对椭圆曲线密码体制进行深入的分析，对椭圆曲线算法的FPGA实现进行了具体的研究设计，为ECC算法提供了实际可行的硬件解决方案。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

In this dissertation , the main works of the author is follows:(1)The method FPI (Fast Plaintext Imbedded to the divisor) is improved, which makes the probability of the plaintext not be imbedded into the divisor nearly to zero and its velocity is fast.

在本论文中，作者主要做了以下几个方面的工作：(1)改进了明文嵌入超椭圆曲线除子的FPI(Fast Plaintext Imbedded to the divisor)方法，该方法使明文不能嵌入到超椭圆曲线的除子的概率几乎为零，且其速度较快，可用于椭圆曲线密码体制。

For the ovalization-curvature curve, the ovalization exhibits the unsymmetric-increasing ratcheting manner with the number of cycles. It is shown that the width does not affect the aforementioned curve, however, the deeper the sharp-notch, the larger amount of the ovalization to bend the tube to a certain magnitude of curvature.

至於椭圆化-曲度的曲线图中显示，椭圆化会随著循环圈数呈现非对称棘齿状的增加，而凹槽宽度对上述曲线没有太大的影响，但尖锐凹槽的深度越深，弯曲至某固定曲度时所产生的椭圆化量就越大。

We get the results that the elliptic flow decreases with the freeze-out time and the correlation between the elliptic flow and the transverse radius changes with the freeze-out time what could be explained with the pressure gradient.

研究了在不同的阶段，椭圆流对末态粒子位置的关系。结果表明椭圆流随冻出时间的单调递减，椭圆流对横向半径的关系随冻出时间发生变化。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。