超椭圆的

In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

In the rest of this dissertation, we apply our above abstract results,"global Morse theory"and other critical point theorems to some semilinear resonant elliptic boundary value problems as well as some asymptotically"linear"or super"linear"p-Laplacian equations, and obtain the existence or multiplicity of solutions.

在后半部分，我们运用上面的抽象结果，以及大范围Morse理论和其他临界点理论，研究一些半线性椭圆共振问题的多重解的存在性，以及一些渐近线性或超线性p-Laplacian方程的解的存在性或多重性。

The topology analysis of vector field around "a singular point" is refered in the study of the topology of three-dimensional symmetric tensor field around a simple degenerated point, which can be classified into three types of hyperstreamline sectors:"hyperbolic sector","parabolic sector" and "elliptic sector".

本文参考矢量场中"奇点"附近的矢量轨迹分布结构，研究了张量场中"退化点"附近的特征向量分布形态。确定了"退化点"附近"超流线体"轨迹的三种形态。"抛物扇区"、"双曲扇区"、"椭圆扇区"及其这些扇区的边界。

On the basis of published paper, an ID-based provable secure and strong designated verifier signature scheme, a modified strong designated verifier signencryption scheme, and a modified extended aggregate signature scheme based on the supersingular elliptic curve is presented in this thesis.

在已有文献的基础上，综合形成了一种基于身份标识的超奇异椭圆曲线上的强指定验证者的数字签名方案、签密方案和可扩展的群签名方案。

However, the situation has changed after Joux gave a simple tripartite one-round Diffie-Hellman key agreement protocol based on Weil pairing on supersingular curves.

然而，2000年Joux利用超奇异椭圆曲线上的Weil对构造了一个一轮三方密钥协商协议，这可以说是密钥协商协议中的重大突破之一。2001年Boneh等又利用双线性对设计出了实用的基于身份的加密方案和短签名方案。

We directly reduced the Duursma-Lee algorithm applying the theory of divison from the defination of Tate Pairing. Then we introduced a new equavalent defination of Tate pairing of supersingular elliptic curve over finite fields with characteristic three or two, that it has lower final exponent. We proposed two refined algorithms of the modified Duursma-Lee algorithm.

应用除子理论由Tate Pairing的定义直接推导了Duursma-Lee算法；对特征值为3和2的有限域上超奇异椭圆曲线Tate Pairing给出一个等价定义，降低了最后的求幂次数；对Modified Duursma-Lee算法提出两个改进算法，分刖将效率提升了约6.7％和13.3％。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。