椭圆的

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

Finally, conclude by saying that Proposition 18 turns the congruent number problem into a problem purely about elliptic curves; decide if the rank of such curves is zero or not.

最后，作结论，表明命题18把同余数问题转化为纯粹椭圆曲线问题，并判别椭圆曲线的rank是不是为零。

The author not only presents pseudo sphere, ellipsoid ,conoid,uniported hyperboloid,elliptic biparted hyperboloid,paraboloid and hyperbolic paraboloid of the second elemental form,but also curve of the second elemental form.

不但给以了伪球面、椭圆面、劈锥曲面、单叶双曲面、双叶双曲面、椭圆抛物面及双曲抛物面的第二基本形式，而且给以了一般曲面的第二基本形式。

Elliptic curve cryptograph is based on the difficulty of solving discrete logarithm on elliptic curve domain, and therefore it has higher security than other cryptography.

椭圆曲线密码机制是基于椭圆曲线域上求离散对数难度，因此具有更高的安全性。

ECC is set up on the basis of solving this mathematics difficult problem of the Elliptic Curve Discrete Logarithm Problem.

椭圆曲线密码体制建立在解椭圆曲线离散对数问题这一数学难题的基础上。

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

anisotropic medium, elliptic cylinder, scattering, mathieu functions, elliptic coordinates, dynamic stress concentration factor

本文利用椭圆坐标中的变量分离方法，由Mathieu函数给出了各向异性介质中椭圆柱面对SH波散射

First in Section 1 we obtain the estimate of holder norm in time direction about the system of elliptic equation and elliptic equations by difference method and the result will be used in Chapt...

首先，在第一节中我们对椭圆型方程问题和椭圆型方程组问题运用差分方法得到时间方向上的h？

The efficient algorithms to select the high-randomicity secure elliptic curve and randomicity base point are devised and implemented.

深入研究了高效实现椭圆曲线公钥密码体制的若干关键问题，设计和实现了高效安全椭圆曲线和随机基点选取算法。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。