双线性

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

In addition, the nonlinear processes such as cross-phase modulation, non-degenerate two-photon absorption, and stimulated Raman scattering must also be considered for double wavelengths propagating in waveguide.

在归纳分析了SOI对光信号处理的研究进展的基础上，进一步完善了超快脉冲在脊形硅波导中演变时所满足的线性和非线性传输方程，在此非线性方程中包括波导线性损耗、群速度色散和三阶色散等线性效应；同时也包含了自相位调制、简并双光子吸收、自由载流子吸收和自由载流子色散等非线性过程；当双光场在波导中传输时，脉冲之间的交叉相位调制、非简并双光子吸收和受激拉曼散射效应等非线性效应也被考虑。

A new identity-based blind signature scheme from pairings is proposed, inwhich there is only one pairing operation.

6给出一个新的基于身份和双线性对的盲签名方案，在方案中只有一个对运算。

A new ID-based Chameleon signature scheme is proposed in this paper which is based on the bilinear pairings. It's secure under Random Oracle.

利用双线性对，提出一个新的基于身份的变色龙签名，在随机预言机下是安全的。

An authenticated encryption scheme based on self certified of public key from bilinear pairings is proposed.

提出了一种基于双线性对和公钥自证明的认证加密方案。

Part II of this paper studies the structure of symmetric self-dual Lie algebras.

假设李代数g带有一个与Killing具有相同性质的型B，即具有双线性性，非退化性，对称性和不变性，由于这样的李代数g的伴随表示与它的余伴随表示等价，我们称李代数g为对称自对偶李代数，称型B为它上的一个不变数积。

Yanowitz algorithm which interpolates the image grey by gradient imformation. Then it can get water meter frame information by horizontal and vertical projection, and extract line by improved Hough transform. Finally, the image can be corrected by affine transform.

Yanowitz算法，能够很好的分割目标和背景；再利用水平和竖直投影提取水表表框信息；然后再利用改进的Hough变换提取表框范围内直线，对结果进行统计分析，求出水表的倾斜角度；最后采用逆仿射变换的方法，对表框图像进行双线性插值旋转，得到表框的矫正图像。

In this thesis, we study the problem about subconvergence and a self-adaptive posteriori error estimates of bilinear finite element.

中文摘要：本文主要是研究双线性有限元的慢收敛和自适应后验误差估计的有关问题。

We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control.

我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

The second part is the controllability of parabolic equation .We study on the controllability of parabolic systems with a nonlinear term involving the state and the gradient ,the null-controllability property of a 1-d parabolic equation involving a fractional power of the Laplace operator ,null controllability of some systems of two parabolic equations with one control force ,and exact controllability of the parabolic system with bilinear control .

第二部分写的是，抛物方程的能控性，我们研究了含有状态和梯度的非线性的项抛物系统的能控性，含有拉普拉斯算子的分数阶的1-d抛物方程的零能控性，带有一个强控制的两个抛物方程的一些系统的零能控性和具有双线性控制抛物系统的精确能控性。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。