实数域

The shortest path between two truths in the real domain passes through the complex domain.

（在实数域中，连接两个真理的最短的路径是通过复数域。

By using unified method , we investigate decomposability of real or complex cubic polynomials in several elements .

这里，本文将运用统一的方法对实数域和复数域上的多元三次多项式的分解问题加以讨论。

After a cubic polynomial with several elements is represents as a product of matrices , a sufficient and necessary condifion for decomposability is given , i.e.

首先介绍实数域和复数域上的二元二次多项式的分解问题，然后引入多元三次多项式分解。

This paper introduces the real number domain and limited domain of the definition of Elliptic Curves, it introduces the basic principles of Diffie-Hellman key exchange in detail which bases on the definition of Elliptic Curve Cryptosystem, and the methods of implementation which makes use of Elliptic Curve. It analysis the advantages and disadvatages of the Diffie-Hellman key exchange technology , and gives a worthwhile improvement in the same time.

本文介绍了在实数域和有限域中椭圆曲线的基本定义，然后以椭圆曲线的基本定义为基础，详细论述了基于椭圆曲线密码的 Diffie-Hellman 密钥交换的基本原理及利用椭圆曲线实现密钥交换的方法，分析了Diffie-Hellman 密钥交换技术的优缺点，并给出了值得改进的地方。

And we know by study, so long as system is controllable and observable at the structure over the field F(z of the rational functions in multi-parameters, it is always controllable and observable over the field R of real numbers.

通过研究我们知道，一个系统只要在结构上多元有理函数域(F上是能控能观的，则意味着实数域上该系统实际上总是能控能观的。

Now the controllability theory in linear systems over the field R of real numbers has been heavily studied. This theory is efficacious for analyzing the characters which are determined by the value of physical parameters and system structure, nevertheless a practical system has a definite structure and has approximate, even unknown parameter sometimes because of a limit to experiment conditions, or a limit to making technology, the errors of observation. It is inconvenience for a linear system over the field R of real numbers to analyze the structure characters of a physical system, such as structural controllability.

目前，实数域上的系统的完全能控性理论研究已经很成熟了，它用于分析系统结构和物理参量的值共同决定的那些性能是有效的，然而，在工程中，由于实验条件或者制造工艺上的限制和观测上的误差，以及人为地对数据的近似处理，一个实际系统往往其结构是确定的，而参数只是近似的甚至未知的，实数域上的系统不便于分析物理系统的结构性质，如结构能控性。

To overcome the local optimal problem existing in some maximum likelihood DOA estimation algorithms, improve the estimation accuracy, a global optimal solution of nonlinear maximum likelihood DOA estimation is obtained by real-valued genetic algorithm proposed in this paper.

所提出的实数遗传算法由含实数域结构和目标函数信息的实数交叉和变异算子构成，是较理想的获取非线性实变量函数全局最优解的方法。

At the same time,comparing the properties and applications of orthogonal matrix,we discuss the properties and applications of the generalized orthogonal matrix.

对照实数域上正交矩阵的性质和应用的研究，讨论了复数域上酉矩阵的性质以及应用。

Two kinds of Unitary transitions are proposed to transfer complex-valued matrix computation to real-valued matrix computation.

给出了两类酉变换矩阵，将复数域的矩阵运算转换到实数域。

In the last two chapters, this thesis first develops two quaternion-based color image filtering methods that are based on the quaternion rotation theory and quaternion unit transform, respectively, then analyzes the fulfillment algorithm of the QSVD (Quaternion Singular Value Decomposition) and its applications to color image processing, and expands the real number-valued PCA to quaternion-valued PCA.

在论文的最后二章，通过利用四元数旋转和色调抵消机制以及四元数单位变换来表达二个彩色像素的色调差异，提出了二个基于四元数理论的彩色图像滤波的新方法；并分析了四元数奇异值分解QSVD (Quaternion Singular Value Decomposition)的实现算法及其在彩色图像处理中的应用；同时将实数域上的主成份分析扩展到四元数域，形成了四元数版本的主成份分析QPCA (Quaternion Principal Component Analysis)。

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。