单位变换

This paper analyzes the property of FNT, the characteristics of Kernel Matrixes and the relationship between Kernel Matrixes of two-dimensional Fermat number transform whose modulus are odd prime and image data, and presents and proves the deduction of the theorem which demonstrates the relationship among different transform matrixes corresponding to different roots of unity under the same odd prime modulus of FNT, and reveals the essence of FNT whose modulus are odd prime.

分析二维Fermat数变换性质、正反变换核的特点、二维模为奇素数的二维Fermat数变换正反变换核以及与图像数据的关系，提出了不同单位根对应变换矩阵间的关系定理的推论，证明了该推论中模为奇素数的二维Fermat数变换的不同单位根对应的变换矩阵之间的关系，揭示了模为奇素数的二维Fermat数变换的本质，在构造离散图象数据Fermat数变换时为单位根的选择奠定了理论基础。

The definition of Wavelet Analysis is that shifting the mother wavelet e.g. which has limited energy, such as shifting for, then proceeding dimensions, we obtained wavelet basis function ,, which make the inside product to the function to analysis With the Fourier transformation to the and, then the equivalent frequency spectrum of wavelet transformation can be expressed as where 、 are the transformations of 、 respectively and i is an imaginary number unit.

小波变换的含义是：把一具有有限能量的母小波，如进行移位后，再进行尺度的伸缩得到小波基函数为然后与待分析的函数作内积，即对和作Fourier变换后，可得到小波变换的等效频域表示为：其中、分别是、的Fourier变换，i为虚数单位。

A substance is through the primary transformation into an upper triangular matrix, the transformation matrix is a unit lower triangular matrix.

实质上是将A通过初等行变换变成一个上三角矩阵，其变换矩阵就是一个单位下三角矩阵。

This is the so-called Duerlite algorithms: from the bottom row of the matrix A do elementary transformation, the diagonal elements into the bottom left of zero, and then show the effect of these lines is equivalent to transform the left by a unit lower triangular matrix, this series of unit lower triangular matrix inverse is the product of L matrices, it is also a unit lower triangular matrix.

这正是所谓的杜尔里特算法：从下至上地对矩阵A做初等行变换，将对角线左下方的元素变成零，然后再证明这些行变换的效果等同于左乘一系列单位下三角矩阵，这一系列单位下三角矩阵的乘积的逆就是L矩阵，它也是一个单位下三角矩阵。

An expression of the unit rank jumping function is the jumping variety of...

综述了Fourier变换、单位脉冲函数、卷积、Laplace变换在电路分析中的应用。

The characteristic vector of the real symmetric matrix should be found out, which is orthogonalized and normalized to a standard orthogonal base and is used as row vector to construct the transformation matrix P, so the P~(-1)AP can be made into diagonal matrix.

实对称矩阵A经相似变换P-1AP可化为对角矩阵，在x =Py 下，不一定能化A的二次型为标准型；应寻求对称矩阵A的特征向量，将其正交化并单位化作为标准正交基，作为列向量构造变换矩阵P，可使P-1AP=Λ为对角阵，在x =Py 下，要将二次型化为标准型，且二次项系数即为对角阵Λ主对角线上元素。

Discrete-time Fourier transform is essentially the unit circle Z transform.

离散时间傅里叶变换实质上就是单位圆上的Z变换。

The algorithm is applied in the segmentation of Magnetic Resonance Imaging of human brain for the 3D reconstruction on dependent of different human tissue structures, in which the problem on wraps between different tissues and fuzzy edges between the different regions in medical volume data may better be settled, which can not be well done by the typical"hard"segmentation using binary logical representation.(3) An accelerated algorithm of volume rendering with X-ray perspective and Phong shading effect based on textures mapping and blending is presented for realizing 3D reconstruction of medical volume data by 2D texture mapping and blending, in which the accelerated algorithm of window transformation is utilized to computing voxels' gray scales and opacities to produce X-ray perspective images, and Phone illumination model is used to import world light sources and an unit spherical surface under the same shading environment as the actual volume rendering is employed to simulate the real reflectional light of per-voxel so that 3D reconstruction possesses illumination effect in the world. Furthermore, 3D matrix transformations of degree rotation and other operations of 3D object are studied, and a fast equivalent method of corresponding shading correction is brought forward to improve its interaction speed in volume rendering process.

该方法利用体数据的窗口变换加速算法将医学体数据转换为计算机显示值，可以得到具有X光透视效果三维图像；该方法提出的Phong明暗处理加速算法利用Phong光照模型引入外部光源，使用一单位球面体来仿真体数据的法线矢量集所产生的反射光强，以快速得到每一个体素的反射光强度，使物体的三维重建达到现实世界中人眼直接观察的逼真效果；此外，还研究了三维重建物体的三维旋转等矩阵变换，提出了一种Phong明暗修正的快速算法来保证了体绘制中三维几何变换的多视角观察的交互速度。

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)。

The control signals of the PWM rectifier are obtained by comparing the current of AC side with triangular wave (or saw-tooth wave) directly, which can implement the steadiness of the voltage of DC side and unit capacity factor of the system. At the same time, harmonic component of the system is abstracted through Instant Reactive Power Method, which can be smoothed by Integrated Learning Boost Converter Control.

本文采用重复学习Boost变换技术，利用滑模变结构控制技术对单相PWM整流器恒频Boost变换进行了分析，提出将交流侧电流直接与三角波相比较得到开关控制信号的方法，实现直流电压恒定不变及系统单位功率因数；同时，利用瞬时无功功率法分析系统谐波，并在谐波域内使用重复学习的控制方法，结合Boost变换技术，有效滤除系统谐波有功电流。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。