正交性

The algorithm transform the line parallelism and plane orthogonality into some new constraints on auto-calibration equations, which makes the affine and Euclidean characteristics of the absolute quadric close to the practical one.

该算法将景物中出现的直线的平行性和平面的正交性转换为新的求解相机自定标方程的约束条件。

An adaptive grid scheme controlling cell area is used to generated grids in the divergent section of symmetric annular nozzle, and the generated grids are used in the flowfield calculation through the uncoupled way. The elliptic equations are used to generate grids in three dimensional regions of FDN divergent section, the source terms used in the equations employ a mathematical form which is independent of the boundary shape and of the boundary grid point distribution, the free parameters contained in the source terms are determined by the two restraint conditions, the intersection angle of transverse grid lines with boundaries and the local curvature of the transverse grid lines at the boundaries, and the interior grid distribution controlled directly by the grid point distribution assigned on the boundaries is realized, it makes the grid more clustering near the nozzle wall. For the generated grids in the whole computational regions have a good smoothness and orthogonality, the accuracy of calculation in the flowfield is ensured.

对轴对称的环形喷管采用控制网格面积的自适应网格方法对扩散段部分进行了网格生成，并通过非耦合方式应用于喷管的流场计算中；对强制偏流喷管扩散段内的三维区域采用椭圆型方程进行网格生成，方程中的源项采用了与边界形状和边界网格点分布无关的数学形式，源项内的自由参数由横向网格线与边界的交角及横向网格线在边界处的局部曲率两个约束条件来确定，实现了由边界上的网格分布直接控制内部的网格点，使壁面附近具有较密集的网格，并且在整个计算区域内的网格都具有良好的光滑性和正交性，从而保证了流场计算的准确性。

Part or all of the mesh can be eliminated by using the compact support, the orthogonality and other properties of the wavelet function and the meshless algorithm to enhance the computing capability and reduce the error.

利用小波函数的紧支性、正交性等性质及无网格算法可以部分或全部消除网格而具有提高计算能力且减少误差的优点。

Bring forward a kind of learning algorithm fitting on the base of spline function, because the spline function has good flexibility and quadratic smoothing property, the search problem of network weight functions training can be converted into the resoluting extreme value problem of the plurality function through using spline function to represent network input and link weight functions, thus the PNN can be trained with the help of the existing neural network learning algorithms;④build a kind of learning algorithm base on the alternate of Walsh function, the complexity of network computing can be decreased through using the complete orthogonality of Walsh function corollary.

应用结果表明该算法收敛速度快，稳定性好；③提出了一种基于样条函数拟和的学习算法，由于样条函数具有很好的柔韧性和二次光滑性，将网络输入函数和连接权函数用样条函数的形式表示，可把网络权函数训练的函数寻优问题转换为多元函数求极值的问题，从而可借助于现有的神经网络学习算法训练过程神经元网络；④建立了一种基于Walsh函数变换的学习算法，利用Walsh函数系的完备正交性，可大大降低网络计算的复杂度。

The orthogonality and completeness of the eigenfunctions are proved according to certain theories of Hilbert space.

借助Hilbert空间的理论证明了特征函数的正交性与完备性。

In chapter 4, Based on the orthogonality relations and duality of C-algebras, we study the decompositions of C-algebras, and give a Fourier inversion formula on C-algebras, which generalizes the Fourier inversion formula on the center of a finite group algebra over complex. As an application, we characterize the integral closure of C-algebras over the ring of integers, and show a necessary and sufficitient condition for elements of C-algbras being algbraic integral over integers.

第四章 我们应用C-代数的正交性及对偶性刻画了C-代数的一个分解，给出了C-代数上这个完全分解的Fourier反演公式，从而推广了Z分解的Fourier反演公式；作为Fourier反演公式的一个应用，我们刻画了Z在整数环Z上的整闭包，进一步我们研究了C-代数在整数环Z上的整闭包，给出了C-代数在整数环Z上为整元的一个充要条件。

These new wavelets inherit some basic properties of the corresponding classical wavelets, such as the orthonormality, the order of regularity, the time-frequency localization characteristics, and so on, meanwhile some performances of the new wavelets are improved.

新子波类中的每一个子波均继承了原始子波的许多基本性质，比如规范正交性，正则阶，时、频局域化特性等，同时也得到某些性能的改善。

First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

School of Information Engineering,Zhengzhou University,Zhengzhou 450052,ChinaA novel chirp-typed watermarking scheme which uses the properties of index additivity and orthonormality of fractional Fourier transform to embed watermark in the different fractional Fourier domain is presented.

提出了一种新的分数阶Fourier域Chirp类数字水印方案，该方案利用分数阶Fourier变换基函数的正交性和旋转相加性，在不同的分数阶Fourier域嵌入Chirp水印，并利用分数阶Fourier域Chirp信号的聚集性进行盲检测。

First of all, the basis of the MRTD method is studied. In Chapter 2, waveletsanalysis and multiresolution analysis, the mathematical basis, are introduced, and thecharacteristics of the wavelets basis functions, including orthonormality, compactsupport, multiresolution and so on, are also introduced. The advantages of theapplications of these functions to the numerical electromagnetic calculations arediscussed. In Chapter 3, the algorithm basis of MRTD: the combination of the waveletsand the method of moments is studied. This Chapter shows that the MoM basedMRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

At the rear was an innovative combination transaxle with the gearbox, clutch, differential, and inboard-mounted drum brakes.

在后面是与变速箱，离合器，差的创新结合变速，和内侧安装鼓式制动器。

For more people can apprecaite and have the master work, there is reproduction painting appears in the market, the large various selection of paint,the high saturation of color plus the plentiful sfumato, to make the reproduction perfect copy and detail as original painting, so as to meet the requirment of amateurs who love art paintings,they do not need to pay high price to get classical paintings.

颜料色域广，色彩饱和度高，色彩层次丰富，图像色彩还原真实，能完美的复制原作，满足艺术爱好者欣赏，艺术爱好者们不用支付昂贵的价格就能拥有经典油画。