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The expansion coefficients Of aperture fields are Obtained after the three-dimensional arbitrary aperture fields have been represented by the sum of three-dimensional Gaussian function in the configuration-spatial wavenumber phase space.

本文利用Gabor原理把三维任意口面场表示成离散结构－波数相位空间中三维高斯基函数的叠加，将二维高斯基函数与相位空间谱双重正交的函数推广到三维，从而得到口面场展开函数。

In this paper we contribute the general integral formula of second order linear differential equation with constant coefficients by means of decreasing order So we can integrate directly to solve this kind differential equation .

本文通过降阶法给出了求二阶常系数线性微分方程通解的方法，并根据特征根的不同情形给出了具体的通解公式，即可通过积分直接求微分方程的通解。

Furthermore, we express a real quaternionic polynomial with four general polynomials which have real coefficients, thus build direct relation between real quaternionic polynomials and general polynomials.

新方法以四元数的复表示及其可对角化的特征结构为理论基础，将问题等价为求解2×2矩阵多项式的可对角化解；进一步将四元数多项式用四个实系数多项式表示，建立了四元数多项式与一般多项式的直接关联。

When the vehicle vibrates, the ratio coefficients of the characteristics of components in fixed position and the corresponding characteristics of suspension are a function of generalized coordinates.

车辆振动过程中，实际安装位置的元件特性与悬挂特性的比例系数是广义坐标的函数。为了使数学模型尽量接近实际情况，本文导出了此比例系数与广义坐标的关系。

The derivatives of the nonsmooth equations are computed to make the generalized derivative matrix nonsingular. Then the nonsmmoth damped Newton method is used to solve them.Analytic solutions of the KdV equation with variable coefficients: Shallow water wave problems belong to problems of free surface wave, and can be molded by the nonsmooth equations model given above in principle.

在前面建立的非光滑方程组数学模型和固定网格法基础上，利用广义导数的概念给出了求解渗流自由面的一种新方法-----非光滑阻尼牛顿法，该法是对非光滑方程组求导，适当的处理广义导数矩阵使其非奇异，利用非光滑牛顿法求解。

By analyzing the bode diagram of HAPF system and minimizing the capacity of HAPF, the paper presents a frequency dividing control method based on fuzzy-PI. In this mean generalized integrator is used for frequency dividing integral and fuzzy arithmetic is for adjusting PI coefficients timely. Compare with other kinds of control methods, the proposed one is more simple and easier realization.

该文由常用的并联型HAPF的结构特点分析出发，从容量和幅频特性2个方面探讨HAPF控制中进行有效分频的必要性，根据HAPF对控制方法的要求，文章提出一种基于广义积分的模糊自整定PI控制方法，即通过广义积分实施对周期量的分频积分，同时由模糊算法进行比例和积分系数的在线调整，从而有效实现对HAPF的分频控制。

For reducing boundary distortion area, the elevations of grid DEM are viewed as a discrete sequence under a generalized coordinate, so that the boundary problem of two-dimensional discrete wavelet transform is turned into the boundary problem of one-dimensional discrete wavelet transform, which not only greatly reduces the boundary distortion area, improves the precision of reconstructed DEM data near the boundary, but also decreases the number of zeros adding on the boundary for wavelet transform, and boosts the compression ratio. On the basis of analyzing the distribution characteristics of coefficients in low and high frequency bands, a mixed entropy coding plan is applied, and a high efficient quantizator called"self-adaptive hard threshold"is established, which is helpful for improving the precision of the reconstructed DEM data and for enhancing compression ratio.

为了减小小波变换山区格网DEM数据压缩中边界失真区域，将山区格网DEM高程值视为广义坐标下的离散随机序列，把二维离散小波变换中的边界问题转换为一维离散小波变换中的边界问题，不仅大大减少了小波变换边界失真区域，提高了重构DEM数据边界点的精度，而且减少了边界补零个数，提高了压缩比；通过对山区格网DEM数据小波变换低频区和高频区变换系数分布特点的分析，采取了霍夫曼—游程混合熵编码方案，设计了高效、低失真的"自适应硬阈值"量化器，即对低频区变换系数不进行量化，直接进行霍夫曼编码；对高频区变换系数则先用"自适应硬阈值"方法量化处理，再进行游程编码。

More specifically, the invention relates to an antenna (1) comprising: first (2) and second (3) linear sub-antennas which are equipped with sensors (21-2M, 31-3N) forming first and second line segments and generating a basic signal, the angle between the respective directional vectors of the first and second tangents to the midpoint respectively of the first and second line segments being between 30 DEG and 150 DEG ; an antenna processing device (4, 5) forming combined signals; a signal-processing device (6, 7) generating combined useful signals; a device (8) for calculating the correlation coefficients (Cij between the combined useful signals; and a device (8) for generating a detection signal (Rij when a correlation coefficient exceeds a threshold.

更具体地，本发明涉及一种天线(1)，包括：带有形成第一和第二线段并产生基本信号的传感器(21-2M，31-3N)的第一(2)和第二(3)线性子天线，第一和第二线段各自中点的第一和第二切线的对应方向矢量之间的夹角在30°和150°之间；形成组合信号的天线处理装置(4，5)；产生有用组合信号的信号处理装置(6，7)；计算有用组合信号之间的相关系数(Cij的装置(8)；以及当某相关系数超过阈值时产生检测信号(Rij的装置(8)。

The topics covered in these sections are the geometric interpretation of systems of linear equations, the classification of finite symmetry groups in two and three dimensions, the exponential of a matrix and its application to solving systems of first order linear differential equations with constant coefficients, and Hurwitz's theorem on the composition of quadratic forms.

这些条文所涉及的主题是线性方程组的几何解释，在两个和三个有限对称群的分类方面，一个矩阵及其应用，以解决一阶常系数线性差分方程，系统指数赫尔维茨定理在二次形式组成。

By the best approximation and the geometric interpretation of signal vectors in adaptive filters, the input noise variance is obtained with the information obtained from the traditional LMS algorithm. Then, based on γ-LMS algorithm, it can iteratively eliminate the input noise effects to obtain the bias in the Wiener solution and the true system coefficients.

根据自适应滤波器的最佳逼近原理和各信号矢量的几何关系，利用传统LMS算法获得的信息来估计输入噪声的功率，再通过γ-LMS算法在迭代过程中逐步修正维纳解，去除输入噪声的影响从而得到系统参数的真实估计。

This is the inheritance of the tribe of the children of Issachar according to their families, the cities and their villages.

19：23 这些城并属城的村庄就是以萨迦支派按着宗族所得的地业。

I've have enough of your garbage.

我听了你的废话。