分解域

A novel direction of arrival and polarization estimation of electromagnetic vector sensors mounted on the airframe is proposed based on biquaternion. The signal processing model for EM-sensor mounted on the airframe is made by biquaternion and then the eigenvalue decomposition of spectral matrix is obtained by means of the EVD of its quaternion adjoint matrix. The memory requirement for data is reduced, and more accurate estimation result is gotten by deducing the stronger orthogonality constraint between the sin- gal and noise subspaces on the field of biquaternion. The performance of the new algorithm is confirmed through numerical examples.

针对机载电磁矢量传感器阵列DOA和极化参数估计问题，提出了一种基于复四元数估计方法，该算法利用四元数建立机载电磁矢量传感器阵列信号处理模型，然后利用四元数联合矩阵的特征分解得到阵列数据相关矩阵的特征分解，一方面使得计算过程中数据的贮存量大大减少，另一方面通过推导得到信号子空间和噪声子空间在四元数域上的正交性从而使DOA和极化参数佑计的精度更高，仿真证实了本算法的有效性。

The uniform design method is used to select initial points. The admissible domain, based on initial points obtained, is partitioned into finite sub-domains. A modified Hooke-Jeeves algorithm is proposed to each sub-domain.

以均匀设计方法选初始点，并依此把允许区域分解为有限多个子域，在每个子域上构造了改进的Hooke-Jeeves优化算法。

However, in order to compute the irreducible ascending chain in Wu's method, polynomial factorizations over successive algebraic extension fields are needed.

而在吴零点分解定理中，多个代数扩域上的因式分解是非常基本的一步，主要用于不可约升列的计算。

Prime ideal decomposition is an important problem in algebraic number theory and is relative closely with the class field theory and so on.

素理想分解问题是代数数论中的一个重要课题，它与类域论的关系极为密切，因而如何判断K的素理想在K的有限扩张中的分解状况是一个十分有意义的问题。

The image diagnosis method is presented based on bidimensional Local Wave Method. The grey image of time-frequency spectrum is set as the study target, from which the character correlative to fault is attracted.

提出了基于二维局域波分解的图像诊断方法，通过对时频灰度图像的二维分解提取表征故障信息的图像细节部分，有效地实现了故障的特征提取。

Experiment proved the practicability and efficiency of this algorithm. We study a class of subband coding schemes allowing perfect reconstruction for a bidimensional signal sampled on the hexagonal grid.

辨析了张量积子波变换与六边形子波变换的特性，尤其是空间取向性的差异，六边形子波变换克服了张量积子波变换在频率域上的"某些方向不确定性问题"，提供了频率域上的尖角分解准理想模式。

Besides, as to inpainting problem in wavelet domain, we introduce a new iterative model. In this model low frequency and high frequency will carry on processing separately, enormous speed up the image repair convergence rate, and even if as high as 90% wavelet coefficient have been lost, this model will also be able to have the very good repair effect. In the old model, to compute the curvature we have to transform the coefficients to the pixel domain, and then transform back to the coefficient domain for several times and this method can solve this problem and speed up the iterative convergence.

其次针对小波域中图像修复的问题，本文提出了一种新的小波域图像修复模型，该模型根据小波变换后系数相关性的特点，将低频和高频分别进行处理，极大的加快了图像修复的收敛速度，并且即使丢失高达90%的小波系数，该模型也会有很好的修复效果，有效的解决了传统的TV- Wavelet模型在计算图像的平均曲率WCURV时，需要反复进行小波分解与重构的计算，迭代速度慢的问题。

The nature of the acceleration unit-impulse response function of unbounded medium tending to vary linearly is proved by means of asymptotic analysis. Thus, the acceleration unit-impulse response function can be regarded as the summation of a linear function and a residual part which converges to zero. Based on this decomposition, two FE-SBFE coupling procedures are presented based on system realization and truncation integral technique respectively.

本文系统研究了相互作用力-运动关系的位移表达、速度表达和加速度表达，通过比较位移、速度和加速度单位脉冲响应函数的SBFE求解过程，确定采用相互作用力的加速度表达；通过渐近分析证明了无限地基加速度单位脉冲响应函数具有随时间延长而趋于线性变化的性质；利用这一性质将加速度单位脉冲响应函数分解为一个线性函数和一个衰减到零的残余函数的和，以此为起点发展出两种FE-SBFE时域耦合方法：基于系统实现的FE-SBFE时域耦合方法和基于截断卷积的FE-SBFE时域耦合方法。

Based on the localization properties of wavefield decomposition and propagation in the beamlet domain, and according to relevant extrapolation formula, the beamlet domain is implemented, and finally imaging values are computed using image-forming condition.

利用小波束域波场分解和传播在空间和方向上的双重局域性，将小波束域波场依据相应的外推公式进行延拓，最终应用成像条件求取成像值。

At first the physical and mathematical models for multiconductor transmission lines are described, and the traditional mode decomposition method in the frequency-domain and the characteristic method in the time-domain are introduced simply.

为了便于理解和比较，作者首先对时域响应分析的物理、数学模型做了必要的阐述，并对传统的频域模式分解方法和时域特征法进行了简单的介绍。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。