分解域

Zhi applied the lifting technique to the factorization over successive algebraic extension fields.

支丽红则将提升技巧用于多个扩域上的因式分解算法。

Wu, Hu, and Wang independently put forward factorization algorithms over successive algebraic extension fields based on methods of equation solving.

为了解决这一问题，吴文俊，胡森、王东明分别提出了基于方程求解的多个扩域上的因式分解算法。

Using wavelet transformation technology, singular value decomposition technology and good characteristics of Morlet wavelet in time domain and frequency domain, a de-noising method based on optimal Morlet wavelet and singular value decomposition is put forward.

利用小波变换技术、奇异值分解技术和Morlet小波良好的时域和频域特性，提出了基于最优Morlet小波和SVD的滤波消噪方法。

Owing to Wei-Norman decomposition＇s application being confined in a little time area, in order to obtain the Unitary evolution matrix at any time, a small division of time is proposed in this paper, and Wei-Norman decomposition is used in every small division to obtain the unitary evolution.

由于Wei-Norman分解适用的范围是小时间变化的邻域，为了求出量子系统在任意时刻的幺正演化矩阵，根据量子系统的特性，提出了对量子系统的控制时间进行分段，利用Wei—Norman分解来获得每段小时间的幺正演化矩阵。

In high strain domains, due to the decomposition of biotite and plagioclase, fibrous sillimanites were concentrated while in the low strain places the microscopic fibrous euhedral sillimanites were developed between plagioclase and quarts grains.

在高应变域，黑云母和斜长石分解，纤维状矽线石富集，低应变域则可有少量不定向显微纤状自形矽线石发育于斜长石和石英粒隙之间，因此这些矽线石不能反映高温条件。

There exits several MDO algorithms. But they are in our opinion either nonefficient or complicated. So we devised an algorithm called Subspace Approximation Optimization . In the SAO algorithm, the whole system is decomposed into one system-level optimization and several disciplinary optimizations so that a large and complicated problem can be divided into several easy-solving sub-problems. The coupling relationships and the coordination among disciplines are presented by equality constraints and these equality constraints are assigned to relevant disciplines. The optimums of design variables in system level optimization are transferred to discipline level optimization. The optimums of design variables in discipline level correspond to the point that is the nearest to the optimums of design variables in system level. If the optimums of design variables in system level are out of feasible region of discipline 1eve1, linear constraints can be built in the system level optimization using the design variable optimums obtained by the discipline level optimization. The system level optimization would improve the design of the whole system with these linear constraints.

目前，国内外已经发展出了多种飞机多学科设计优化算法，本文的重点是针对协同优化算法的不足，提出了子空间近似优化算法(Subspace ApproximatingOptimization，SAO)，SAO算法中，整个系统的优化问题被分解成一个系统级优化和若干学科级优化，而各个学科之间的耦合与权衡关系则被当作等式约束，这些等式约束将被分配到各个学科级优化中去，系统级优化的任务是寻找整个系统的最优解，而学科级优化的目标函数是以系统级优化分配下来的设计点为圆心的超球半径的平方，因此，如果系统级优化分配下来的设计点在学科级优化可行域内，则学科级优化目标函数为0，反之，则学科级优化的最优点是系统级优化当前设计点距离可行域最近的点。

With fault signals of vibration tested in practice, this paper takes frequency-domain half-power bandwidth Gauss wavelets of continuity, index wavelets decomposition and equivalent bandwidth equivalent sampling discrete bi-orthogonal wavelets decomposition as basis, presents scaling correlated analysis correspondingly toward wave making vibration signals, and accurately realizes to decompose different stress wave speeds, and provides a method of analysis and calculation for accurated location and recognition of the polygenetic faults.

根据上述故障力学模型，我们提出并设计了相应的测试系统，对实测的故障振动信号，以频域半功率带宽连续高斯小波、指数小波分解和等带宽等采样离散双正交小波分解为基础，提出了相应的对波致振动信号的尺度相关分析，准确地实现了分离不同的应力波速，为多源故障的精确定位识别提供了分析和计算方法。

The model has the following features: 1 The security information provided by the assessment result is more dependable because of the consideration of some main uncertain factors; 2 The improved analytic method of power system DSR and the dynamic equivalent technologies are applied to reduce the computing time and to make the model more practical; 3 Step-up assessment strategy is adopted in order to balance the precision and computing time requirements; 4 Decompounding of system insecurity indexes to each system component, or to each generator and consumer, and the visualization of assessment results, will help the operators to understand the security status of the power system more clearly; 5 The assessment results can be beneficial to the preventive control in traditional power systems and the security pricing in power market environments.

模型具有如下特点： 1由于综合考虑了一些不确定因素对系统安全性的影响，使得评估结果更加可靠； 2采用求解电力系统动态安全域的改进解析法，结合动态降维技术，大大减少了动态安全域的计算时间，使得模型比较实用； 3采取逐步递进的评估策略，以适应计算精度和计算时间要求； 4可定量分解出各元件或各发电与用户对系统不安全的贡献，配以形象直观的评估结果显示，使操作人员清楚了解系统的安全状况； 5评估结果在传统电力系统可帮助制定预防控制措施，在电力市场可用于安全性定价。

Aimed at the difficulty to extract the fault information of a low speed shaft in a large gearbox, wavelet analysis was used to realize the local analysis of signals in a time and frequency domain simultaneously. The signals were dissembled to a sieres of compactly supported wavelet bases non-redundantly and without leaking.

针对大型齿轮箱低速轴故障信息难以提取的问题，采用小波分析方法对故障数据进行处理以实现信号在时/频域的局域性分析，将其无冗余、无泄漏地分解到一组具有紧支撑性的小波基上。

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)。

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。