数学化

The characteristic of matrematical teaching has profound logicality systematization and a high degree of abstraction and summarization.

数学教学的特点是：具有很强的逻辑性和系统性以及高度的抽象性和概括性。将几何图形化静态为动态，化抽象为具体，能够寓趣味性、技巧性和知识性于一体。

Based on mathematic operation function of ANSYS parametric design language, reliability calculation of component was realized by programming with APDL according to the perturbation method of reliability theory.

基于ANSYS参数化设计语言的数学运算功能，运用可靠性理论的摄动分析法，利用APDL编程实现零件的可靠度计算，避免了有限元建模、分析和结果的参数化提取等步骤。

The methodology classified the objects of module partition to improve the flexibility and maneuverability. In addition, the methodology focused on research of module partition method, which faced the category of "modular transformation of the existing products ". The methods commendably meet the current needs of enterprises and have strong practical significance. In the end, presented the corresponding mathematical methods.

针对两类方法的优缺点，提出了一种柔性化模块划分方法，该方法突出了模块划分的对象分类，在提高划分方法柔性的同时，也更具可操作性；并着重研究分析了"面向已有产品模块化改造"范畴的模块划分分组方法，并明确了相应的谱系聚类数学方法，该方法较强地适应了当前企业的设计需求，具有较强的实践意义。

Visualization of geologic information is the basis of visual design for large-scale hydropower projects,and is the research focus and nodus in the fields of mathematical geology and engineering geology.

地质信息可视化是大型水电工程可视化设计的基础，同时也是工程地质和数学地质领域的研究热点和难点。

Adopting homogenous experimental design and applying the response surface method,the effects of corn variety,screw speed and water content on radial expansion ratio and extrusion index were studied,and the quadratic polynomial mathematical models of expansion ratio and extrusion index were constructed.

采用均匀试验设计方法，应用响应面分析了玉米品种、螺杆转速和物料水分含量对膨化率和挤压指数的影响，并建立了膨化率和挤压指数的二次多项式数学模型。

In Chapter II, we introduce the bosonization and renormalization group methods with Hubbard model as an example.

众所周知，t－J模型中不允许电子双占据状态的存在，这种数学上的约束条件使得通常的玻色化方法和重整化群技术不能直接用来研究模型的物理性质。

It is found that the internal relation between the wavelet method and multi-scale representation will determine the law by which the graphic information varies following the change of the scale. That work mark a new step towards the successful application of wavelet theory in the automatic map generalization and provide a new basis and mechanism for the multi-scale representation in GIS.

发现了小波理论与GIS图形数据多比例表达之间的内在联系，挖掘出GIS图形数据中一些信息随尺度的变化规律，因而为利用小波理论来解决GIS图形数据多比例尺表达中的问题作出了一些基础性工作，为GIS图形数据多比例尺表达和自动制图综合找到了新的数学机制和依据，使这项工作的在自动化、模型化、数量化、客观化的方向上又迈出一步。

English Outline Describes the classification and characteristics of biochemical reactions, major metabolic pathways; biochemical thermodynamics, biokinetics, immobilization technology, bioreactor construction, experimental design, mass transfer, heat transfer, and flow pattern; mathematical modeling, computer simulation, and optimization; the classification of reactors, aerobic and anaerobic, their operational characteristics and applications.

Chinese Outline 探讨生物化学反应种类及其特性，主要代谢路径；生物热力学、生物动力学、酵素特性探讨与酵素动力学，固定化技术、生物反应器之组装、实验设计、反应器内质传、热传及流动型态解析；数学模式，电脑模拟及最适化；简介反应器种类：好氧及厌氧反应器，其操作特性与应用。

In preprocessing part, it is contained normalization, segmentation, binarization, denoising, thinning and so on. And characteristic matching algorithm is used a mathematical model which is irrespective with circumrotation and displacement.

其中预处理部分由归一化、分割、二值化、去噪、细化等算法组成，且在特征匹配算法中使用了对图像旋转和平移无关的数学模型。

Then, the relation between vibration and sound, the acoustic holography method, the indeterminacy and identifiability of BSS, the BSS algorithm are discussed in detail. Based on above researches, the dissertation is divided in following four sections. The first section investigates the BSS algorithm suitable to acoustic feature separation. The algorithm of the joint approximate diagonalization of eigen-matrices is proposed. The spectra or the time-frequency distributions of source signals are the interesting features in ABD and they are separated from mixing signals by JADE algorithm. Then, the convolutive mixing model is transformed into a high-dimension instantaneous mixing model, and the deconvolution of source signals is achieved by the joint approximate block diagonalization of eigen-matrices. The proposed algorithm has a global minimum, and it is unsensitive to noise interference.

论文首先概述国内外声学诊断研究进展与盲分离研究进展，给出机器噪声声场与盲分离的数学描述，讨论了声振辐射、声全息、盲分离模型、盲分离可解性、盲分离结果不确定性、分离算法等基本问题，在此基础上，论文的研究工作分为以下四个部分：第一部分研究适用于声学特征分离的盲分离算法，提出基于特征提取的联合近似对角化盲分离算法，该算法以频谱特征或时频特征作为分离目标，从混合信号中分离源信号频谱特征或时频特征，最大限度地保留了与声学特征提取有关的频谱特征或时频特征，采用模型变换把卷积混合模型变换为一个高维瞬时混合模型，通过联合近似分块对角化算法实现源信号频谱特征与时频特征的盲反卷积。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。