数学化

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

Based on theanalysis of topology structure of parallel mechanisms and using differential topology anddifferential manifolds as mathematical tools, we propose a new classification method. Thismethod classifies singularities of parallel mechanisms into two basic types, i.e. topologysingularity and parameterization singularity. This kind of classification has clear physical andmathematical meaning and fully reveals the characteristic of configuration space of parallelmechanisms.

采用微分拓扑和微分流形等现代数学工具，在对并联机构位形空间的拓扑结构进行分析的基础上，提出了一种新的奇异位形的分类方法，即把奇异位形分为拓扑奇异位形、参数化奇异位形两种类型，这种分类方法充分体现了并联机构位形空间的特点，具有十分明确的物理和数学意义。

In inequality in the equivalent transformation process requires a lot of mathematical ideas, discuss issues such as classification, the overall for-yuan,数形结合, transformation and so on as appropriate to the infiltration of these thinking, to improve the mathematical abilities of students have great help.

在不等式的等价转化过程中需要用到诸多的数学思想，如分类讨论问题、整体换元、数形结合、转化化归等等适当地渗透这些思想方法，对提高学生的数学能力有极大的帮助。

The mathematical programming formulation and related solution procedure are established by the traditional BEM. Through the discretization of space and time, the elastoplastic stress simulation method and reduce-basis technique are adopted to construct the self-equilibrium stress field. The numbers of variables and constraint equations in the resulting mathematical programming formulation are reduced greatly and then the dimension obstacle of computation in 3-D limit and shakedown analysis is overcome.

采用常规边界元方法建立了三维结构极限与安定分析的数学规划格式，通过对时间和空间的离散化，并采用弹塑性模拟法构造自平衡应力场和引入减缩基技术，大大减少了所形成的数学规划格式中的未知变量和约束方程的数目，有效地克服了三维结构极限与安定分析中的维数障碍问题。

So it can make some of the contents which are hard to understand in the mathematical analysis easy through the image of the geometric interpretation, to learn mathematics easier.

使数学分析中有些难以理解的内容，通过形象的几何解释，化难为易，使数学学习更加容易。

The results are as follows:Defatted wheat germ was micronized useing both hammer mill and colloid mill to increase the extraction rate of protein, followed by alkali extraction and ultrafiltration, respectively. A quadratic mathematical model was statistically constructed by using of Box-Behnken central composite design and response surface methodology. Under the optimized processing parameters of 23μm particle sizes, pH 9.5 and 51℃, a maximum extraction rate, 68.6%, was achieved, which is 30.63% higher than that of non- micronized wheat germ (passing through 80 mesh sieve).

首先采用锤式粉碎与胶体粉碎相结合的方法对脱脂麦胚进行微细化处理，然后利用碱提、超滤浓缩法提取制备麦胚蛋白，并通过Box-Behnken中心组合设计及响应面分析建立预测麦胚蛋白提取率的二次多项数学模型，优化蛋白质的提取工艺，在麦胚粒度为23μm、pH值9.5、提取温度51℃的条件下，经微细化处理的蛋白提取率为68.6％，比未经微细化处理的(过80目筛)提高30.63％。2。

Regularization is often used to overcome the ill-posedness, and Tikhonov regularization is the most common regularization method, but this kind of regularization will cause the sharp edge of the reconstruction result to be blurred.

从数学上来说，超分辨率图像重建问题是一个病态问题，为了克服其病态性，需要对其进行规整化，其中最常用的Tikhonov规整化方法，但这种规整化会导致重建高分辨率图像边界被模糊。

In the former representation, if no restrictions are imposed on formulas, then there is no algorithm to realize the reasoning in the resulted knowledge base; in the latter representation, the reasoning in the ontology represented by the description logic is decidable, while in general, for mathematical knowledge described by the first order logic which contains the ontology represented by the description logic, there is no algorithm to realize its reasoning.

在前者的表示中，如果对公式不作任何限制，那么得到的知识库中的推理不是可算法化的；在后者的表示中，以描述逻辑描述的本体中的推理是可算法化的，而以本体为逻辑语言的一部分的一阶逻辑所表示的数学知识中的推理一般是不可算法化的。

E. thickness of the copper wire wall, length of the single conductor wire, height of the solenoid, the exciting current and the current density, the working temperature of the conductor, time of exciting and demagnetizing, the cooling water pressure and flux density, etc..

所建立的数学模型包含3个目标函数（即能耗极小化目标函数、铜耗极小化目标函数和纯铁用量极小化目标函数）、7个设计变量（即铜管规格参数a、b、t，线圈匝数N〓、N〓，铁铠磁通密度B〓和冷却水压p）和8类14个约束条件（即铜管壁厚、单饼导线长度、螺线管高度、激磁电流与电流密度、导体工作温度、激退磁时间，冷却水压和铁铠磁通密度等约束条件）。

Aiming to a method for the synthesis of silicon nitride powder by direct nitridation process based on fluidization technology, a two-dimensional mathematical model of thermal process in a suspended bed was established, the thermal process was simulated based on the commercial CFD software FLUENT, and the effects of the flow velocity of nitrogen gas, the ratio of particle to gas and nitridation temperature on the temperature of the bed and the conversion rate of silicon were analyzed.

针对基于流态化技术利用硅粉直接氮化合成氮化硅粉的新工艺，建立了悬浮床内热过程的二维数学模型，并借助CFD商业软件FLUENT对悬浮床内热过程进行了数值模拟，分析了氮气速度、粉气比和氮化温度等因素对温度场和硅转化率的影响。

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。