近似方法

First of all, analysis and comparison are made for several approximation methods of solving elastic vibration problem.

首先，对弹性体振动问题的几种近似处理方法进行了分析比较。

An approximate arc length parameterization method which plays animportant role in blade modeling is also presented.

另外，本文还分析了建立叶身曲面模型的关键技术，并对其中涉及到的近似弧长参数离散的方法进行了研究。

Experiments of flow conductivity closure stress of typical propping agent are done, propping agent short-term flow conductivity alteration index is defined, by this, the relation between fissure short-term flow conductivity and closure stress, it is close to exponential relation. 4. Establishing the mathematical simulator of hydraulic fractured well's production in a steady state, finding the relation curve between dimensionless flow conductivity and fracture penetration coefficient by means of calculation and analyses, it is the basis of hydraulic fracture. 5. Expatiating the importance of optimized hydraulic fracturing design in reservoir engineering, advancing the optimizing design method, fracture dimension can be calculated easily when the physical parameters are known. 6. Production rate decline standard curve of vertical fractured wells is achieved by mathematical simulation, when the flow pressure is certain , by asymptotic analyze, this decline curve is close to exponential relation.

完成了国内外典型支撑剂的导流能力闭合应力影响实验，在数据分析中定义了支撑剂短期导流能力变异系数，并由此发现裂缝短期导流能力随闭合应力变化的近似符合指数关系式； 4 建立了一种水力压裂井稳态产能的数学模拟器，计算分析找到了最优无量纲导流能力与裂缝穿透比之间的新型关系曲线，它是水力压裂优化设计的基础； 5 阐述了水力压裂油藏工程优化设计的重要性，提出了优化设计方法，在已知支撑剂物性参数条件下可简洁计算最优裂缝尺寸； 6 数学模拟给出了垂直裂缝井产量递减标准曲线，在井底定压条件下通过渐近分析表明，该递减曲线满足指数关系式。

Approximate methods have been developed, including the method of averaging, boundary layer method, methods of matched asymptotic expansion and multiple scales and so on.

近似求解方法已被发展，包括平均法，边界层法，匹配渐近展开和多尺度法等等。

This paper presents an asymptotic procedure based on transmission line analogy to determine the radiative characteristic of external calibration loads composed of doubly periodic tapered microwave absorbers.

华中理工大学电子与信息工程系，武汉 430074 本文给出了近似求解二维周期渐变形状吸收体构成的微波辐射计外部定标负载辐射特性的方法。

Using real data from a seismic exploration, we achieved the migration sections of converted wave beneath volcanic area, and it is proved that the method is effective for computing common asymptotic conversion point and pre-stack time migration.

实际资料的成像结果表明，本文采用的近似转换点计算以及转换波叠前时间偏移方法是有效的。

The wave number is expanded into asymptotic series in terms of a small parameter. This method is exact and can approach any accuracy desired.

这一方法本身是精确的，它能达到任意所需的精度，然而四层和五层波导结构的数值计算实例表明，仅二阶近似解就足够精确了。

In Chapter 1, two solutions to the elliptical boundary value problem have been constructed through a monotone iterative process, and they might be identical. In Chapter 2, the author expresses the local solution to the parabolic initial boundary value problem taking advantage of Green function. In Chapter 3, the asymptotic solution to the initial value problem of Duffing equation is obtained and the method for finding the approximate solution to the inverse problem is put forward.This paper is planned with a view to the author's research means.

从研究结果看：第一章通过单调迭代过程构造出椭圆型方程的边值问题的两个解，并且指出二者可能是同一个解；第二章利用格林函数给出了抛物型方程的初边值问题的局部解的解析表达式；第三章中，先对Duffing方程的初值问题写出解的渐近展开式，再对其反问题提出一种求近似解的方法。

In chapter 2 of this dissertation, we give the mathematical definition of selfsimilarity, and describe some of its properties. How to justify a self-similar process and get its autocorrelation coefficient (or self-similar parameter) are also discussed.

由于对于非马氏过程的排队系统进行数学分析是十分困难的，因此，对自相似业务流特性及网络性能的研究，大多采用某种近似的数学求解，或直接进行计算机仿真，这就需要有快速、准确的自相似序列生成方法。

Then we define the stable distribution with four equivalent ways and analyze its properties carefully. To study the stable distribution, we must know how to simulate its random variables. We can learn it intuitively by watching its plot of density function.By adding an auxiliary variable in the Chapter 4, we estimate the four parameters using Gibbs sampler.

接着给出了稳定分布的四种等价定义方法，详细的分析了稳定分布的性质，提出如何利用简单随机数产生稳定分布的随机变量以便我们进行分析研究，借助稳定分布近似密度函数的图形我们对它的特征会有更加直观的认识。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新