查询词典 approximation methods in physics

Formally,the process is considered as fuzzed of the lower and upper approximation sets. Finally, an example shows that membership degrees more visualy and reasonably describe that objects belong to the lower and upper approximation of the set.

实例分析说明在不完备信息系统中，考察对象对于上、下近似的隶属度能更直观、合理地反应对象隶属于某一集合的上、下近似的情况。

Comparison of theoretical predictions with corre-sponding computer simulation data uncloses the superiority of the Rogers-Young approxima-tion over Hypemetted chain approximation and rescaled mean spherical approximation forfreezing.

理论预言与相应的计算机模拟数据的比较揭示了Rogers-Young近似比超网链近似与重标度平均球形近似精度高。

The method includes dividing a digital image, formed from M rows and N columns of pixels, into a plurality of band-shaped areas by partitioning at each of a prescribed number of rows; averaging, for each column, the gradation values of pixels in said band-shaped areas for each of said plurality of band-shaped areas; computing an approximation line which approximates, in each of said plurality of band-shaped areas, a distribution of said average of gradation values; and judging whether there exists a succession of d columns at which the difference between said gradation value derived from said approximation line and said average of gradation values for each column exceeds a prescribed threshold.

该方法包括：通过以规定行数为单位进行分割，将由M行N列个像素形成的数字图像划分为多个带状区域；对于所述多个带状区域的每一个，针对各列来对所述带状区域中的像素的浓淡值求平均；计算近似线，该近似线在所述多个带状区域的每一个中近似于所述浓淡值的平均值的分布；并且判断是否存在如下连续的d个列，在所述连续的d个列中，从所述近似线得到的所述浓淡值与针对各列的所述浓淡值的平均值之间的差值超出一指定阈值。

We describe the GW approximation which has turned out to be a fruitful approximation to the self-energy.

通过理论的推导和计算试验将表明GW方法能很好地近似求解自能。

A smooth approximation algorithm is then proposed based on hinge-finding algorithm via curved faces approximated to the hinging hyperplanes model, which can obtain a smooth approximation result and hold some good properties of hinge-finding algorithm such as simplicity and effectiveness.

本文对找链接算法做了两点改进，其一是扩充了链接超平面模型，在二维空间上弥补了链接超平面模型表示能力不足这一弱点。仿真实验显示使用扩充后的模型得到了更好的分片线性逼近结果。另一点改进是使用双曲光滑函数构造出了基于找链接算法的光滑逼近算法。理论分析证明了算法的可行性。仿真实验验证了理论分析。

The study of direct and inverse theorems on the approximation of linear operators to functions in normed linear spaces is an important subject in the approximation theory.

线性算子对赋范线性空间中函数逼近正逆定理的研究是逼近论中重要的研究课题之一，在理论和实际应用上都具有重要的意义。

The most common and most widely studied methods of all analytical approximation methods for nonlinear differential equations are the perturbation methods.

非线性振动由于其振动方程的特点，到现在还没有通用的解析求解方法，只能根据系统的特点采用一些特殊的方法来求解。

Based on the three dimensional surface data of the face and skull, methods of geometric analysis on them are presented through these parameters with their numerical calculating methods under the landmarks of the anthropologist and anthropometrist are proposed,which is the foundation of the statistical model that will be used in the field; 4Geometric analysis methods that based on the approximation coefficients of spherical harmonic functions are proposed.

以三维面皮和颅骨数据为基础，分别给出了基于公安法医学标志点和人体测量学标志点的几何分析主要途径和方法，确定了几何分析的主要参量，并给出了相关的计算方法，为建立颅面统计模型奠定基础； 4基于球面调和函数的颅面形态学的几何分析方法。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

Chapter 4, lists the teaching cases in teacher's teaching, combined the cases dissecting the teaching methods of mathematics and mathematical cerebration and methods in the point of view of psychology, then infers that to proceed the teaching of mathematical cerebration and methods is necessary. In the other hand, I compared and studied the association between the basic mathematical cerebration and methods and other mathematical knowledge, answer the questions that which mathematical cerebration and methods are more worthy to jut out. At last, infers a mode of the teaching in mathematical cerebration and methods.

第四章列举了教师在授课中的教学案例，结合案例从心理学角度对中学数学教学与数学思想方法教学进行剖析，得出进行数学思想方法教学是十分必要的；同时对中学数学教学中的数学基本思想方法与其它数学知识的关系进行了对比分析，对在中学数学教学中突出哪些数学基本思想方法为好做了解答；最后给出了数学思想方法教学的一个教学模式。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。