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In this paper, full-space late-time and all-time apparent resistivity formula was derived based on homogeneous full-space response equation of central loop. By comparing with half-space formula and analyzing measured data, the application efficiency of this formula was studied.

从全空间中心回线源响应公式出发，推导了全空间晚期和全区视电阻率公式；通过与半空间公式比较和对实测资料的分析，研究了全空间视电阻率公式的应用效果。

The main content of this thesis is to find and prove some summation and transformation formulae of basic hypergeometric series by the modified Cauchy method,operator method and inversion techniques,which include many well-known results as special cases,for example,q-Saalschiitz summation formula,Baileys _6ψ_6 summation formula,non-terminating Watson transformation formula and Rogers-Ramanujan identities etc.

本文的主要内容是利用修正的Cauchy方法、算子方法和组合反演技巧来发现和证明一些基本超几何级数求和公式和变换公式，其中包含一些著名的公式，如q-Saalschüz求和公式、Bailey的_6ψ_6求和公式和非终止的Watson变换公式等作为其特殊情况。

It Newton iteration is used in the analysis of math value,and the simplicity formula is given to resolve(including original initial value formula and advanced approximation formula),which can be characterized by fast speed and easy remembering.

采用数值分析中的牛顿迭代法求反渐开线函数的根，并给出了符合精度要求的解算反渐开线函数的简单公式(包括原始初值公式和近似值精化公式)，具有迭代收敛速度快、简单易记的优点，它们适用于[0，π/2]的全区段，免除了分段计算的烦恼，并运用VB编写计算机程序，从而实现反渐开线函数快速求根的目的。

For example, in a calculus course it's not terribly difficult to memorize the formula for integration by parts for integrals. However, if you don't understand how to actually use the formula and identify the appropriate parts of the integral you will find the memorized formula worthless.

例如，你会发现通过微积分来学习微积分学是很容易的，但是，如果你不了解怎么正确地使用这些公式和区分不同的微积分，你会发现你所学的公式都是毫无用处的。

Moreover,we also gave the proofs of generalization formula of integration by parts,the Green s formula of first type and the Green s formula of second type by using the divergence theorem .

首先指出数学分析中反映二重积分和第二类平面线积分联系的Green公式可以看成是散度定理的一种特殊情形，然后利用散度定理给出广义分部积分公式、第一Green公式和第二Green公式的证明

A formula of rock resistant coefficient is derived based on unified strength theory, which can be adopted to obtain rock resistant coefficient in other situations or strength thoeries simplified by assuming the parameter value in the formula. The strength differential effect, intermediate principal stress effect and the ground water permeation effect are considered in the formula.

基于统一强度理论，将巷道围岩视为多孔介质，考虑地下水渗流作用的影响，推导出了巷道围岩抗力系数计算统一公式，改变公式中的参数可以退化为其他围岩条件或者其他强度理论条件下的围岩抗力系数计算公式。

After building big data storage structure and constructing decimal code array, an algorithm for high-accuracy value of two-dimensional normal distribution is built through using Laguerre Polynomial expansion, and accelerating operation with Compound Simpson formula, Compound Cotes formula and Romberg formula.

以数组作为大数存储结构，解决受到计算机字节长度制约无法实现高精度运算的问题；并引入复化辛普森公式、复化柯特斯公式和龙贝格公式加速收敛，最终得到所需要的结果。

This paper introduces the Taylor formula of one dollar and multi-definition, then the proof of the value from the formula, respectively, that inequality in the value of derivatives is estimated that about industry estimates, demand infinity limit, the median point of the limit function limits, approximation, function equations and so on Taylor formula to do the induction.

本文首先介绍了一元和多元泰勒公式的定义，然后分别从证明中值公式，证明不等式，导数的中值估计，关于界的估计，求无穷远处的极限，中值点的极限，函数的极限，近似计算，函数方程中的应用等方面对泰勒公式的应用做了归纳。

First by testing the practical multilayer insulation in a cryogenic tanker, which is the carilometer in my paper,some affecting factors on multilayer insulation are analysed, then by using the low-temperature and vacuum environment caused by multilayer insulation, the effective thermal conductivity of multiple fiber paper with 5 layers is tested.Through Newton interativemethod,an empirical formula is deduced to computer the thermal conductivity of fiber paper,The errors between experimental thermal conductivity and the calculated conductivity by empirical formula are below10%,so the formula of fiber conductivity can be applied to practical enginnering.

为探索改善工程应用中高真空多层绝热层绝热性能的方法，本文实验研究中首先测量了包扎在实际低温储罐上不同结构的高真空多层绝热层的绝热性能，并分析了环境温度、环境压力，层数、不同隔热材料的组合等因素对工程应用中的高真空多层材料绝热性能的影响；然后利用多层绝热层中的低温真空环境测量5层干法纸在不同温度区间内的表观导热系数，在有限实验数据的基础上用牛顿迭代数值拟和出计算5层干法纸表观导热系数的经验公式，对比经验公式计算值和实验测量值，发现二者的误差在10%以内，因此在工程应用中可用本文的经验公式计算干法纸在低温下的导热系数。

Plot --- composite numerical quadrature formula to solve the problem of integration functions for composite trapezoidal plot formula and compound parabolic formula, the right to issue integral calculation.

数值积---复合求积公式对积分问题的求解功能用复合梯形求积公式和复合抛物线公式，对给定的积分问题进行计算。

According to our present broadcasting situation,the thesis proposes using new technology to update and reform the present HFC. It also suggests broadcasting using self-advantage and arranging EPON in order to win the supermarket.

论文从我国广电的现状出发，结合实际，积极倡导采用新技术更新、改造我国现有的HFC网络；倡导广电现阶段利用自身优势，部署EPON网络来赢取市场。

A new general kinetic equation was derived in which the effect of the removal of condensation water was taken into account completely, and was applied to the polyesterification kinetic study of AA/HPHP and AA/NPG. It was found that the reaction order of self-catalyzed polyesterification was not constant. For these polyesterifications, the reaction order was 2.5 at a low temperature, while 3.0 at a high temperature.

考虑缩合水的排除对反应体系的影响，用体积浓度单位推导出一个新的聚酯反应总包动力学方程，并应用到AA/HPHP和AA/NPG两个聚酯化反应的动力学研究中，研究发现，自催化聚酯反应的反应级数并不是固定值，对于AA/HPHP和AA/NPG两个聚酯化反应而言，低温时反应级数为2.5，高温时反应级数为3.0。