函数的积分

Based on the higher mathematics method proved inequalities are summarized, and the proposed using the function extreme value and the monotonicity and concave and convex function sex, and mean value theorem, Taylor formula, integral these common higher mathematics method, combining with concrete examples of each kind of method to solve the problems for type, and the key problem of the specific steps, and points out that the inequality proof of higher mathematics method used properly, improve the difficult easy to ability to solve problems.

本文对不等式证明中的高等数学方法作了归纳总结，提出了利用函数的单调性，极值与最值，函数凹凸性，中值定理，泰勒公式，积分这些常用的高等数学方法，并结合具体实例阐述了每一种方法的适用类型、解决问题的关键和证明问题的具体步骤，指出在不等式证明中恰当地运用高等数学方法可以化难为易，提高解题能力。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all th...

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all the angular interactions and spin sums involved in the problem have been worked out explicitly by using irreducible theory.

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Sensitivity function and control sensitivity function are obtained by Youla parameterization of controller,which is used to describe an integral square performance criterion containing tracking error and control energy.

由控制器Youla参数化得到控制系统的敏感度函数和控制敏感度函数用来表示一个包含跟踪误差和控制能量在内的积分平方性能指标，针对不同类型的时滞过程运用谱分解的方法最小化该性能指标，从而导出相应控制器的设计方法，可使系统在控制能量约束条件下具有最优的控制性能。

The digital algorithms of integral and discrete wavelet transform are presented for purpose of electric power system protection, based on the analysis of wavelet transform for sampled digital signals under the Shannon sampling theorem.

从电力系统继电保护应用的角度，结合香农采样定理，深入探讨了连续信号和离散信号的小波变换的关系，给出了离散信号的积分小波变换和离散小波变换的数字计算方法。从理论上研究了信号小波变换的误差与尺度函数和小波函数的关系。

Firstly, the basic principles of MOM are reviewed, including the selection of integral equations, the choice of basis function and weight function, the solution of matrix equation and so on.

首先，本文回顾了矩量法的基本原理，介绍了积分方程方法的选取，以及快速多极子方法的基础-矩量法的关键技术，例如基函数和权函数的选择，矩阵方程的求解方法等。

In order to reduce these shortcomings, on the basis of enriched polynomial basis functions, weighted orthogonal basis functions are used to obtain the MLS approximation by using a Schmidt orthogonalization. In the end, the improved LBIE method for elasticity fracture is proposed.

为了改善这些不足，本文在扩展的多项式基函数的基础上，利用Schmidt正交化方法构造带权的正交基函数，建立了断裂力学的改进的局部边界积分方程方法。

The method is to add a term into the original singular kernel while it subtracts its analytical solution from the original equation. Since the singularity of Green's function can be eliminated by such a mathematical technique, shape function does not need to be supposed while solving the unknown. The calculation can be directly applied to the real shape of the object by taking the integral points distributed on the object as nodes that satisfy boundary conditions.

由於格林函数的奇异性经过数学上的技巧加以消除，因此当求解未知数时已经不需要再假设形状函数，即可直接使用物体真实的外型来做计算，也就是直接将物体上分布的积分点视为满足边界条件的节点。

In this paper, a sort of recursive formulas of spherical harmonics integrals, which often appear in the gravitational gradient harmonic analysis, are deduced according to the recursive formulas between every other order of spherical harmonics and the trigonometric functions＇properties. And the calculated formulas on the recursive initialization also are brought forward.

本文根据球谐函数的跨次递推公式和三角函数的性质，详细推导了在重力梯度调和分析中出现的一类球楷函数积分的跨次递推公式和递推初始值的计算公式。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。