积分的

Concretely speaking, using the irreducible tensor theory, we deuced the formulism for fine-structure energies of boron-like atoms in the ground and first excited states, which involves spin-orbit, spin-spin and spin-other-orbit interactions; completing all the angular integrations and spin summations needed, we make the final expression for fine-structure energies of boron-like atoms in the ground and first excited states in a combination of radial integrations. Afterwards, employing the wave functions we got in Chapter Three, we accomplished all the radial integrations and so obtained the fine-structure energies.

具体地说，利用不可约张量理论导出了类硼离子基态以及第一激发态的精细结构的表达式，给出了自旋-轨道、自旋-自旋、自旋-其它轨道相互作用等所涉及的所有角向积分和自旋求和的解析计算方法，完成了角向积分、自旋求和的计算，使类硼离子基态以及第一激发态精细结构能级最终可以表示为径向积分之和；在此基础上利用以前所得到的非相对论性波函数，进一步完成了所有径向积分的计算，从而得到了对应能级的精细结构的理论计算值。

This paper gives a method to solve double integration by integral subsection integration.

本文给出了用定积分的分部积分法求解二重积分的一种方法。

Integral Calculus: definite and indefinite integrals; fundamental theorem of calculus; techniques of integration; Taylor's Theorem; applications in geometry, physics and engineering.

积分学：定积分与不定积分、本定理、积分的方法、勒定理、分学在几何、理和工程学上的应用。

By analyzing the bode diagram of HAPF system and minimizing the capacity of HAPF, the paper presents a frequency dividing control method based on fuzzy-PI. In this mean generalized integrator is used for frequency dividing integral and fuzzy arithmetic is for adjusting PI coefficients timely. Compare with other kinds of control methods, the proposed one is more simple and easier realization.

该文由常用的并联型HAPF的结构特点分析出发，从容量和幅频特性2个方面探讨HAPF控制中进行有效分频的必要性，根据HAPF对控制方法的要求，文章提出一种基于广义积分的模糊自整定PI控制方法，即通过广义积分实施对周期量的分频积分，同时由模糊算法进行比例和积分系数的在线调整，从而有效实现对HAPF的分频控制。

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof.

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较，得到了相应的反常积分敛散性极限审敛法的等价定理，并给予证明，从而可运用等价定理灵活的判断反常积分的敛散性。

This software carried out the calculation of the integral calculus of Bernhard Riema with draw the function sketch of the Bernhard Riema integral calculus function and together the function that two calculation and integral calculus zone diagrams of the heavy integral calculuses of a function draw.

本软件将实现黎曼积分的计算与绘制黎曼积分函数的函数图形、齐次函数的二重积分的计算与积分区间图的绘制的功能。

For simplifying and unifying the defini- tions,and for understanding and mastering the concepts of Lebesgue integral from different angle,it is very significant to study how to define Lebesgue integral,and to prove the equivalence of different defin- tions.

关于L积分理论的研究，特别是关于L积分定义的研究，研究新的定义方法以简化L积分的定义，证明各种定义的等价性以统一L积分的定义，引起了国内外专家学者的广泛关注，并进行了许多深人的研究l一6〕。

Through the hypersingular integral equations of 3-d crack perpendicular to the interface given in the preceding, the principles of finite-part integrals and of limit are further made use of to pick the hypersingular integral equations of 3-d crack terminating at the interface On the basis of the equations, starting strictly from 3-d theory of elasticity, stress singularities of intersection-line near the front edge of the 3-d crack terminating at the interface are analyzed by virtue of dominant-part analysis of 2-d hypersingular integrals.

根据前面所得到的与界面垂直的单片裂纹超奇异积分方程，进一步运用有限部积分原理和极限理论，推导出了与界面垂直相抵的三维平片裂纹的超奇异积分方程。在此基础上，严格从三维理论出发，使用二维超奇异积分的主部分析方法，对与界面垂直相抵的三维平片裂纹前沿交线上的应力奇性指数进行了分析。

Reasonable grounds include any abuse or attempted abuse of the scheme, or any use or attempted use of a VIP card, or points in a manner which is contrary to these terms and conditions or any reasonable suspicion of dishonesty on the part of a member in connection with the scheme.

天桥商贸有限公司拥有以下权利：停止该贵宾系统；拒绝向某些申请者发行该VIP卡；在有充分理由的情况下收回，取消VIP积分卡或者所集积分，或者变更天桥VIP积分系统章程；我们所说的充分理由的情况包括：任何滥用或者试图滥用天桥VIP卡的行为；任何违反天桥VIP卡章程使用VIP卡以及VIP积分的行为；所有合理的怀疑与天桥工作人员有关的不诚实行为。

Reasonable grounds include any abuse or attempted abuse of the scheme, or any use or attempted use of a VIP card, or points in a manner which is contrary to these terms and conditions or any reasonable suspicion of dishonesty on the part of a member in connection with the scheme.

国芳购物广场拥有以下权利：停止该贵宾系统；拒绝向某些申请者发行该贵宾卡；在有充分理由的情况下收回，取消贵宾积分卡或者所集积分，或者变更国芳贵宾积分系统章程；我们所说的充分理由的情况包括：任何滥用或者试图滥用国芳贵宾卡的行为；任何违反国芳贵宾卡章程使用贵宾卡以及贵宾积分的行为；所有合理的怀疑与国芳工作人员有关的不诚实行为。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。