函数的积分

Two kinds of electron transition processes which lead transition metal complexes to show their colours were discussed.

讨论了导致过渡金属配合物显色的二种电子跃迁过程，只有当电偶极跃迁矩积分的被积函数的对称性允许时，才有可能产生颜色；分裂能的差别，导致跃迁能的不同，因而呈现出不同的视色。

In the case of inapplicability of hammering excitation to the arm of industrial robot for extracting its dynamic characteristics,according to the Duharmal integral theory and applying the specific upper triangle construction of input matrix of system as well as the technique of time average ,an efficient de-noising average recursive algorithm is presented in this paper.

针对锤击激励方式不适用于工业机器人操作臂动态性能测试的情况，根据Duharm a l积分理论，利用系统输入矩阵的上三角形的特殊结构，并结合时域平均技术，导出了具有抗噪性能的高效的求取系统脉冲响应函数的平均递推算法。

By using the approach of weight function, a new Hilbert-type integral inequality with some parameters and a best constant factor is given. The reverse form and the equivalent forms are also considered.

应用权函数的方法，建立一个新的含多个参量的具有最佳常数因子的Hilbert型积分不等式，并考虑了它的逆向形式及相应的等价形式。

Then the explicit expression of it under exponential claims and the differential equation are obtained.Thus we discuss the effects of credit and debit interests on it through data analysis. Through the research of the mean,the moment generating function and the higher moments of discounted aggregate dividend payments,we discuss the optimal dividend payments problems.

而对于Gerber-Shiu函数的研究，则是通过随机过程及随机微分方程的知识得到它满足的积分-微分方程及边值问题，然后得到了它在指数索赔下的明确表达式以及Erlang(2)索赔下满足的微分方程，并通过数值分析得到贷款利息及存款利息对它的影响。

We have improved the method to avoid the complicated calculating of probability and numeral integral.

由于原先的方法中需要进行繁琐的数值积分和概率的计算，我们对能量函数的计算进行了改进，避免了这种繁琐的计算，使得算法更加简便、易行。

The analytical expression of a kind of integral including the product of the sums of two Bessel functions is given for the power calculation.

六、根据研究工作数值计算的需要，给出了一类包含有两个贝塞尔函数的和的积的积分公式。

In some literatures, another equivalence between the WKB method and the path integral approach has been discussed, a set of rules of constructing semiclassical green functions with respect to the position and energy which is the fourier transformation of the semiclassical path integral propagator with respect to position and time was established.

一些文献讨论了WKB方法和路径积分方法的等价性，得到了求解作为坐标和时间域的传播子的傅立叶变换的坐标和能量空间的格林函数的一套规则。

With the use of the dislocation method of complex potential function, this paper studies the interaction between the interface macrocrack and the interface or beneath-interface microcracks by the construction and numerical solution of singular integral equations .

采用复势函数的位错解方法，通过对奇异积分方程的建立和数值求解，研究了界面主裂纹同界面及基体微裂纹之间的干涉。结果表明远场载荷角ψ同Dunder's参数α对界面微裂纹及基体中水平微裂纹同主裂纹干涉的影响都很显著，而ψ对屏蔽区的影响则远小于α对其的影

Based on the extended Huygens-Fresnel principle and the quadratic approximation of phase structure function, we have derived the analyticl expression of the spatial degree of coherence for partially coherent flattened beams propagating through the slant turbulent atmosphere with the help of tensor integral, then analyzed the effects of different zenith angle, propagation distance, coherence of source and outer scale of turbulence on the spatial degree of coherence on the receiver.

基于广义惠更斯-菲涅耳原理和相位结构函数的平方近似，运用张量积分的方法导出了部分相干平顶光束通过斜程湍流大气传输后接收面光束空间相干度的解析表达式，分析了不同天顶角、传输距离、光源相干性以及湍流外尺度对接收面光束空间相干度的影响。

The stress intensity factors defined in terms of the integral are derived from the Betti's reciprocal work theorem and expressed in terms of relative quantities on a path and semi-weight function.

由功能互等定理导出用半权函数和积分围道裂纹尖端的参考场所表示的所研究情况的应力强度因子的表达式。

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。