变分导数

As to its computing methods, this paper synthesizes six kinds, they are: utilizing a general integral method of complex function directly; utilizing Cauchy integral theorem; utilizing Cauchy integral formula; utilizing Cauchy high-level differential coefficient; utilizing Cauchy residue theorem; utilizing the residual of logarithm.

关于周线积分的计算方法，本文综合了六种，它们分别是：直接利用一般的复变函数积分的方法；利用柯西积分定理；利用柯西积分公式；利用柯西高阶导数公式；利用柯西留数定理；利用对数留数。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

In the third chapter,the Lévy-Feller advection-dispersion equation describing anomalous diffusion,with asymmetric fractional derivative,is considered.

更多程不同的是，在三维情形中，分数阶导数的复杂性使得在构造差分格式时所添加的摄动项也非常复杂，由此所构造差分格式的理论分析也变得比较复杂。

The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.

研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题；提出并证明了完全泛函的变分问题的定理，采用偏微分算子，给出了完全欧拉方程组。

On the basis of the un conditional variational problem of higher order derivatives, this paper studies conditional variational problem .

在含高阶导数的泛函无约束变分问题基础上，进一步研究条件变分问题。

The spectrum of cut-off frequencies is discussed in electromagnetical symplectic system. The wave number k is given and the cut-off frequencies are computed.

在电磁波导辛体系内讨论波导的通过谱，给出一定的波数并建立相应的变分原理，得出本征值方程并计算了波导的截止频率。

When the output branch number is more than 2, we can construct a cascade connection of Y-branch waveguides. However, it occupies a large optical circuit area. The power dividers with 2N output branches can be setup by arranging (2N-1) branch waveguide. However, the design of dividing structures with output branches of odd number such as three or five are difficult.

当输出波导数大於2时，可以用串接的方式来增加输出波导数，但是所需空间会变大，而光功率分配器的2N分岔输出是可以由(2N-1)的分岔输出结构改变而来的，所以在设计奇数波导输出像是3或是5的波导数输出结构就成为一个必须的课题。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。