解析函数

Analytical expressions for electromagnetic fields of a vertical or horizontal electric dipole over the finitely conducting plane are derived subject to the boundary conditions; Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series of spherical Hankel function.

在此边界条件下，推导出有限导电平面上垂直和水平电偶极子电磁场的解析表达式；赫芝位函数中的索末菲型积分被表达成零阶汉克尔函数与绝对收敛的球汉克尔函数级数之和的形式。

A stress function involving several unknown co efficients was constructed in the solution process, and the stress and displacement expressions were obtained through traditional Airy stress function methodology. After the fixed end boundary condition was treated with two methods, the unknown coefficients in stress function were determined with stress and displacement boundary conditions, and the analytical solutions were achieved.

在求解过程中，构造了一个含待定系数的应力函数，通过Airy应力函数解法，给出了应力和位移的表达式，对固支端边界条件采用两种处理办法，利用应力和位移边界条件，确定应力函数中的待定系数，得到了应力和位移的解析解结果。

If you know the function calling convention and the mapping of the C types to the machine types used by the platform you are on, you can resolve the name of each function to find where the code associated to this function is located in memory, and then construct a valid argument list for the function.

如果你了解函数调用和 C 类型至你所在平台的机器类型的映射关系，你可以在内存中解析到每个函数的名字从而找到这些代码所关联的函数的位置，并且构造出一个用在这个函数上的参数列表。

Inequality proof of various ways, they were: use derivative testify inequality nature, Includes using functional monotonicity and extreme value, the function and the concave and convex inequality, proving is concave and convex function in the original definition of equivalent definitions and a lemma is proposed on the basis of relevant concave and convex function of several theorems about inequality, and briefly discusses how to use the definitions and theorems in proof of inequality.

不等式的证明方法多种多样，它们分别是：用导数性质证明不等式；包括利用函数单调性，极值与最值，函数凹凸性证明不等式，其中在给出凹凸函数原始定义等价的解析定义和一个引理的基础上提出有关凹凸函数关于不等式的几个定理，并简要阐述了利用定义和定理在证明不等式中的运用。

And established the mechanics model,optimization parameter model,optimization mathematics model for the elastic element of the extensometer,programs analysis file and optimization control file by using the ANSYS parameter design language.

解析设计方法：依据弹性元件的受力特点建立其力学模型，运用已成熟的力学理论，如薄板弯曲理论、梁弯曲理论、柱拉压理论、剪切理论等获得弹性体的应力应变的解析值，从而获得目标函数和状态变量的解析值。

An integral operator I(subscript n+p) defined by Hadamard product is introduced. Making use of this operator, the subclass S(superscript * subscript n+p) of p(superscript -) valent analytic function is defined in the open unit disk, the inclusion relation of S(superscript * subscript n+p+1)S(superscript * subscript n+p) and the best dominant function of differential subordination q1 are obtained. Furthermore, some conclusions are made according to the special parameters A and B.

用Hadamard卷积定义线性算子I，并利用算子I定义在单位圆内的解析的p叶函数类S(上标*下标 n+p)，给出了此函数类的包含关系S(上标*下标 n+p+1)S和微分从属的最佳控制函数q1，并根据参数A，B取不同的特殊值得出了相应的推论。

Optimal algorithm of combined nonlinear Hopfield network appears powerful validity in solving nonlinear planning, which includes nonlinear objective function, linear constrains and high-demension of decision-making variants, for its ability of nonlinear parallel computation. It is prominent among optimal algorithms because of its function of simply implement with electrocircuit hardware. Genetic algorithm is expressly suitable for optimal calculation regarding the planning of massive, highly nonlinear, inconsecutively differentiable and multiobjective function as well as objective function without analytical expression. However, it inclines to prematurity, as well as its limitation in ability of partial optimal search. Introducing the optimal algorithm of niche genetic simulated annealing to standard Genetic algorithm, can therefore improve the full-scale or partial search ability of Genetic algorithm effectively. It has a far-flung perspective in the field of systemic planning of water pollution control.

组合式非线性Hopfield网络优化算法所具有的非线性大规模并行计算能力在求解具有非线性目标函数、线性约束条件及高维决策变量的非线性规划问题方面显示出了强大的生命力，它易于电路硬件实现的功能更是在优化算法中独树一帜；遗传算法采用概率搜索技术，不受目标函数与约束条件的限制，特别适合大规模、高度非线性的不连续可微的多峰目标函数及无解析表达式的目标函数的规划问题的优化计算，但其存在容易早熟、局部寻优能力较差等缺点，本文在标准遗传算法中引入小生境技术及模拟退火算法有效地改善遗传算法的全局和局部搜索性能，提高了全局最优解的寻优质量，小生境遗传退火模拟优化算法在水污染控制系统规划中的应用前景极为广阔。

Secondly, we introduce the integral operator , where is an operator-valued functions, and derive some argument properties of the integral operator and some interesting corollaries as the special case.

二、将一类被积函数为复值函数的积分算子推广到被积函数为解析算子值函数的情况，并讨论了这类积分算子的辐角性质。

The closed-characteristic expression is proven to be of a A-class entire function and some related propositions are also given. Based on them a series of nathematic deviations are done, which brings an analytic expression between the controller parameters and the cost funtion as well as the restrictions on the optimization problem. In this way the original proposition is concretized for solving.

从系统的传递函数出发，首先证明系统闭环特征函数为A-类整函数的性质并给出其它有关定理，然后进行一系列数学推导，得出了控制器参数与目标函数间的解析关系式及优化的约束条件，由此产生参数优化的具体命题。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失