双曲余弦

In chapter 2, using the favorable characters of the function Q = ch{x - 1, we construct the hyperbolic cosine penalty function and algorithms and proved its convergence .

在第二章中，我们利用函数Q=ch-1良好的性质，提出一种用双曲余弦函数作罚项的双曲余弦罚函数及算法，证明了该罚函数和算法的合理性及迭代点列的收敛性。

In this paper we introduce the hyperbolic cosine function and construct the new hyperbolic cosine penalty function and algorithms, further more, we construct the new hyperbolic cosine multipier penalty function .

本文在传统形式的罚函数基础上引入双曲余弦函数做罚项，构造了新的对于一般约束优化问题的双曲余弦罚函数和求解迭代公式；进一步地，又提出了求解具有等式约束优化问题的双曲罚函数乘子法。

In chapter 3, combining the traditional augmented Lagrange function and the hyperbolic cosine function, we construct a new hyperbolic penalty function multiplier method for the equality constrained optimization and deduced the iterative formulas, and proved the convergence under some conditions.

在第三章中，我们把传统的增广Lagrange函数和双曲余弦函数结合，构造了一类新的在等式约束下的双曲罚函数乘子法，推导出了双曲乘子迭代公式。

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

The potential is evaluated as a hyperbolic function of the distance from anode.

这时，管壁电位随着离阳极的距离按双曲余弦函数衰减。

Focusing properties of elegant cosh square Gaussian and Sinh square Gaussian beams through a thin lens are studied in detail. And intensity distribution on the axis and focusing intensity distribution are analyzed. Also focal shift of Sinh square Gaussian beams are studied.

详细研究了复宗量双曲余弦平方-高斯光束和双曲正弦平方-高斯光束通过薄透镜时的聚焦特性，分析了光束的轴上光强分布和聚焦场的光强分布，讨论了双曲正弦平方-高斯光束的焦移。

Then based on the second-order moment method, the closed-form expression of the beam width is obtained, and the beam waist width and waist location for elegant cosh square Gaussian and Sinh square Gaussian beams are also deduced.

基于二阶矩定义，分别推导了复宗量双曲余弦平方-高斯光束和双曲正弦平方-高斯光束的光斑尺寸、束腰宽度及其位置，并对结果作了详细的分析和讨论。

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

The propagation of elegant cosh-squared-Gaussian beams has been investigated and the analytic solutions have been obtained by means of an angular spectrum technique in uniaxially anisotropic crystals.

基于光束在单轴晶体中传输的角谱理论，对复宗量双曲余弦平方-高斯光束在单轴各向异性晶体中的传输作了研究，得到了一般的解析传输公式，并用数值的方法讨论了晶体内源于复宗量双曲余弦平方-高斯光束的两偏振分量的传输特性，结果表明，在适当参数的条件下，两偏振分量在晶体中的传输波形结构基本保持不变。

It is shown that the M×N ChG beams in turbulent undergo three stages of evolution with increasing propagation distance,and turbulence accelerates the evolution of three stages.The turbulence results in a spreading and degradation of the maximum intensity in the far field.But β-parameter decreases with increasing beam numbers M,separate distances xd and beam parameter δ.And there exists optimal values of xd and δ,and SR of the corresponding M×N ChG beams reaches its maximum.

研究表明：在湍流大气中，双曲余弦高斯列阵光束的传输将经历三个阶段的变化，并且湍流使得光束传输经历三阶段的进程加快；湍流导致双曲余弦高斯列阵光束扩展、最大峰值光强下降，但是，β参量随光束数目M、相邻子光束间距xd和光束参量δ的增加而减少，即光束扩展受湍流的影响减小；并且，存在最佳xd和δ值使得Strehl比取得极大值。

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。