标题： 对“等离子体电子结构的广义径向网格生成的注记”的评论 显示英文标题

标题： Comment on "A note on generalized radial mesh generation for plasma electronic structure"

摘要： 在最近的一篇注释[高能密度物理。7, 161 (2011)]中，B.G. Wilson 和 V. Sonnad 提出了一个非常有用的显式表达式，用于高效生成解析对数线性径向网格。该注释的核心是一个涉及 Lambert 函数 W[x] 的参数 h 的隐式方程。作者提到，他们不知道该方程的直接证明（他们是通过使用通过符号操作对隐式定义进行解析微分得到的高阶系数重新求和来获得该方程的）。在本评论中，我们提供了该方程的直接证明。 显示英文摘要

摘要： In a recent note [High Energy Density Phys. 7, 161 (2011)], B.G. Wilson and V. Sonnad proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we present a direct proof of that equation.