Inversion of a "discontinuous coordinate transformation" in general relativity

Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in General Relativity

The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is defined only locally, and is done using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the $θ$--divisor. For a representation of the hyperelliptic functions the Klein--Weierstraß multivariable sigma function is introduced. It is shown that all parameters needed for the calculations like period matrices …

反演Radon变换标准方法的一种额外可能性

An additional possibilities of the standard method of inverting the Radon transform

本文针对有限维欧几里得空间中Radon变换反演问题，指出现有公式仅适用于可微函数，提出通过修改光滑函数的证明来获得不连续函数情形的反演公式。

二阶后牛顿阶解析坐标时间

Analytical coordinate time at the second post-Newtonian order

本文推导了广义相对论中二阶后牛顿阶下偏心轨道致密双星系统坐标时间关于偏近点角的解析表达式，通过参数化减少不连续三角函数并处理无穷级数，便于实际截断分析。