{'fraction_non_alphanumeric': 0.027287319422150885, 'fraction_numerical': 0.0, 'mean_word_length': 5.709677419354839, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Geometrical optics in nonstationary media

Summary form only given. To establish the basic equations of geometrical optics in inhomogeneous and nonstationary (time-varying) media it is advantageous to combine the three spatial coordinates and the time to four-dimensional space-time coordinates. The restriction to Minkowski coordinates (for a "flat" space-time) is not necessary and would restrict the applications to plane-stratified media. Therefore curvilinear spatial coordinates are employed. The four-dimensional propagation vector is comprised of the customary spatial propagation vector and the circular frequency.