{'fraction_non_alphanumeric': 0.01674641148325359, 'fraction_numerical': 0.0, 'mean_word_length': 5.758064516129032, '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}}
Modern Applications of the Bateman-Whittaker Theory

The Bateman-Whittaker theory, which was developed more than a century ago, is shown to be a comprehensive basis for deriving a large class of null spatiotemporally localized waves characterized by intriguing vorticial structures. In addition, it provides the proper modeling for studying topological structures dealing with linked and knotted electromagnetic waves.