{'fraction_non_alphanumeric': 0.015918958031837915, 'fraction_numerical': 0.0, 'mean_word_length': 5.290909090909091, '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}}
Small-amplitude free-surface waves generated by moving oscillatory disturbances

The problem of capillary–gravity waves generated by certain moving oscillatory surface-pressure distributions is investigated. The main difficulty of the problem lies in finding the real roots of the modified frequency equations. This is dealt with by the use of certain geometric considerations. The critical condition that results from the formation of double roots of the modified frequency equations is represented as a surface. This surface divides the whole space into several distinct regions. For points in different regions the propagation of waves is different. The waves are determined in all cases.