{'fraction_non_alphanumeric': 0.030303030303030304, 'fraction_numerical': 0.0, 'mean_word_length': 4.7875, '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}}
Minimum-time running: a numerical approach.

The article deals with the minimum-time running problem. The time of covering a given distance is minimized. The Hill-Keller model of running employed is based on Newton's second law and the equation of power balance. The problem is formulated in optimal control. The unknown function is the runner's velocity that varies with the distance. The problem is solved applying the direct Chebyshev's pseudospectral method.