{'fraction_non_alphanumeric': 0.03339517625231911, 'fraction_numerical': 0.0037105751391465678, 'mean_word_length': 4.869565217391305, '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}}
An inverse-variational principle for the Sturm-Liouville equation

The inverse-variational problem is considered, of how to construct a Sturm-Liouville differential equation, over an interval (0,a), and for a range of values of the parameter lambda , which will give the closest fit at the endpoint x=a of a given function of lambda , to the solution subject to prescribed initial conditions at x=0. Integral conditions are derived for the solution to the problem, and the results are applied to a simple case, using a numerical algorithm.