{'fraction_non_alphanumeric': 0.011467889908256881, 'fraction_numerical': 0.0022935779816513763, 'mean_word_length': 5.242857142857143, '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}}
First Order Approximation of an Elliptic 3D Singular Perturbation Problem

A three‐dimensional elliptic singular perturbation problem with discontinuous boundary values is considered. The solution of the problem is written in terms of a double integral. A saddle point analysis is used to obtain a first approximation, which is expressed in terms of a function that can be viewed as a generalization of the complementary error function.