{'fraction_non_alphanumeric': 0.025830258302583026, 'fraction_numerical': 0.0, 'mean_word_length': 6.140350877192983, '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}}
Green's functions, linear second‐order differential equations, and one‐dimensional diffusion advection models

Green's functions to linear second‐order ordinary differential equations with general separated boundary conditions (BCs) are derived, where the parameters used in the BCs are allowed to take negative values. Previous results only considered the nonnegative parameters and such separated BCs arise in the usual Thomas–Fermi BCs. Properties of the Green's functions with possibly negative parameters are obtained and are new. As applications, we study the steady‐state solutions of the one‐dimensional diffusion advection models arising in chemical reactor theory and mathematical biology. We exhibit that the BCs arising from the one‐ dimensional diffusion advection models contain negative parameters.