{"id":"W4293229249","doi":"10.14311/ap.2022.62.0165","title":"On generalized Heun equation with some mathematical properties","year":2022,"lang":"en","type":"article","venue":"Acta Polytechnica","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Prince Edward Island","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Polynomial; Orthogonal polynomials; Recurrence relation; Factorization; Pure mathematics; Differential equation; Property (philosophy); Algebra over a field; Simple (philosophy); Applied mathematics; Mathematical analysis; Algorithm","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001422841,0.0001702093,0.0002005841,0.00005152287,0.0002831343,0.00004084571,0.0002550896,0.00002140622,0.001033661],"category_scores_gemma":[0.000003539769,0.000133921,0.00008150168,0.0001511346,0.00003176669,0.0001132401,0.0001338563,0.0002560103,0.00006616562],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004033753,"about_ca_system_score_gemma":0.00007614029,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001845035,"about_ca_topic_score_gemma":2.076777e-7,"domain_scores_codex":[0.9988956,0.00005748019,0.0001880283,0.0002528564,0.0003454486,0.0002605611],"domain_scores_gemma":[0.9993616,0.00004111988,0.0001057598,0.000407218,0.00002155856,0.00006269723],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009041696,0.0003483904,0.00001709222,0.000008326134,0.00004924531,0.000002241805,0.00009587807,0.0001249508,0.02222367,0.9734688,0.002057103,0.001513838],"study_design_scores_gemma":[0.0019984,0.001483803,0.00004892768,0.0000809671,0.0001054547,0.00001070707,0.0003525912,0.02285965,0.07830508,0.8841916,0.009633228,0.0009295982],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9797193,0.00004370827,0.007322149,0.00158673,0.0001341325,0.0006403826,0.00006026209,0.0001967247,0.01029657],"genre_scores_gemma":[0.9979867,0.000001087635,0.0004283152,0.0002949198,0.0001340798,0.0002826497,0.00004017346,0.00004191794,0.0007901019],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08927726,"threshold_uncertainty_score":0.9998795,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02164440418722191,"score_gpt":0.2303603212721184,"score_spread":0.2087159170848965,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}