{"id":"W4404080263","doi":"10.1137/23m160846x","title":"Building Hierarchies of Semiclassical Jacobi Polynomials for Spectral Methods in Annuli","year":2024,"lang":"en","type":"article","venue":"SIAM Journal on Scientific Computing","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"Engineering and Physical Sciences Research Council; Deutsche Forschungsgemeinschaft; Leverhulme Trust","keywords":"Mathematics; Semiclassical physics; Jacobi polynomials; Jacobi method; Applied mathematics; Gegenbauer polynomials; Orthogonal polynomials; Algebra over a field; Pure mathematics; Classical orthogonal polynomials; Calculus (dental); Quantum","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001656959,0.0004996884,0.0010506,0.001808475,0.001718187,0.002180313,0.001733667,0.001113229,0.00559668],"category_scores_gemma":[0.004827762,0.0007309657,0.0009926613,0.001009397,0.002044059,0.003078481,0.003809614,0.002948193,0.001854976],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001160781,"about_ca_system_score_gemma":0.001083748,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00138438,"about_ca_topic_score_gemma":0.003572679,"domain_scores_codex":[0.9990415,0.0002696737,0.00006281759,0.0000957746,0.0003801563,0.0001501096],"domain_scores_gemma":[0.9976973,0.0008142963,0.0001287343,0.0005663238,0.0004541136,0.0003392395],"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":[0.000042272,0.00009165247,0.0004659189,0.0001317915,0.00001897811,0.00008206058,0.0005195946,0.02096999,0.007057162,0.9267716,0.003207073,0.04064184],"study_design_scores_gemma":[0.0000165948,0.00003864774,0.0001575563,0.00006712977,0.00001141695,0.00004957086,0.0001219041,0.2931166,0.002992806,0.6917622,0.01163817,0.00002735905],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.06284832,0.000621967,0.9121575,0.0004018479,0.000265531,0.00007986903,0.000115765,0.001069162,0.02244007],"genre_scores_gemma":[0.4273112,0.0006911824,0.5616341,0.0004135284,0.0002428514,0.0001776917,0.0003523639,0.0008897297,0.008287469],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.00559668,"threshold_uncertainty_score":0.01872271,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1292507934940085,"score_gpt":0.5006620404765456,"score_spread":0.3714112469825371,"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."}}