{"id":"W1995268357","doi":"10.1007/s11425-010-3138-0","title":"Ultimate generalization to monotonicity for uniform convergence of trigonometric series","year":2010,"lang":"en","type":"article","venue":"Science China Mathematics","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":54,"is_retracted":false,"has_abstract":false,"ca_institutions":"St. Francis Xavier University","funders":"","keywords":"Mathematics; Monotonic function; Sequence (biology); Trigonometric series; Generalization; Series (stratigraphy); Convergence (economics); Uniform convergence; Bounded function; Function series; Space (punctuation); Discrete mathematics; Pure mathematics; Combinatorics; Mathematical analysis; Fourier series","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":[0.006575986,0.0009489354,0.001477708,0.002704075,0.001962021,0.002808744,0.002087878,0.001618092,0.007791108],"category_scores_gemma":[0.02174833,0.0005668622,0.00237428,0.00173667,0.004616116,0.01194365,0.006157274,0.006411013,0.0008615584],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001464021,"about_ca_system_score_gemma":0.0009951859,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001134857,"about_ca_topic_score_gemma":0.0007898588,"domain_scores_codex":[0.9973781,0.000999703,0.0001970397,0.0005908195,0.0005295118,0.0003048375],"domain_scores_gemma":[0.9894856,0.005344755,0.000563245,0.001314274,0.002531746,0.0007603441],"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":[0.00003220869,0.00001455139,0.0003093997,0.0000683464,0.00001678271,0.00008113806,0.0001851839,0.0008760442,0.0005871991,0.990432,0.001170594,0.006226656],"study_design_scores_gemma":[0.00000689567,0.0000322098,0.0004684186,0.00003294396,0.0000198415,0.0002305095,0.00008999342,0.01608131,0.0007835674,0.9783388,0.0039002,0.0000153992],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.122594,0.004319598,0.7317082,0.005433637,0.001404867,0.00008616367,0.0004469038,0.0004262918,0.1335804],"genre_scores_gemma":[0.8540178,0.003861885,0.0972708,0.002799247,0.002373451,0.0002482293,0.0005366228,0.000503899,0.03838813],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007791108,"threshold_uncertainty_score":0.03477758,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03161625102823948,"score_gpt":0.3318972188979447,"score_spread":0.3002809678697052,"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."}}