{"id":"W2052244282","doi":"10.1006/jmaa.1999.6688","title":"Bounds for A–G, A–H, G–H, and a Family of Inequalities of Ky Fan's Type, Using a General Method","year":2000,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Guelph","funders":"","keywords":"Mathematics; Generalization; Type (biology); Inequality; Upper and lower bounds; Combinatorics; Ky Fan inequality; Calculus (dental); Pure mathematics; Discrete mathematics; Mathematical analysis; Rearrangement inequality; Log sum inequality","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001029609,0.0001497352,0.0009518705,0.0002058228,0.0000907429,0.00003059258,0.0001583404,0.00008040904,0.0002126219],"category_scores_gemma":[0.0001857136,0.0001099744,0.0003119248,0.0005891175,0.0001674944,0.00007580318,0.00003247063,0.00009184025,6.01663e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001182134,"about_ca_system_score_gemma":0.0000400789,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001677426,"about_ca_topic_score_gemma":0.000002282614,"domain_scores_codex":[0.9979937,0.00006602352,0.001375806,0.0001465257,0.0002672996,0.0001506453],"domain_scores_gemma":[0.9970409,0.001454527,0.0007054861,0.00027456,0.0004059696,0.0001185463],"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":[0.00002642235,0.0003947639,0.0000437248,0.0008074068,0.0007354693,1.612022e-7,0.0006076494,0.00003786268,0.004413233,0.9879566,0.00009571805,0.004880947],"study_design_scores_gemma":[0.00035163,0.0001113352,0.00007719346,0.0000917698,0.002618575,0.00002262314,0.00083853,0.01786214,0.001296219,0.9752653,0.001322297,0.0001423877],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.3136533,0.0001967529,0.6850874,0.0001303634,0.000002810332,0.0002475277,0.00005635071,0.000005285553,0.0006201311],"genre_scores_gemma":[0.2147171,0.0001775627,0.7843201,0.00004251105,0.00009134896,0.00005579312,0.000004729138,0.00002021879,0.0005706854],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.0992326,"threshold_uncertainty_score":0.4484625,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1076929313749188,"score_gpt":0.4117629459054475,"score_spread":0.3040700145305287,"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."}}