{"id":"W1987506629","doi":"10.1016/s0723-0869(01)80006-2","title":"An arithmetic-geometric mean inequality","year":2001,"lang":"en","type":"article","venue":"Expositiones Mathematicae","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Inequality of arithmetic and geometric means; Logarithmic mean; Geometric mean; Inequality; Logarithm; Weighted geometric mean; Arithmetic; Harmonic mean; Ky Fan inequality; Weighted arithmetic mean; Young's inequality; Rearrangement inequality; Algebra over a field; Pure mathematics; Mathematical analysis; Log sum inequality; Statistics","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":[0.001680581,0.000631818,0.0007289081,0.001654521,0.001219487,0.002676241,0.001082489,0.001163753,0.00790068],"category_scores_gemma":[0.005630078,0.0003641338,0.001045794,0.001821096,0.002411476,0.00439369,0.00230614,0.004827398,0.00125456],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001819749,"about_ca_system_score_gemma":0.0009766174,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007652033,"about_ca_topic_score_gemma":0.0007579738,"domain_scores_codex":[0.9988725,0.0002750822,0.00004623734,0.0002587914,0.0004358698,0.0001116855],"domain_scores_gemma":[0.9979248,0.001062655,0.0001549423,0.0002025047,0.0005208202,0.0001342857],"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":[0.00001664087,0.000005788785,0.00009290843,0.00003828064,0.000008858035,0.00002649416,0.00004269484,0.0008909589,0.0005793013,0.9857594,0.002895577,0.009643215],"study_design_scores_gemma":[0.000003960447,0.00001334123,0.0002574284,0.00001548144,0.000009915569,0.00008693942,0.00002328496,0.007264636,0.0003137962,0.9821725,0.009830794,0.000007781113],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03958183,0.01058952,0.6727715,0.01424726,0.002643307,0.00003711979,0.0004992326,0.0002402731,0.2593899],"genre_scores_gemma":[0.7229946,0.01100192,0.1592857,0.00441967,0.006559496,0.0002465757,0.0006738233,0.0003452114,0.09447298],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00790068,"threshold_uncertainty_score":0.02643043,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.113731687486305,"score_gpt":0.3805023158881636,"score_spread":0.2667706284018586,"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."}}