{"id":"W7027558578","doi":"","title":"Convex functions, majorization properties and the convex conjugate transform","year":2005,"lang":"en","type":"dissertation","venue":"eScholarship@McGill (McGill)","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"McGill University","keywords":"Regular polygon; Convex set; Convex function; Majorization; Function (biology); Convex analysis; Logarithmically convex function; Proper convex function","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.001313564,0.0007435924,0.001079529,0.0001634371,0.001619826,0.0002061783,0.0004835086,0.0006418213,0.0008573533],"category_scores_gemma":[0.0009272788,0.0005276579,0.0003369257,0.000327962,0.0003040131,0.0004655926,0.00006744517,0.001106197,0.0002464385],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001968025,"about_ca_system_score_gemma":0.00005338886,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001115347,"about_ca_topic_score_gemma":0.0006264177,"domain_scores_codex":[0.9962208,0.0003283078,0.001413378,0.0007448616,0.0007236986,0.000568986],"domain_scores_gemma":[0.9969197,0.0009275734,0.0006427618,0.0008156475,0.0004592398,0.0002350681],"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":[0.0002278463,0.0001554606,6.736154e-7,0.001244158,0.0002179721,0.000001723216,0.00009715955,0.000001514103,0.001364614,0.9791591,0.00005999868,0.01746976],"study_design_scores_gemma":[0.003009768,0.00009883094,0.00002005132,0.0007708205,0.0010176,0.00003851123,0.004350158,0.0004244442,0.0166693,0.8482402,0.1241622,0.001198164],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5382823,0.001247079,0.00004535315,0.00105237,0.000964732,0.005957542,0.001926193,0.0008399659,0.4496844],"genre_scores_gemma":[0.9135599,0.0008996222,0.001060581,0.0005523915,0.0001632103,0.001669551,0.0007922251,0.0002659982,0.08103658],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3752775,"threshold_uncertainty_score":0.9997175,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04981746397900445,"score_gpt":0.2702949029287462,"score_spread":0.2204774389497418,"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."}}