{"id":"W1978753631","doi":"10.1155/s1025583402000061","title":"Duality theorem over the cone of monotone functions and sequences in higher dimensions","year":2002,"lang":"en","type":"article","venue":"Journal of Inequalities and Applications","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Monotone polygon; Duality (order theory); Cone (formal languages); Dual cone and polar cone; Pure mathematics; Combinatorics; Mathematical analysis; Regular polygon; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0004560263,0.00007126175,0.0002007146,0.0000600988,0.00008307288,0.00002432797,0.00006296862,0.00003858755,0.000374048],"category_scores_gemma":[0.0001299759,0.00004082312,0.00004095376,0.0001333386,0.0001659596,0.0001122176,0.00002029917,0.0001225522,0.000001294096],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001175649,"about_ca_system_score_gemma":0.000009218236,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001696442,"about_ca_topic_score_gemma":0.00001258969,"domain_scores_codex":[0.9990685,0.00007634728,0.0005730808,0.00006357713,0.0001497534,0.00006872068],"domain_scores_gemma":[0.9986944,0.0006849383,0.000333742,0.0001249407,0.0001227519,0.00003922679],"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":[0.00000403583,0.0001179067,0.0001694446,0.00005787122,0.00001588325,1.355029e-7,0.001079198,0.000001797806,0.0002140656,0.9966232,0.001023152,0.0006933098],"study_design_scores_gemma":[0.0003456834,0.00006298204,0.0009627449,0.00008091546,0.00004332322,0.0000205624,0.005743066,0.001950935,0.0001797846,0.985634,0.004898521,0.00007746915],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9495111,0.0008852004,0.03396318,0.006705074,0.00009678966,0.0005188551,0.00004410946,0.00001569908,0.008260037],"genre_scores_gemma":[0.9937065,0.0002277678,0.004735162,0.0001220028,0.00008694145,0.00004025211,0.000001122701,0.000005682029,0.001074628],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04419539,"threshold_uncertainty_score":0.4095564,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1048653497467985,"score_gpt":0.319990440178845,"score_spread":0.2151250904320465,"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."}}