{"id":"W4393170176","doi":"10.3934/math.2024558","title":"Classes of completely monotone and Bernstein functions defined by convexity properties of their spectral measures","year":2024,"lang":"en","type":"article","venue":"AIMS Mathematics","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Convexity; Monotone polygon; Mathematics; Spectral properties; Pure mathematics; Monotonic function; Applied mathematics; Mathematical analysis; Physics; Economics; Geometry","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":[0.002038619,0.0006477982,0.0007403719,0.001990582,0.001041963,0.00287293,0.0009332418,0.0008418001,0.005874995],"category_scores_gemma":[0.005983329,0.0005007328,0.0010686,0.001060129,0.00319587,0.003523978,0.001477579,0.001515977,0.0005231271],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002478485,"about_ca_system_score_gemma":0.001287831,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003226498,"about_ca_topic_score_gemma":0.001920674,"domain_scores_codex":[0.9985523,0.0004273651,0.00004981847,0.0002489024,0.0004094805,0.0003121036],"domain_scores_gemma":[0.9963102,0.001677194,0.0004626964,0.0001792047,0.0007480389,0.0006226727],"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":[0.00003135808,0.00001314169,0.0005515211,0.00002068287,0.0000115597,0.00004164282,0.0001262283,0.00286894,0.00134192,0.9899237,0.0006430335,0.004426368],"study_design_scores_gemma":[0.00003094757,0.00007300896,0.003122478,0.0000348989,0.0000154665,0.0003051021,0.0003295858,0.07876284,0.001609601,0.9106135,0.005045715,0.00005675898],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5212103,0.001062906,0.4083311,0.001803559,0.0001873437,0.00008376023,0.0004757493,0.0001830664,0.06666221],"genre_scores_gemma":[0.9624943,0.0005989959,0.02553457,0.0002776355,0.000156816,0.0001051475,0.0003769743,0.00008542462,0.01037017],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005874995,"threshold_uncertainty_score":0.0196538,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08825573332132798,"score_gpt":0.277512260818336,"score_spread":0.1892565274970081,"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."}}