{"id":"W2325026335","doi":"10.4006/0836-1398-25.1.38","title":"Basic completely monotone functions as coefficients and solutions of linear<i>q</i>-difference equations with some applications","year":2012,"lang":"en","type":"article","venue":"Physics Essays","topic":"Differential Equations and Boundary Problems","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Monotone polygon; Physics; Applied mathematics; Pure mathematics; Mathematics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001664243,0.0001808635,0.0002576963,0.00007339111,0.0005784726,0.00004507567,0.0001340647,0.00004963296,0.00003924281],"category_scores_gemma":[0.00003852213,0.0001573791,0.0000604339,0.0003658116,0.0002629863,0.0002926368,0.00009055465,0.0001472432,0.00005014251],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002913495,"about_ca_system_score_gemma":0.0000828854,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001046452,"about_ca_topic_score_gemma":0.00001983516,"domain_scores_codex":[0.998813,0.00004756614,0.0003094407,0.0002075477,0.0002931209,0.0003293017],"domain_scores_gemma":[0.998686,0.0003737849,0.0002021698,0.0003996428,0.0002040838,0.000134378],"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":[0.000006830537,0.001065952,0.0004336625,0.00007085683,0.00006511891,7.730348e-8,0.00054105,0.0001353576,0.002168115,0.9915272,0.0000524599,0.003933333],"study_design_scores_gemma":[0.000899896,0.0001766127,0.0003964827,0.00008314962,0.0003872543,0.000008518377,0.0005581569,0.01201862,0.0007373288,0.9837856,0.0005414554,0.0004069088],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08952579,0.0001034989,0.9051731,0.00008855053,0.00006542917,0.0006030531,0.0001288585,0.00008289087,0.004228806],"genre_scores_gemma":[0.9940413,0.00001108031,0.004937656,0.00003151553,0.0001475412,0.0002928505,0.0001018574,0.00002922674,0.0004070085],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9045154,"threshold_uncertainty_score":0.6417731,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09083099879774272,"score_gpt":0.3012906146277446,"score_spread":0.2104596158300019,"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."}}