{"id":"W2011632766","doi":"10.1016/j.jmaa.2007.11.006","title":"A note on iterative roots of PM functions","year":2007,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Zhàng; Monotone polygon; Iterative method; Class (philosophy); Applied mathematics; Pure mathematics; Combinatorics; Mathematical analysis; Mathematical optimization; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001299028,0.0001180998,0.0004750978,0.0004673441,0.0001128475,0.00002245158,0.0001190438,0.00006574123,0.0001907718],"category_scores_gemma":[0.0008646565,0.00008476845,0.000336204,0.001087368,0.0001139936,0.0000857514,0.0000243177,0.0001854057,0.00001659774],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004774858,"about_ca_system_score_gemma":0.00003783707,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001839933,"about_ca_topic_score_gemma":0.00001966119,"domain_scores_codex":[0.9981885,0.00004320146,0.001057432,0.0001398012,0.0004465131,0.000124545],"domain_scores_gemma":[0.9956079,0.002784404,0.0006343267,0.0002788985,0.0005656998,0.0001287568],"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":[0.0001997993,0.002985785,0.001089499,0.0002158193,0.001855036,0.000003076533,0.0006913379,0.0004966078,0.003771057,0.9783143,0.0006030543,0.009774622],"study_design_scores_gemma":[0.0007714329,0.0003819632,0.01185703,0.0001032642,0.003234562,0.00004491997,0.0007153209,0.003602124,0.001874816,0.9751033,0.00208358,0.0002276379],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1095407,0.00002690205,0.8856491,0.000580361,0.00001309468,0.0001845789,0.00002615799,0.000009433839,0.003969618],"genre_scores_gemma":[0.9584215,0.000007338141,0.04101367,0.0000341871,0.000116846,0.00001615499,0.000005096203,0.000009132516,0.000376092],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8488808,"threshold_uncertainty_score":0.3456757,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03226359092178849,"score_gpt":0.3347460203205706,"score_spread":0.3024824293987821,"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."}}