{"id":"W2059983606","doi":"10.2140/pjm.2005.218.343","title":"A family of isochronous foci with Darboux first integral","year":2005,"lang":"en","type":"article","venue":"Pacific Journal of Mathematics","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Integrable system; Mathematics; Focus (optics); Center (category theory); Homogeneous; Class (philosophy); Polynomial; Pure mathematics; Algebraic number; Differential (mechanical device); Mathematical physics; Mathematical analysis; Combinatorics; Physics","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":[0.0004620609,0.0001925144,0.0006377456,0.000132509,0.0000648846,0.00002802949,0.000249949,0.00007966595,0.00006649374],"category_scores_gemma":[0.0003086129,0.0001234467,0.0001873776,0.0001798949,0.0001052103,0.0001656651,0.00002947672,0.0002342132,0.00001121396],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009851258,"about_ca_system_score_gemma":0.0000740791,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000430071,"about_ca_topic_score_gemma":0.00002422685,"domain_scores_codex":[0.9980217,0.0000366798,0.001098638,0.0001007652,0.0005252687,0.0002169194],"domain_scores_gemma":[0.9975117,0.0005396919,0.001188331,0.0002901805,0.000355954,0.0001140745],"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":[0.0003876418,0.00790555,0.001350246,0.003732734,0.001407808,0.00007288501,0.02751611,0.003320394,0.005730266,0.917424,0.002986924,0.02816544],"study_design_scores_gemma":[0.00649372,0.002749489,0.000324899,0.004729289,0.0009811404,0.00127717,0.03670055,0.07032136,0.002307724,0.8680387,0.004865207,0.001210748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2835012,0.0002104207,0.7102511,0.0001573248,0.0000956295,0.0001891672,0.00001059639,0.00001988489,0.005564663],"genre_scores_gemma":[0.7993071,0.00003094076,0.2003365,0.000005451358,0.0001247007,0.000003202315,8.131488e-7,0.00002752651,0.0001637368],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5158058,"threshold_uncertainty_score":0.5034009,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02798869128582672,"score_gpt":0.278500290415817,"score_spread":0.2505115991299903,"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."}}