{"id":"W1611973489","doi":"10.1090/s0002-9939-02-06614-5","title":"Oscillation of linear Hamiltonian systems","year":2002,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":32,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; National Science Foundation","keywords":"Eigenvalues and eigenvectors; Hamiltonian system; Monotone polygon; Oscillation (cell signaling); Mathematics; Hamiltonian (control theory); Mathematical analysis; Applied mathematics; Pure mathematics; Physics; Mathematical optimization; Quantum mechanics; 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":[0.0007132846,0.0002641237,0.0008679435,0.00002993299,0.0001230477,0.0000256481,0.0007041285,0.00007704086,0.0001074003],"category_scores_gemma":[0.001248684,0.0001745985,0.0006004513,0.0007922878,0.001101824,0.0001386934,0.0002010821,0.0002670834,0.00003081526],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007873549,"about_ca_system_score_gemma":0.000009741098,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006575384,"about_ca_topic_score_gemma":7.050812e-8,"domain_scores_codex":[0.9976844,0.00002499346,0.0008727104,0.0002605209,0.0008030844,0.0003542648],"domain_scores_gemma":[0.9971115,0.0008374159,0.001258899,0.0003628313,0.0003310311,0.00009833047],"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":[0.0000107257,0.000516747,0.0004523508,0.001831768,0.0001643144,7.518477e-8,0.003198489,0.00001049128,0.01749787,0.9725576,0.003596708,0.0001628726],"study_design_scores_gemma":[0.0002339236,0.0001291681,0.00020908,0.0003851567,0.0001614565,0.00001158924,0.001959676,0.02911492,0.009514903,0.9579571,0.00007388892,0.0002490646],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9689863,0.00003517318,0.002436497,0.0004529891,0.00005920265,0.0006442599,0.00001162823,0.0001263815,0.02724757],"genre_scores_gemma":[0.9377773,0.00001951068,0.06147825,0.00005735542,0.000100926,0.00002568478,1.626574e-7,0.00005357515,0.0004872614],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05904176,"threshold_uncertainty_score":0.7119921,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03876710803972606,"score_gpt":0.2882003494148237,"score_spread":0.2494332413750976,"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."}}