{"id":"W4230372370","doi":"10.1134/s1560354710510015","title":"Criteria for existence of a Hamiltonian structure","year":2010,"lang":"en","type":"article","venue":"Regular and Chaotic Dynamics","topic":"Navier-Stokes equation solutions","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Diagonalizable matrix; Hamiltonian (control theory); Mathematics; Pure mathematics; Hamiltonian system; Tensor (intrinsic definition); Mathematical physics; Physics; Eigenvalues and eigenvectors; Quantum mechanics; Mathematical optimization; Symmetric matrix","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":[0.000168137,0.0001044829,0.000197353,0.0000542013,0.00008370531,0.00001961806,0.0001173565,0.0001132035,0.00003488844],"category_scores_gemma":[0.0002441228,0.00009791867,0.00006207756,0.00008947212,0.0001319221,0.00005754383,0.00003353833,0.0001100872,6.67598e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001894698,"about_ca_system_score_gemma":0.00003584315,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004546256,"about_ca_topic_score_gemma":0.0002385279,"domain_scores_codex":[0.9993215,0.00001689771,0.0002304722,0.000152281,0.0001246325,0.0001541795],"domain_scores_gemma":[0.9992412,0.0001333671,0.0001123705,0.0003241033,0.0001278212,0.00006116657],"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":[0.00001111583,0.00004506464,0.0001885259,0.0002847216,0.00002716292,7.271386e-7,0.000518682,0.000003046315,0.01414532,0.9818557,0.0001418811,0.00277809],"study_design_scores_gemma":[0.0007199677,0.00008401765,0.001470772,0.00006178798,0.0001202331,0.00005659599,0.0003210604,0.1440673,0.001100582,0.8506209,0.001137172,0.0002396257],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.895391,0.00003871234,0.1026298,0.0003850507,0.0003405971,0.0003926042,0.000298491,0.00004192171,0.0004818271],"genre_scores_gemma":[0.8935201,0.000004450523,0.1056217,0.00002140646,0.00005488604,0.00001001839,0.00003103386,0.00001937733,0.0007170932],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1440642,"threshold_uncertainty_score":0.3993007,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03286120194394611,"score_gpt":0.3347642041475158,"score_spread":0.3019030022035697,"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."}}