{"id":"W2083826735","doi":"10.1016/s0895-7177(02)00169-3","title":"Translational symmetry of certain integrals with application to the calculus of variations and optimal control","year":2002,"lang":"en","type":"article","venue":"Mathematical and Computer Modelling","topic":"Control and Stability of Dynamical Systems","field":"Engineering","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Symmetry (geometry); Scalar (mathematics); Lemma (botany); Optimal control; Lyapunov function; Applied mathematics; Partial differential equation; Translational symmetry; Bellman equation; Calculus (dental); Mathematical analysis; Mathematical optimization; Nonlinear system","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001555532,0.000672456,0.001009474,0.001687417,0.001080756,0.002018687,0.0009716359,0.0009987154,0.003457842],"category_scores_gemma":[0.003112003,0.0003021643,0.001470218,0.001429771,0.003134595,0.002768599,0.001259361,0.002204327,0.0004457125],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001015488,"about_ca_system_score_gemma":0.0008558994,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001306734,"about_ca_topic_score_gemma":0.0006865587,"domain_scores_codex":[0.9994869,0.0001684604,0.00003318243,0.00008032863,0.0001579661,0.00007310267],"domain_scores_gemma":[0.9992125,0.0003153562,0.0001443139,0.00009853763,0.0001464327,0.00008281755],"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":[0.00001638262,0.0000150794,0.00005283918,0.00002093695,0.000007634103,0.00004081196,0.00007939828,0.002738857,0.0008006074,0.9895452,0.000513653,0.006168631],"study_design_scores_gemma":[0.00001148449,0.00002214188,0.0001490842,0.000007302159,0.000006780033,0.00006909226,0.00003097497,0.04074696,0.000370461,0.9570217,0.001551014,0.00001296744],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1282822,0.004827919,0.8028069,0.00187632,0.001105122,0.00007011346,0.0001389729,0.0003037549,0.06058864],"genre_scores_gemma":[0.884713,0.004196525,0.08716232,0.0004965999,0.00167382,0.0001174676,0.0001582656,0.0003670108,0.02111498],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003457842,"threshold_uncertainty_score":0.01156765,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008833489975686597,"score_gpt":0.1769434521092417,"score_spread":0.1681099621335551,"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."}}