{"id":"W1795440635","doi":"10.1090/s0002-9939-03-07015-1","title":"Existence of solutions to projected differential equations in Hilbert spaces","year":2003,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Nonlinear Differential Equations Analysis","field":"Mathematics","cited_by":67,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Guelph; Queen's University","funders":"","keywords":"Lipschitz continuity; Mathematics; Uniqueness; Hilbert space; Vector field; Dimension (graph theory); Mathematical analysis; Locally convex topological vector space; Regular polygon; Pure mathematics; Field (mathematics); Normed vector space; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001849744,0.001104555,0.0009903385,0.001266231,0.001014705,0.002716462,0.001100244,0.001865292,0.002385046],"category_scores_gemma":[0.009552624,0.0007004347,0.0009346923,0.0007904427,0.003476035,0.004808324,0.004823178,0.00305185,0.0003730735],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001033627,"about_ca_system_score_gemma":0.001098206,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000482933,"about_ca_topic_score_gemma":0.0002425173,"domain_scores_codex":[0.9991679,0.0002182872,0.00004946144,0.0001387539,0.000284367,0.0001413422],"domain_scores_gemma":[0.9976509,0.0008808209,0.000290281,0.0001185262,0.000662427,0.0003970309],"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":[0.00006732512,0.00003795235,0.0005388371,0.0001467039,0.00002639403,0.0002367486,0.000532656,0.017065,0.007785853,0.962756,0.0005915419,0.01021488],"study_design_scores_gemma":[0.00004566757,0.0001175213,0.0002802693,0.00006796348,0.00001545062,0.0002967613,0.0003524022,0.2568768,0.007691767,0.7310671,0.003146902,0.0000413815],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2135765,0.0007029223,0.7741987,0.001236111,0.0001579922,0.0001190169,0.0001148259,0.0001951323,0.009698926],"genre_scores_gemma":[0.8498051,0.001350428,0.1365874,0.0001916938,0.0001449819,0.0002590583,0.0002210879,0.0001317427,0.01130865],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002716462,"threshold_uncertainty_score":0.009782493,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04755606780654668,"score_gpt":0.3135104354970096,"score_spread":0.2659543676904629,"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."}}