{"id":"W2500169897","doi":"10.1090/fim/025/08","title":"Weak derivatives and Sobolev spaces","year":2009,"lang":"en","type":"book-chapter","venue":"American Mathematical Society eBooks","topic":"Differential Equations and Boundary Problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Sobolev space; Pure mathematics; Mathematics","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":[0.0003579504,0.00129989,0.0006886813,0.001885566,0.0006546061,0.002159071,0.000551469,0.0008107847,0.01689512],"category_scores_gemma":[0.0008906887,0.0004036554,0.000271632,0.00204474,0.001540291,0.003090197,0.001021745,0.003030008,0.006951382],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001159183,"about_ca_system_score_gemma":0.0006971831,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001321967,"about_ca_topic_score_gemma":0.001889149,"domain_scores_codex":[0.9998617,0.0000259613,0.000008070339,0.00002365011,0.00007029485,0.00001022211],"domain_scores_gemma":[0.9998016,0.0000781023,0.00001135988,0.00002644502,0.00006424385,0.00001836735],"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":[0.0000106371,0.00002551913,0.00005946189,0.0001922339,0.000007032769,0.00004029944,0.0002663965,0.0004803081,0.0007121433,0.8087674,0.1000803,0.08935822],"study_design_scores_gemma":[0.000003881351,0.00001015024,0.0002343975,0.0001578255,0.000007170023,0.0001065843,0.00007212204,0.0008453112,0.000293593,0.4318072,0.5664521,0.000009679749],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.002929686,0.1075713,0.02567201,0.004675247,0.005275671,0.00002520017,0.0002644533,0.0002294221,0.853357],"genre_scores_gemma":[0.03943994,0.07732331,0.009476284,0.001137462,0.003654454,0.00008995461,0.0003258433,0.0003648739,0.8681878],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.01689512,"threshold_uncertainty_score":0.05651981,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0379131765413007,"score_gpt":0.2827343910260398,"score_spread":0.2448212144847391,"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."}}