{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002705908,0.0006430816,0.001157283,0.00005571315,0.0002936288,0.0002670147,0.0002720116,0.0002724831,0.0004271073],"category_scores_gemma":[0.00007211394,0.0005309772,0.0005318123,0.0000302693,0.001690608,0.00006189274,0.0001847456,0.0005542915,0.00007613705],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007183661,"about_ca_system_score_gemma":0.0001026263,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000130606,"about_ca_topic_score_gemma":0.000007049057,"domain_scores_codex":[0.9977364,0.00003142215,0.0006761332,0.0005653223,0.00055662,0.0004340985],"domain_scores_gemma":[0.9978667,0.0006720529,0.000600371,0.0005306965,0.0001010549,0.0002290826],"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":[0.000004233105,0.00005412978,9.950454e-7,0.0002731155,0.0002785473,0.000003379158,0.001610122,5.619972e-8,0.00006068909,0.9205438,0.002659682,0.07451117],"study_design_scores_gemma":[0.0002115302,0.0002129753,0.000003121323,0.0004124776,0.0002763791,0.00002394698,0.0009328537,0.0001340639,0.00002641986,0.9451092,0.05205762,0.0005993668],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00134027,0.000123821,0.01491213,0.0004942123,0.00003977603,0.0006758149,0.00002733376,0.0002842577,0.9821024],"genre_scores_gemma":[0.006993388,0.0001689354,0.1170795,0.0005750811,0.0002638017,0.00004883782,0.00001847436,0.0002071365,0.8746448],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.1074576,"threshold_uncertainty_score":0.9997142,"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."}}