{"id":"W2501630932","doi":"10.1090/surv/187/13","title":"Optimal Euclidean Sobolev inequalities","year":2013,"lang":"en","type":"book-chapter","venue":"Mathematical surveys and monographs","topic":"Fatigue and fracture mechanics","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Sobolev space; Inequality; Euclidean geometry; Mathematics; Pure mathematics; Mathematical analysis; 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":[0.000721615,0.001132369,0.0007328311,0.001217869,0.0004623538,0.001582725,0.0007853066,0.0006762919,0.01595602],"category_scores_gemma":[0.001488485,0.0003837057,0.0004608224,0.001451079,0.001389454,0.002307214,0.00162266,0.002398843,0.003069309],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001494548,"about_ca_system_score_gemma":0.0009095576,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001006097,"about_ca_topic_score_gemma":0.001276,"domain_scores_codex":[0.9994621,0.000110374,0.00002930079,0.0000830423,0.000257777,0.00005734251],"domain_scores_gemma":[0.9997135,0.00009781824,0.00002545106,0.00005192442,0.00008135443,0.00002981607],"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":[0.00001460602,0.00001648035,0.00003280333,0.0001323165,0.000009581164,0.00001443451,0.0000396466,0.002720982,0.0006642055,0.919225,0.01721313,0.05991674],"study_design_scores_gemma":[0.000007261363,0.00001980486,0.0002330846,0.0001229988,0.00001285831,0.00006546861,0.00003643953,0.009213396,0.0009570778,0.8317438,0.1575713,0.00001655012],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01047879,0.04396783,0.3323831,0.004341482,0.002573581,0.00004924354,0.0006752207,0.0002774308,0.6052533],"genre_scores_gemma":[0.2919643,0.09124646,0.1197999,0.002093998,0.005678411,0.000296739,0.001651536,0.0009417367,0.486327],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.01595602,"threshold_uncertainty_score":0.05337816,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02465559323902205,"score_gpt":0.2101908491244393,"score_spread":0.1855352558854173,"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."}}