{"id":"W2082803464","doi":"10.4153/cmb-2008-016-5","title":"First Variations of the Best Sobolev Trace Constant with Respect to the Domain","year":2008,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; TRACE (psycholinguistics); Constant (computer programming); Sobolev space; Domain (mathematical analysis); Bounded function; Embedding; Ball (mathematics); Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0003620147,0.0001821647,0.0002848672,0.00008433704,0.0005896465,0.00003344073,0.0004957311,0.00007688074,0.003311475],"category_scores_gemma":[0.001589374,0.0001012551,0.0001094746,0.0004116861,0.0003366296,0.00001697481,0.00005320182,0.0002193392,0.001931339],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001271664,"about_ca_system_score_gemma":0.000489164,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001120752,"about_ca_topic_score_gemma":0.03818897,"domain_scores_codex":[0.9984244,0.000139775,0.0004403311,0.0002077555,0.0004022868,0.0003854601],"domain_scores_gemma":[0.9975999,0.0009999608,0.0001243566,0.0007842309,0.0001430469,0.0003485224],"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":[0.00001775144,0.000197382,0.00008735028,0.00006938695,0.00006786024,0.0000210234,0.003125435,0.00007623247,0.00008864327,0.9721054,0.02409871,0.0000447976],"study_design_scores_gemma":[0.001831315,0.0004702932,0.002021429,0.001159812,0.000496393,0.0005167329,0.002934201,0.001683539,0.001551719,0.6871172,0.2990794,0.001138023],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5242053,0.00008053659,0.1699232,0.2208736,0.0003064774,0.004763693,0.000688956,0.0001338108,0.07902445],"genre_scores_gemma":[0.9703241,0.000002367133,0.02578462,0.0005000933,0.0001147274,0.0001105167,0.000002694914,0.0000474493,0.003113454],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4461188,"threshold_uncertainty_score":0.9988458,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04038929696341321,"score_gpt":0.2625989922715319,"score_spread":0.2222096953081187,"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."}}