{"id":"W2964012583","doi":"10.1515/ans-2017-0012","title":"Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities","year":2017,"lang":"en","type":"article","venue":"Advanced Nonlinear Studies","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":46,"is_retracted":false,"has_abstract":true,"ca_institutions":"Pacific Institute for the Mathematical Sciences; University of British Columbia","funders":"National Science Foundation","keywords":"Mathematics; Combinatorics; Physics; Analytical Chemistry (journal); Crystallography; Chemistry","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":[],"consensus_categories":[],"category_scores_codex":[0.0002540241,0.0002370937,0.0006627429,0.0000690495,0.0005017751,0.00004207782,0.0002308742,0.00006958607,0.000009781004],"category_scores_gemma":[0.003979352,0.0002079982,0.0001173085,0.0000458035,0.000592827,0.0002208652,0.0002320855,0.00009379355,0.000003032359],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002921366,"about_ca_system_score_gemma":0.00004854055,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000234658,"about_ca_topic_score_gemma":0.000270641,"domain_scores_codex":[0.9986519,0.00004176792,0.0005145149,0.0002992852,0.0001991453,0.0002933746],"domain_scores_gemma":[0.9973122,0.001157418,0.0004913835,0.0005568221,0.0004138148,0.00006829154],"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":[0.003036899,0.00228059,0.008294517,0.008546851,0.007481035,0.00004250335,0.02506557,0.0006009928,0.02535057,0.8149857,0.004931028,0.09938373],"study_design_scores_gemma":[0.02997429,0.002977514,0.003998027,0.00365531,0.002709609,0.00002980202,0.0391071,0.04475723,0.11442,0.7206174,0.03348723,0.004266507],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.973923,0.003212901,0.01434394,0.001611436,0.0009275859,0.001793143,0.001709968,0.0001761971,0.002301874],"genre_scores_gemma":[0.6959702,0.001467777,0.3005794,0.0000577863,0.0002452332,0.0001759952,0.00003213534,0.00007024595,0.001401225],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2862355,"threshold_uncertainty_score":0.8481922,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2125534708754957,"score_gpt":0.4548675874567111,"score_spread":0.2423141165812155,"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."}}