{"id":"W2124749764","doi":"10.1080/03605302.2014.1003073","title":"Symmetry Results for Fractional Elliptic Systems and Related Problems","year":2015,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Monotonic function; Monotone polygon; Fractional Laplacian; Hamiltonian (control theory); Hamiltonian system; Symmetry (geometry); Laplace operator; Pure mathematics; Elliptic operator; p-Laplacian; Mathematical physics; Combinatorics; Mathematical analysis; Geometry; Boundary value problem","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":[0.0009048579,0.0005965772,0.0005877259,0.0008849571,0.000851667,0.0009080275,0.000724803,0.0009445534,0.003300749],"category_scores_gemma":[0.001675353,0.0002497032,0.0008865877,0.0003661386,0.00164235,0.001861285,0.001945266,0.001011316,0.000308709],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008744994,"about_ca_system_score_gemma":0.0005473655,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001047131,"about_ca_topic_score_gemma":0.0004689676,"domain_scores_codex":[0.9996586,0.0001152641,0.00001760777,0.00004116244,0.000104598,0.00006277282],"domain_scores_gemma":[0.9994496,0.0001657408,0.000152753,0.00005427495,0.00008323107,0.00009440413],"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":[0.00002245588,0.00003149691,0.0004200654,0.00006450999,0.00002069775,0.0002239494,0.0001887887,0.02077481,0.003578308,0.9692672,0.0008893057,0.004518438],"study_design_scores_gemma":[0.00002937495,0.00005507262,0.0005033219,0.00001971637,0.000009979103,0.0002079079,0.0001863195,0.2367534,0.001268832,0.7587856,0.002161377,0.00001909659],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4537727,0.002694535,0.46277,0.004369073,0.0003794498,0.0001397364,0.0001960504,0.0001188352,0.07555971],"genre_scores_gemma":[0.96357,0.001034855,0.01985343,0.0003010368,0.0002361313,0.00009505401,0.0001094174,0.00006397363,0.01473609],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003300749,"threshold_uncertainty_score":0.01104212,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.210792822951407,"score_gpt":0.3915548931449809,"score_spread":0.1807620701935738,"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."}}