{"id":"W2074624672","doi":"10.4310/maa.2014.v21.n2.a5","title":"Liouville theorems for the polyharmonic Hénon-Lane-Emden system","year":2014,"lang":"en","type":"preprint","venue":"Methods and Applications of Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; University of Alberta","keywords":"Dimension (graph theory); Sobolev space; Conjecture; Mathematics; Bounded function; Exponent; Combinatorics; Mathematical analysis; Mathematical physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001969828,0.001184439,0.0008601586,0.003376001,0.001956475,0.00286471,0.001465776,0.002039595,0.007902603],"category_scores_gemma":[0.004807502,0.0004097967,0.0009807588,0.000991623,0.0026111,0.003332758,0.003362842,0.002676906,0.001026898],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002672177,"about_ca_system_score_gemma":0.001054226,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003269326,"about_ca_topic_score_gemma":0.002353787,"domain_scores_codex":[0.9994535,0.0001980556,0.00002182797,0.00009249048,0.0001448884,0.00008928932],"domain_scores_gemma":[0.9981305,0.0006474942,0.0003243483,0.00008285546,0.0004954889,0.0003193959],"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":[0.00001482427,0.00001975102,0.0003160368,0.00005672764,0.00001682051,0.00007967514,0.0002432933,0.006703941,0.001544145,0.9871972,0.001411086,0.002396463],"study_design_scores_gemma":[0.00002040453,0.00003988059,0.0005566264,0.00003718492,0.00001779513,0.0001463236,0.0002062242,0.1930778,0.001016163,0.7992433,0.00559333,0.00004482476],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2282348,0.004280517,0.5862386,0.007126575,0.001228225,0.0001554827,0.0004836419,0.00027097,0.1719811],"genre_scores_gemma":[0.8467417,0.002687596,0.04724591,0.001356899,0.001093786,0.0002719449,0.0003829796,0.0002628909,0.0999563],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007902603,"threshold_uncertainty_score":0.02643681,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06745592790425284,"score_gpt":0.4458746678492553,"score_spread":0.3784187399450024,"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."}}