{"id":"W2170337217","doi":"10.1112/jlms.12024","title":"Eigenvalues of the fractional Laplace operator in the unit ball","year":2017,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Analytic and geometric function theory","field":"Mathematics","cited_by":31,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada; Narodowe Centrum Nauki","keywords":"Eigenvalues and eigenvectors; Unit sphere; Antisymmetric relation; Operator (biology); Ball (mathematics); Laplace transform; Laplace operator; Conjecture; Complement (music)","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":[0.00124691,0.0005666034,0.0008261769,0.0008516597,0.0006310946,0.001320048,0.001195106,0.001152837,0.002363515],"category_scores_gemma":[0.004574724,0.0002793536,0.0004583363,0.0004585758,0.001683447,0.001362984,0.001866907,0.001168408,0.0005349839],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008199317,"about_ca_system_score_gemma":0.0007161993,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001746886,"about_ca_topic_score_gemma":0.00114002,"domain_scores_codex":[0.9994451,0.0001532552,0.00002801937,0.0000561675,0.0002448425,0.0000726296],"domain_scores_gemma":[0.9987295,0.0007101621,0.0001296409,0.0001537956,0.0001777618,0.00009908088],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003038115,0.0001125087,0.0009497257,0.0001597191,0.00003065351,0.0002407832,0.0004240438,0.5281181,0.02695751,0.4076716,0.001235701,0.03379593],"study_design_scores_gemma":[0.00001160347,0.00001751754,0.00005141975,0.000007483409,0.00000166006,0.00001900279,0.00001829583,0.9712468,0.002928038,0.02506402,0.0006240878,0.00001015288],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08463786,0.000175376,0.9047083,0.0002134268,0.00006487739,0.00004101388,0.00003590364,0.0002238619,0.009899382],"genre_scores_gemma":[0.6917459,0.000142962,0.3019379,0.0001091029,0.00004124163,0.0001276764,0.00007405117,0.0001273007,0.005693821],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002363515,"threshold_uncertainty_score":0.007906735,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05650911523932209,"score_gpt":0.3313170853829212,"score_spread":0.274807970143599,"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."}}