{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003700426,0.0001446328,0.000377313,0.00002882675,0.0005004144,0.00008894217,0.001641197,0.0001210854,0.0004297431],"category_scores_gemma":[0.004360595,0.00005724025,0.0008013023,0.0002581627,0.0004054978,0.0001648024,0.0002244085,0.0006913616,0.00001589602],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006751945,"about_ca_system_score_gemma":0.0001291973,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005571158,"about_ca_topic_score_gemma":0.000002447652,"domain_scores_codex":[0.9978375,0.0002700619,0.0006944444,0.00009244971,0.0009191451,0.0001864421],"domain_scores_gemma":[0.9959068,0.00187147,0.001146091,0.0008033247,0.0002230959,0.00004920946],"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":[0.0001738569,0.001812452,0.01968341,0.0006075908,0.0009210326,0.000008441679,0.008909372,0.0003576498,0.0004757968,0.8470699,0.1193394,0.0006411326],"study_design_scores_gemma":[0.001039763,0.00006904792,0.01545793,0.0002914328,0.00027775,0.0001428832,0.00379471,0.002061674,0.0006292434,0.9721355,0.003966203,0.0001338685],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9448884,0.0003291737,0.01835002,0.02179627,0.0008687521,0.0005707204,0.00001375545,0.0000118549,0.0131711],"genre_scores_gemma":[0.9898081,0.00004802169,0.003735147,0.0008102916,0.0002991396,0.000004097978,1.121129e-7,0.00001870869,0.005276363],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1250656,"threshold_uncertainty_score":0.5220354,"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."}}