{"id":"W2057874262","doi":"10.1007/s00013-009-0073-9","title":"Spectral properties of the twisted bi-Laplacian","year":2009,"lang":"en","type":"article","venue":"Archiv der Mathematik","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Sobolev space; Eigenfunction; Laplace operator; Eigenvalues and eigenvectors; Context (archaeology); Pure mathematics; Spectral theory; p-Laplacian; Spectral properties; Mathematical analysis; Quantum mechanics; Physics; Hilbert space; Geology","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":[0.0007359571,0.000864869,0.0005946562,0.003693474,0.001147026,0.002343343,0.0009071584,0.001123532,0.009262822],"category_scores_gemma":[0.002260292,0.0003010891,0.0004622382,0.001335351,0.002243215,0.003708113,0.001804559,0.001579408,0.001391918],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007650852,"about_ca_system_score_gemma":0.0004055784,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006114644,"about_ca_topic_score_gemma":0.0003512139,"domain_scores_codex":[0.9996215,0.00009531243,0.00001957446,0.00006576641,0.0001256354,0.00007224709],"domain_scores_gemma":[0.9986608,0.0002876451,0.0001888269,0.0001197451,0.0003609583,0.000382042],"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":[0.00003848962,0.00002091639,0.0002270523,0.00002609868,0.000005871528,0.0001107813,0.0001982188,0.001438019,0.004650515,0.9895127,0.0006887699,0.003082647],"study_design_scores_gemma":[0.00001146397,0.00002585602,0.000406913,0.00001328347,0.000006327782,0.000276741,0.0001689231,0.035825,0.001183097,0.9608585,0.001198262,0.00002551977],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7341719,0.001174782,0.1647238,0.002647659,0.0005459875,0.00004134047,0.0002614057,0.0003284242,0.09610472],"genre_scores_gemma":[0.9694613,0.0006103705,0.007649759,0.00027992,0.0004163483,0.00003787453,0.0001670366,0.000165187,0.02121207],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009262822,"threshold_uncertainty_score":0.03098726,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07312665988702047,"score_gpt":0.3117129406624011,"score_spread":0.2385862807753807,"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."}}