{"id":"W2117566540","doi":"10.1007/s10915-006-9106-8","title":"On The Eigenvalues of the Spectral Second Order Differentiation Operator and Application to the Boundary Observability of the Wave Equation","year":2006,"lang":"en","type":"article","venue":"Journal of Scientific Computing","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Observability; Eigenvalues and eigenvectors; Mathematical analysis; Operator (biology); Discretization; Galerkin method; Boundary value problem; Boundary (topology); Wave equation; Spectral method; Applied mathematics; Finite element method; Physics","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":[0.0009612784,0.0007153057,0.0004781632,0.001056346,0.0006457705,0.001142296,0.0004951811,0.0008068709,0.003160393],"category_scores_gemma":[0.004467226,0.0002795295,0.0004248895,0.0006566435,0.002015881,0.001811914,0.001081618,0.001376818,0.00022043],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003932523,"about_ca_system_score_gemma":0.0005220757,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001237346,"about_ca_topic_score_gemma":0.0009942515,"domain_scores_codex":[0.9998121,0.00005910338,0.000008700822,0.00003061235,0.00006848048,0.00002095807],"domain_scores_gemma":[0.9979264,0.00147743,0.0001499718,0.00008913724,0.0002414061,0.0001157268],"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":[0.00011913,0.0001088548,0.0006953322,0.0001400724,0.00001905811,0.0004509041,0.0006810981,0.05182933,0.02719138,0.8824416,0.001188648,0.03513472],"study_design_scores_gemma":[0.00001653899,0.00004672511,0.0006321439,0.00003743149,0.000009149655,0.0002367706,0.000182601,0.5819451,0.003293741,0.4119908,0.00157032,0.00003870059],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1885266,0.001012687,0.7876711,0.00130792,0.0002609862,0.00004408534,0.00006073464,0.0001512257,0.02096468],"genre_scores_gemma":[0.9409644,0.001200464,0.04729772,0.0001696841,0.0001786352,0.00004759397,0.00005228741,0.0001102456,0.009978942],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003160393,"threshold_uncertainty_score":0.01057255,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0140537306195956,"score_gpt":0.2048993929416592,"score_spread":0.1908456623220636,"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."}}