{"id":"W2509828162","doi":"10.1155/2016/7396951","title":"Estimates on the Lower Bound of the Eigenvalue of the Smallest Modulus Associated with a General Weighted Sturm-Liouville Problem","year":2016,"lang":"en","type":"article","venue":"International Journal of Differential Equations","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Division of Mathematical Sciences; Uppsala Universitet; Luleå Tekniska Universitet","keywords":"Mathematics; Eigenvalues and eigenvectors; Sturm–Liouville theory; Upper and lower bounds; Dirichlet distribution; Modulus; Dirichlet eigenvalue; Combinatorics; Mathematical analysis; Pure mathematics; Dirichlet's principle; Geometry; Boundary value problem","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":[0.002759854,0.001947386,0.001345794,0.003446199,0.0009477924,0.002040331,0.001714911,0.001433205,0.007880687],"category_scores_gemma":[0.01359845,0.0004464496,0.001136202,0.00122242,0.00323578,0.004905373,0.003182853,0.004688578,0.001123227],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001121217,"about_ca_system_score_gemma":0.0005299996,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004639399,"about_ca_topic_score_gemma":0.000446188,"domain_scores_codex":[0.9993157,0.0002051483,0.00003328767,0.0001429996,0.0001891581,0.0001136842],"domain_scores_gemma":[0.9896705,0.006673203,0.0007820955,0.0005445046,0.001149834,0.001179924],"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":[0.0001589652,0.0001024609,0.00138081,0.0003896024,0.00005265733,0.0004170551,0.0005016069,0.02015585,0.01841733,0.9433585,0.002744505,0.01232054],"study_design_scores_gemma":[0.00002376412,0.0001428486,0.001895123,0.0001205173,0.00004356034,0.0003526835,0.0002059134,0.1826952,0.005020341,0.8055354,0.003897646,0.00006686508],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2127165,0.003728192,0.7197912,0.004925129,0.0006419498,0.00006430671,0.0002588142,0.0003827212,0.05749124],"genre_scores_gemma":[0.870101,0.003172238,0.09674115,0.0005536716,0.00164959,0.0003584075,0.0004166832,0.0005760454,0.02643117],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007880687,"threshold_uncertainty_score":0.02636355,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03544263160856155,"score_gpt":0.2921057550863449,"score_spread":0.2566631234777834,"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."}}