{"id":"W1479693586","doi":"10.1090/tran/6712","title":"A multi-scale analysis scheme on Abelian groups with an application to operators dual to Hill’s equation","year":2016,"lang":"lv","type":"preprint","venue":"Transactions of the American Mathematical Society","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Foundation; National Science Foundation","keywords":"Omega; Abelian group; Eigenfunction; Eigenvalues and eigenvectors; Combinatorics; Physics; Mathematics; Mathematical physics; Quantum mechanics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009265704,0.0006870221,0.001316397,0.0002363684,0.0003640754,0.0001369019,0.001839406,0.0001898358,0.0000312275],"category_scores_gemma":[0.0001264911,0.0004547337,0.0009247366,0.003183153,0.0004540975,0.0002866488,0.000245511,0.0007152616,0.0001106479],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000483708,"about_ca_system_score_gemma":0.0001255402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007026386,"about_ca_topic_score_gemma":0.00002638669,"domain_scores_codex":[0.9955292,0.000194611,0.001113396,0.001336109,0.001156184,0.0006705431],"domain_scores_gemma":[0.9948262,0.0005653779,0.0005846166,0.0030029,0.000389661,0.0006312735],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00007052372,0.001360064,0.00003244004,0.0003444388,0.001096164,4.086879e-7,0.008068401,0.959537,0.01414187,0.006536778,0.000009253697,0.008802634],"study_design_scores_gemma":[0.0002929565,0.0005149654,0.0004071385,0.0004965953,0.0006803514,0.000003893279,0.0006104008,0.9884827,0.002405872,0.005427471,0.00001320875,0.0006644557],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.07152435,0.000003844303,0.9239559,0.002448978,0.00008139641,0.001627168,0.00009220294,0.0002258907,0.00004027257],"genre_scores_gemma":[0.4443892,0.000004827037,0.5547433,0.0003095322,0.00003801346,0.0003909821,0.000003107825,0.00005413919,0.00006689537],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3728648,"threshold_uncertainty_score":0.9997904,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02207408877350434,"score_gpt":0.2849317051620536,"score_spread":0.2628576163885492,"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."}}