{"id":"W2889943766","doi":"10.1080/03081087.2018.1517720","title":"Normality, self-adjointness, spectral invariance, groups and determinants of pseudo-differential operators on finite abelian groups","year":2018,"lang":"en","type":"article","venue":"Linear and Multilinear Algebra","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University; Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Abelian group; Normality; Pure mathematics; Differential operator; Rank of an abelian group; Differential (mechanical device); Elementary abelian group; Statistics; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001069317,0.0005414687,0.0004493236,0.002256003,0.0008706445,0.002132766,0.0006000524,0.0007255345,0.002693912],"category_scores_gemma":[0.00283107,0.00023102,0.0007056275,0.0007856045,0.004357849,0.00319707,0.001906112,0.001332829,0.0005307839],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006525317,"about_ca_system_score_gemma":0.0003884994,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004042675,"about_ca_topic_score_gemma":0.0002149472,"domain_scores_codex":[0.9989458,0.0002456428,0.00006099413,0.0001643326,0.0004428094,0.0001405433],"domain_scores_gemma":[0.9981884,0.0005379186,0.0002764873,0.0002022497,0.0004655571,0.0003293363],"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":[0.00001829429,0.00002710834,0.0004535269,0.00002067814,0.000006103792,0.0000983584,0.0003368838,0.0006840823,0.002825611,0.9906276,0.000346081,0.004555585],"study_design_scores_gemma":[0.00000600045,0.00003459306,0.0004525155,0.000006432768,0.000004606693,0.000186556,0.0001079395,0.006627261,0.001608171,0.9893567,0.001593715,0.00001555552],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6938905,0.0008352903,0.2462042,0.001528023,0.0004309271,0.00006257321,0.0001970382,0.0002919783,0.05655945],"genre_scores_gemma":[0.9841713,0.0002733373,0.00928431,0.000148671,0.000269673,0.00003471033,0.00009405967,0.00004294092,0.005680813],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002693912,"threshold_uncertainty_score":0.009012043,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02806128786896033,"score_gpt":0.3075299296482011,"score_spread":0.2794686417792408,"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."}}