{"id":"W2073390066","doi":"10.1016/j.laa.2005.04.011","title":"Generalized hyperbolic functions, circulant matrices and functional equations","year":2005,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Circulant matrix; Mathematics; Pure mathematics; Hyperbolic function; Algebra over a field; Matrix (chemical analysis); Mathematical analysis; Combinatorics","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":[0.0009282943,0.001100965,0.0009022966,0.001655856,0.001087781,0.002106661,0.0008493087,0.001452349,0.005304168],"category_scores_gemma":[0.002330934,0.0003323513,0.0004684147,0.001746996,0.003080314,0.002972386,0.00106574,0.001973727,0.0006347256],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001287495,"about_ca_system_score_gemma":0.0007701196,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002451208,"about_ca_topic_score_gemma":0.001979353,"domain_scores_codex":[0.9997558,0.0001080013,0.00001000138,0.00004338003,0.00005848671,0.00002424028],"domain_scores_gemma":[0.9991585,0.000395102,0.000143853,0.0000654728,0.0001592847,0.00007783085],"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":[0.000007002209,0.000007341549,0.00005475288,0.00002703022,0.000004657409,0.00001751163,0.00007236665,0.00183052,0.0003222293,0.993749,0.0009934531,0.002914031],"study_design_scores_gemma":[0.000003238953,0.000004076078,0.00006145441,0.000006128285,0.000001993399,0.00001652681,0.000030162,0.006969857,0.00006611362,0.9913708,0.001464473,0.000005157591],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2595929,0.03252548,0.5158443,0.01260873,0.002251758,0.00005228624,0.000424905,0.000349309,0.1763504],"genre_scores_gemma":[0.9036409,0.01103074,0.03288031,0.001335611,0.003240132,0.00009206869,0.0003105069,0.0001312257,0.04733847],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005304168,"threshold_uncertainty_score":0.01774418,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04687680455761797,"score_gpt":0.2896265136576303,"score_spread":0.2427497091000123,"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."}}