{"id":"W4226413944","doi":"10.1109/access.2022.3157736","title":"Linear Version of Parseval’s Theorem","year":2022,"lang":"en","type":"article","venue":"IEEE Access","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Windsor","funders":"","keywords":"Parseval's theorem; Invariant (physics); Nonlinear system; Mathematics; Discrete Fourier transform (general); Fourier transform; Signal processing; Linear system; Discrete mathematics; Applied mathematics; Pure mathematics; Computer science; Algorithm; Digital signal processing; Mathematical analysis; Fourier analysis; Fractional Fourier transform; Quantum mechanics; 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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0009674335,0.00008844068,0.0002794947,0.00007426921,0.0001196433,0.00001267717,0.0004489271,0.00002530438,0.003278753],"category_scores_gemma":[0.0001012342,0.00006838762,0.0001668285,0.0002985361,0.00003681878,0.00009003981,0.0001050679,0.0001376828,0.00001082984],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001791983,"about_ca_system_score_gemma":0.00001906177,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001055616,"about_ca_topic_score_gemma":0.000002049437,"domain_scores_codex":[0.998848,0.0001617705,0.0003169456,0.0001406842,0.000396202,0.000136354],"domain_scores_gemma":[0.999012,0.0004729506,0.0001249739,0.0002986821,0.00004865058,0.00004276142],"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":[0.0002852816,0.002060912,0.001393383,0.001393106,0.0005372371,0.00003336092,0.002250994,0.0009940288,0.008371143,0.9550241,0.01113347,0.01652303],"study_design_scores_gemma":[0.0004431275,0.00007942162,0.00004214639,0.00002059109,0.0001719758,0.000005305368,0.0002006584,0.005765229,0.04472965,0.9451293,0.003257502,0.0001551072],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8677705,0.00004404799,0.1026591,0.000269884,0.0002938604,0.0002874999,0.00004458901,0.00007277964,0.02855773],"genre_scores_gemma":[0.9877369,0.00000783308,0.01158391,0.00006683318,0.0000415588,0.00002462808,0.000003305473,0.00001571994,0.0005193128],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1199664,"threshold_uncertainty_score":0.9976324,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1182989465061821,"score_gpt":0.4183361819041456,"score_spread":0.3000372353979635,"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."}}