{"id":"W4312340338","doi":"10.1007/978-3-031-19377-4_10","title":"The Laplace Transform","year":2022,"lang":"en","type":"book-chapter","venue":"","topic":"Control Systems and Identification","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"","keywords":"Laplace transform; Laplace transform applied to differential equations; Two-sided Laplace transform; Inverse Laplace transform; Mathematics; Transfer function; Z-transform; Laplace–Stieltjes transform; Mellin transform; Integral transform; Bounded function; Linear system; Applied mathematics; Representation (politics); Post's inversion formula; Stability (learning theory); Mathematical analysis; Computer science; Green's function for the three-variable Laplace equation; Fractional Fourier transform; Fourier transform","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":[0.00009296735,0.00009181553,0.00008882344,0.00002141071,0.00009906226,0.00004145192,0.0001090072,0.000053702,0.002127153],"category_scores_gemma":[9.02935e-7,0.00006604542,0.00007479616,0.000006466598,0.000006642411,0.00002770298,0.000006505213,0.0001507681,0.0001994627],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006442672,"about_ca_system_score_gemma":0.000006357142,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000205683,"about_ca_topic_score_gemma":0.0002795935,"domain_scores_codex":[0.9995906,0.000001767786,0.0001451424,0.00007128683,0.0001167027,0.00007443725],"domain_scores_gemma":[0.9997376,0.00002788341,0.0000148282,0.000193176,0.00000976524,0.00001676225],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.000002733046,7.114921e-7,9.317274e-8,0.00003310903,0.0000847765,0.000001259025,0.00005185875,0.0002274724,0.00006383798,0.8382112,0.08932853,0.07199444],"study_design_scores_gemma":[0.00004851893,0.000003794494,0.00000212161,0.000005070376,0.00001149153,0.000001832527,0.000007484894,0.001020589,0.000006345495,0.002097566,0.9967101,0.00008515076],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.000001226011,0.002160695,0.0003621981,0.0002196106,0.0007677687,0.0001937163,0.00001210497,0.0001709038,0.9961118],"genre_scores_gemma":[0.005272661,0.0008003517,0.000002442507,0.00000766935,0.000117685,0.00003068272,0.00001698697,0.00003514287,0.9937164],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.9073815,"threshold_uncertainty_score":0.998785,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006409381678519361,"score_gpt":0.1655319743535008,"score_spread":0.1591225926749814,"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."}}