{"id":"W4206004776","doi":"10.4236/jamp.2021.912208","title":"A Proof of the Non-Singularity of the &amp;lt;i&amp;gt;D&amp;lt;/i&amp;gt; Matrix Used in Deriving the Two—Step Butcher’s Hybrid Scheme for the Solution of Initial Value Problems","year":2021,"lang":"en","type":"article","venue":"Journal of Applied Mathematics and Physics","topic":"Material Science and Thermodynamics","field":"Engineering","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Butcher; Singularity; Mathematics; Scheme (mathematics); Matrix (chemical analysis); State (computer science); Order (exchange); Applied mathematics; Mathematical analysis; Pure mathematics; Algorithm; Law; Economics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001747306,0.0006471984,0.0005099708,0.0004622391,0.0007276121,0.0007826597,0.0008419128,0.001230785,0.006738888],"category_scores_gemma":[0.00891488,0.0003007812,0.0007182087,0.0002312903,0.002913387,0.001620374,0.002400631,0.003678208,0.0007940892],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000366028,"about_ca_system_score_gemma":0.001057394,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006937109,"about_ca_topic_score_gemma":0.0003937895,"domain_scores_codex":[0.9993947,0.0001309043,0.00004103017,0.00008838806,0.0002958709,0.00004924409],"domain_scores_gemma":[0.9967446,0.001679303,0.0002552875,0.0004211277,0.0006920286,0.0002075372],"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":[0.000112813,0.0001101076,0.0009035828,0.0003945845,0.00002908733,0.001120607,0.0005931521,0.02475297,0.04501939,0.9037675,0.00301887,0.02017734],"study_design_scores_gemma":[0.0001103666,0.0003091249,0.001547085,0.0001049765,0.0000217379,0.001340642,0.0001628076,0.6203169,0.04092736,0.3215085,0.01358415,0.00006651157],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03370012,0.0002464885,0.9442109,0.001054769,0.0003822562,0.0001837485,0.00009937858,0.0001929153,0.01992942],"genre_scores_gemma":[0.6530333,0.0004681226,0.3317954,0.0008563864,0.0002542038,0.0002768952,0.0001231122,0.000252934,0.01293977],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006738888,"threshold_uncertainty_score":0.02254385,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02366799821386029,"score_gpt":0.2696165408176228,"score_spread":0.2459485426037625,"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."}}