{"id":"W2943969851","doi":"10.5539/jmr.v11n3p14","title":"On Liouvillian Solutions of Third Order Homogeneous Linear Differential Equations","year":2019,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Homogeneous; Exponent; Invariant (physics); Combinatorics; Logarithm; Exponential function; Differential equation; Constant (computer programming); Mathematical physics; Pure mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002171882,0.00008407587,0.000232665,0.0006642279,0.0001506304,0.00007869802,0.001060863,0.00006084714,0.0001587877],"category_scores_gemma":[0.0005981733,0.00006357268,0.0001708033,0.0008519677,0.00009023341,0.0001519859,0.0002320236,0.0004767964,0.000110196],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003045541,"about_ca_system_score_gemma":0.0001714563,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002171794,"about_ca_topic_score_gemma":0.000002108412,"domain_scores_codex":[0.9978551,0.0002136809,0.0004582172,0.000115473,0.001074236,0.0002832873],"domain_scores_gemma":[0.9967611,0.001509797,0.0002407597,0.000511196,0.0008738713,0.0001032458],"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":[0.00002606603,0.0009377073,0.00003238782,0.0001060308,0.00009077436,0.00001184544,0.00182802,0.0009580677,0.008433742,0.9849858,0.0009693666,0.00162015],"study_design_scores_gemma":[0.001282057,0.002792954,0.0002059492,0.0007067871,0.00003539376,0.0001289338,0.0006913288,0.2058055,0.008015427,0.7791851,0.0008625826,0.0002880502],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2712113,0.00008651823,0.7248312,0.0004562245,0.0002797901,0.0001569232,0.000003042705,0.00001381608,0.002961236],"genre_scores_gemma":[0.9707881,0.00003001507,0.02866082,0.00001341223,0.00007217497,0.000002102371,3.148582e-7,0.00000885252,0.0004242107],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6995768,"threshold_uncertainty_score":0.2592418,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09084313278958654,"score_gpt":0.3563194632935208,"score_spread":0.2654763305039343,"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."}}