{"id":"W4285092299","doi":"10.3390/math10142433","title":"Monotonicity Results for Nabla Riemann–Liouville Fractional Differences","year":2022,"lang":"en","type":"article","venue":"Mathematics","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Nabla symbol; Monotonic function; Type (biology); Mathematics; Integer (computer science); Fractional calculus; Pure mathematics; Riemann hypothesis; Mathematical analysis; Applied mathematics; Physics; Computer science; Omega","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":[],"consensus_categories":[],"category_scores_codex":[0.0006682656,0.0002135745,0.0003322555,0.000179621,0.001213156,0.00006113791,0.0003464964,0.00006873759,0.0006183048],"category_scores_gemma":[0.001772537,0.0002122616,0.0002210455,0.0003090194,0.00007928044,0.0001410719,0.0001957263,0.0003094586,0.00004951055],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002747679,"about_ca_system_score_gemma":0.0001362768,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002272811,"about_ca_topic_score_gemma":0.00003107153,"domain_scores_codex":[0.9979005,0.00009421481,0.00067215,0.0003239615,0.0006955764,0.0003135602],"domain_scores_gemma":[0.9962758,0.002574492,0.0004104962,0.0004678159,0.0001876257,0.00008372164],"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":[0.00008308746,0.001372763,0.0000325505,0.000110853,0.0001214617,0.000001485262,0.0008983838,0.0006378753,0.0001975247,0.9527516,0.04364953,0.0001428578],"study_design_scores_gemma":[0.001036233,0.0001525746,0.0004054334,0.00002053727,0.0001104382,0.00002653246,0.001386038,0.06546374,0.0001561961,0.9151113,0.01581569,0.0003152908],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2683091,0.00008846135,0.6854351,0.004826824,0.001810563,0.003100194,0.002876806,0.0007344348,0.03281849],"genre_scores_gemma":[0.8849871,0.000004811023,0.1050467,0.0001095099,0.0001921372,0.001432453,0.0001786356,0.00005675274,0.007991953],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.616678,"threshold_uncertainty_score":0.9330734,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09897659588230281,"score_gpt":0.3387312429963581,"score_spread":0.2397546471140553,"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."}}