{"id":"W2064827546","doi":"10.1016/j.jat.2013.12.002","title":"New moduli of smoothness on the unit ball, applications and computability","year":2014,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Moduli; Unit sphere; Convexity; Banach space; Pure mathematics; Ball (mathematics); Computation; Smoothness; Computability; Mathematical analysis; Discrete mathematics; Algorithm","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":[0.002717152,0.001064688,0.001334419,0.003935626,0.00187273,0.006361762,0.002074312,0.003255148,0.005501015],"category_scores_gemma":[0.02010708,0.000815094,0.0009831837,0.002103609,0.006482502,0.01480523,0.005459875,0.005960145,0.0003765946],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002048019,"about_ca_system_score_gemma":0.000634519,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006949079,"about_ca_topic_score_gemma":0.0004924097,"domain_scores_codex":[0.9988081,0.0003113621,0.00008805493,0.0002578443,0.0003879053,0.0001466417],"domain_scores_gemma":[0.9924642,0.00431139,0.0007016928,0.0008836216,0.0007188145,0.0009203032],"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":[0.00002685656,0.00001146272,0.0001810403,0.00002933105,0.000004053814,0.0000276605,0.00008016076,0.0009184711,0.0002784732,0.9950771,0.0005699046,0.002795576],"study_design_scores_gemma":[0.000009431189,0.0000117401,0.000260077,0.0000129418,0.00000538946,0.00006721222,0.00005584404,0.009673622,0.0001890632,0.9881282,0.001577321,0.000009079614],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5562087,0.01080923,0.3220087,0.02099035,0.00130665,0.0000770566,0.0005373699,0.0004485378,0.08761335],"genre_scores_gemma":[0.9428801,0.002885701,0.03893656,0.0006247215,0.001759149,0.00007842592,0.0002337044,0.0001765726,0.012425],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006361762,"threshold_uncertainty_score":0.0184027,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04184650338122833,"score_gpt":0.3002947418116217,"score_spread":0.2584482384303934,"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."}}