{"id":"W2963018319","doi":"10.1002/mma.5750","title":"Some characteristic properties of the weighted particular Schur polynomial mean","year":2019,"lang":"en","type":"article","venue":"Mathematical Methods in the Applied Sciences","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Schur polynomial; Schur's theorem; Symmetric polynomial; Elementary symmetric polynomial; Polynomial; Complete homogeneous symmetric polynomial; Power sum symmetric polynomial; Alternating polynomial; Schur product theorem; Pure mathematics; Schur complement; Combinatorics; Orthogonal polynomials; Matrix polynomial; Classical orthogonal polynomials; Schur decomposition; Macdonald polynomials; Gegenbauer polynomials; Mathematical analysis; Eigenvalues and eigenvectors","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":[0.0007314055,0.0002605802,0.0004249462,0.001133167,0.0006726977,0.0009844927,0.0005256249,0.0003861197,0.003599484],"category_scores_gemma":[0.004300106,0.0001769866,0.0005875942,0.001164439,0.001054849,0.002006797,0.0007939545,0.001216044,0.0003375204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001064727,"about_ca_system_score_gemma":0.0006973795,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007809172,"about_ca_topic_score_gemma":0.0007203096,"domain_scores_codex":[0.9995152,0.00008217185,0.00002081606,0.0001094965,0.0001640131,0.0001082589],"domain_scores_gemma":[0.9982652,0.0006509505,0.0003837057,0.0001312102,0.0003924179,0.0001765273],"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":[0.00004876921,0.00001265224,0.001229124,0.00005703025,0.00001871724,0.0001453911,0.0001363908,0.007854017,0.006351727,0.9718084,0.0007868798,0.01155097],"study_design_scores_gemma":[0.0000159688,0.00006706535,0.002327685,0.00002243438,0.00002450802,0.0005344176,0.0001453605,0.09636851,0.005090459,0.8903539,0.005005592,0.00004414637],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3904599,0.001096948,0.5742198,0.0007781361,0.0001143197,0.0000500595,0.0003589565,0.0001436083,0.03277819],"genre_scores_gemma":[0.9751748,0.0005973703,0.019359,0.0001085101,0.0001550458,0.00004945381,0.0001402637,0.00004931709,0.004366078],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003599484,"threshold_uncertainty_score":0.01204151,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.155261038383091,"score_gpt":0.3981006460659919,"score_spread":0.2428396076829008,"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."}}