{"id":"W2949296389","doi":"10.2969/jmsj/80878087","title":"Hardy and Rellich inequalities with exact missing terms on homogeneous groups","year":2019,"lang":"en","type":"article","venue":"Journal of the Mathematical Society of Japan","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Division of Mathematical Sciences; Pacific Institute for the Mathematical Sciences","keywords":"Homogeneous; Mathematics; Inequality; Bessel function; Pure mathematics; Algebra over a field; Calculus (dental); Mathematical analysis; Combinatorics; Orthodontics; Medicine","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.001263056,0.000275489,0.0008419165,0.00003262639,0.0001036302,0.00006118172,0.0005079693,0.0001205834,0.0001668319],"category_scores_gemma":[0.0004452366,0.0001448832,0.0005086924,0.0001678811,0.0003573924,0.0001406025,0.0001138506,0.0005120917,0.00001694316],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008113612,"about_ca_system_score_gemma":0.00004070159,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.479366e-7,"about_ca_topic_score_gemma":1.809073e-7,"domain_scores_codex":[0.997689,0.0001428064,0.0008634551,0.0001674177,0.0008427552,0.0002945759],"domain_scores_gemma":[0.9959148,0.002360123,0.0009086383,0.0005575311,0.0001280757,0.0001308921],"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":[0.0002216327,0.001201165,0.0006503717,0.003261049,0.0007172198,0.000002959389,0.01412058,0.00004945793,0.01093541,0.9663767,0.001589913,0.0008735775],"study_design_scores_gemma":[0.0006775461,0.0005952351,0.0001727662,0.001471214,0.0001765614,0.00021968,0.002069017,0.0006236165,0.00882853,0.9849158,0.00004808815,0.0002019317],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9895693,0.00003541731,0.004529906,0.001316003,0.00007566716,0.0003272244,0.000003848368,0.00002147164,0.004121133],"genre_scores_gemma":[0.9578945,0.00001542317,0.0410818,0.0002284235,0.0001345961,0.00000239485,1.636276e-7,0.00005633592,0.0005863777],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0365519,"threshold_uncertainty_score":0.5908167,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02910259984147044,"score_gpt":0.2788475826601389,"score_spread":0.2497449828186685,"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."}}