{"id":"W2135198084","doi":"10.5539/jmr.v2n2p128","title":"On a Generalization of Hilbert’s Inequality and Its Applications","year":2010,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Generalization; Inequality; Pure mathematics; Kantorovich inequality; Hilbert space; Algebra over a field; Mathematical analysis; Linear inequality","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003072442,0.001037679,0.001246118,0.002519984,0.001167146,0.00179004,0.001504911,0.002073705,0.005515694],"category_scores_gemma":[0.006143042,0.000355332,0.001770017,0.002493682,0.003854201,0.008174909,0.003788661,0.005390196,0.001084634],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001100029,"about_ca_system_score_gemma":0.0007053289,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008640506,"about_ca_topic_score_gemma":0.0004818332,"domain_scores_codex":[0.9979821,0.0008932204,0.0001348265,0.0004178426,0.0004346606,0.0001372393],"domain_scores_gemma":[0.9969021,0.001960588,0.0001838949,0.000272233,0.0004907167,0.0001905738],"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":[0.00002593712,0.00002459293,0.0002187755,0.0001913807,0.00002364312,0.0002208276,0.0001902013,0.001730963,0.001651944,0.9662514,0.003821448,0.02564882],"study_design_scores_gemma":[0.000009910452,0.00006750241,0.0004310207,0.00008914482,0.00002420566,0.0004647973,0.00008898904,0.0154936,0.0009771285,0.9369406,0.04535364,0.00005957305],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01918399,0.01996094,0.8302504,0.01010647,0.00521755,0.00007756353,0.0002465632,0.0001331807,0.1148233],"genre_scores_gemma":[0.5271046,0.0394154,0.3630901,0.007116538,0.01559661,0.0003794725,0.0004839153,0.0003922603,0.0464212],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005515694,"threshold_uncertainty_score":0.01845181,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2780116285163073,"score_gpt":0.4916708208977826,"score_spread":0.2136591923814752,"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."}}