{"id":"W2912998819","doi":"10.1109/access.2019.2897680","title":"New Quantum Hermite-Hadamard Inequalities Utilizing Harmonic Convexity of the Functions","year":2019,"lang":"en","type":"article","venue":"IEEE Access","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Institute of Population and Public Health; King Saud University","keywords":"Hadamard transform; Hermite polynomials; Convexity; Mathematics; Pure mathematics; Convex function; Connection (principal bundle); Harmonic; Regular polygon; Harmonic analysis; Harmonic function; Applied mathematics; Mathematical analysis; Quantum mechanics; Physics; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003174159,0.0001579722,0.0003315943,0.00003993337,0.0001157113,0.00008020322,0.0006783624,0.00008229732,0.001616399],"category_scores_gemma":[0.0002193835,0.0001081312,0.000177568,0.0002879353,0.0000746451,0.0002139921,0.0001685457,0.0001893414,0.0001062903],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002994789,"about_ca_system_score_gemma":0.000107621,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003069092,"about_ca_topic_score_gemma":0.00004741846,"domain_scores_codex":[0.9986107,0.00008380799,0.0005425903,0.0002035198,0.0003200719,0.000239356],"domain_scores_gemma":[0.9976522,0.001041061,0.0002862453,0.0008356964,0.0001085594,0.00007620182],"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":[0.000009573829,0.0001008751,0.001665426,0.0005577988,0.00005239322,1.85243e-7,0.0007341888,0.000009660889,0.001197885,0.9728991,0.02241456,0.0003583674],"study_design_scores_gemma":[0.0005944032,0.00004043541,0.001563036,0.0002818143,0.0001128966,0.000005073136,0.002935362,0.001692204,0.02195299,0.9598396,0.01063187,0.0003503082],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9524254,0.00005525788,0.02418828,0.001012163,0.0006223959,0.000650947,0.00005406766,0.0001058495,0.02088569],"genre_scores_gemma":[0.9867644,0.000007789006,0.0006858041,0.000203253,0.0001129481,0.0000426105,0.000002655223,0.00002650236,0.01215406],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03433903,"threshold_uncertainty_score":0.9992962,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1815743392557596,"score_gpt":0.3800896816178033,"score_spread":0.1985153423620438,"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."}}