{"id":"W2527610066","doi":"10.6000/1927-5129.2017.13.04","title":"Smoothness and Monotone Decreasingness of the Solution to the BCS-Bogoliubov Gap Equation for Superconductivity","year":2017,"lang":"en","type":"article","venue":"Journal of Basic & Applied Sciences","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Smoothness; Monotone polygon; Lipschitz continuity; Differentiable function; Superconductivity; Condensed matter physics; Mathematics; Mathematical analysis; Derivative (finance); Mathematical physics; Function (biology); Physics; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002487656,0.000106348,0.0002759939,0.0000430097,0.0008410431,0.0001086894,0.0007217791,0.00003622715,0.000002826256],"category_scores_gemma":[0.00130386,0.00005450134,0.00008327837,0.0001271677,0.0006244809,0.000420717,0.000148975,0.0001234957,6.875904e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003251772,"about_ca_system_score_gemma":0.0001026271,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008937014,"about_ca_topic_score_gemma":0.00001104778,"domain_scores_codex":[0.9987693,0.00003902689,0.0003895856,0.0001461704,0.0004725677,0.0001833549],"domain_scores_gemma":[0.9977658,0.0008126791,0.0008183576,0.0003574107,0.0001858372,0.00005992286],"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":[0.0000793798,0.0002131105,0.0001646425,0.000209303,0.00003126042,2.094723e-7,0.002399426,0.0004147245,0.1551469,0.8238755,0.0002105797,0.01725497],"study_design_scores_gemma":[0.0002961362,0.00007012655,0.0009646799,0.0001102814,0.00005186891,0.000008060979,0.0005094409,0.001042897,0.04350728,0.953317,0.00004279453,0.00007942662],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7268959,0.00002641138,0.2693756,0.002296526,0.000172787,0.0005117089,0.00000273725,0.00000413902,0.0007142215],"genre_scores_gemma":[0.9706994,0.000004086754,0.02910588,0.00004138197,0.00009912552,0.00002076141,4.614935e-8,0.000008032411,0.00002127951],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2438036,"threshold_uncertainty_score":0.6468709,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1776295457448235,"score_gpt":0.3797261933944209,"score_spread":0.2020966476495974,"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."}}