{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001105453,0.0007981809,0.0006492281,0.0009422613,0.0005120829,0.0009937737,0.0007400188,0.001138791,0.001578673],"category_scores_gemma":[0.007555536,0.0002476471,0.0007807356,0.0003563928,0.002157953,0.001321209,0.001058735,0.001429087,0.0001723055],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008644023,"about_ca_system_score_gemma":0.0009827834,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003928783,"about_ca_topic_score_gemma":0.001658439,"domain_scores_codex":[0.9996674,0.0001160849,0.00001566517,0.00005705626,0.00008025859,0.00006369014],"domain_scores_gemma":[0.9983493,0.0008521358,0.0002711582,0.00007005898,0.0003144189,0.0001429086],"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":[0.0003723761,0.00010133,0.003791107,0.0005016788,0.00007447103,0.0008875249,0.0009367437,0.2224119,0.08462214,0.6717698,0.003060278,0.01147061],"study_design_scores_gemma":[0.00003070901,0.00007394757,0.001936197,0.00003873872,0.00001817936,0.0002420655,0.0001009797,0.8812056,0.004554703,0.1107642,0.0009841917,0.00005045196],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6785487,0.001681234,0.2870184,0.005393381,0.000217637,0.00007857696,0.0003913102,0.0003590134,0.02631173],"genre_scores_gemma":[0.967275,0.0008176031,0.02256586,0.0002356018,0.0001160484,0.00008041075,0.0002146443,0.000150723,0.008544271],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003928783,"threshold_uncertainty_score":0.007811844,"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."}}