{"id":"W2077195797","doi":"10.1007/s10688-010-0014-1","title":"On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues","year":2010,"lang":"en","type":"article","venue":"Functional Analysis and Its Applications","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":42,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Isoperimetric inequality; Eigenvalues and eigenvectors; Domain (mathematical analysis); Bounded function; Limit (mathematics); Pure mathematics; Disjoint sets; Disjoint union (topology); Simply connected space; Sequence (biology); Combinatorics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004072546,0.002215373,0.001713656,0.004021254,0.001526971,0.002946121,0.001802883,0.00267322,0.009404759],"category_scores_gemma":[0.01328447,0.0006520853,0.001461893,0.002127387,0.004626041,0.005778441,0.003587541,0.004790024,0.001196424],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002060226,"about_ca_system_score_gemma":0.001286195,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002033218,"about_ca_topic_score_gemma":0.001652678,"domain_scores_codex":[0.9988214,0.0005685296,0.00006687988,0.0001593058,0.0002435967,0.0001401639],"domain_scores_gemma":[0.9946176,0.003735399,0.0003649296,0.0001996374,0.0007266371,0.0003557625],"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":[0.0000413471,0.00001739622,0.0001058349,0.00008935838,0.00001442937,0.00005867418,0.0001222729,0.005016939,0.001109734,0.9862025,0.00147118,0.005750301],"study_design_scores_gemma":[0.00001709898,0.00002729893,0.0002385001,0.00005467666,0.00001177586,0.00007476465,0.00007939286,0.05596724,0.0004455711,0.9408853,0.002163601,0.00003481979],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07828951,0.009080456,0.7571126,0.006724733,0.001144996,0.0001489603,0.000567114,0.0001438315,0.1467879],"genre_scores_gemma":[0.8523777,0.009212638,0.08357833,0.001647055,0.001636978,0.000417938,0.0005516008,0.0002844479,0.05029339],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009404759,"threshold_uncertainty_score":0.03146201,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0279852835471191,"score_gpt":0.2566741959155747,"score_spread":0.2286889123684556,"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."}}