{"id":"W2951812898","doi":"10.48550/arxiv.0808.2968","title":"On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues","year":2008,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Isoperimetric inequality; Mathematics; Domain (mathematical analysis); Eigenvalues and eigenvectors; Bounded function; Disjoint sets; Limit (mathematics); Pure mathematics; Inequality; Sequence (biology); Simply connected space; Combinatorics; Mathematical analysis; Physics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002503888,0.0003502851,0.0003426308,0.0001376679,0.0002216407,0.0000813204,0.001892267,0.0001896732,0.000008105176],"category_scores_gemma":[0.0002481615,0.0002945652,0.0002522423,0.0002225997,0.0001070522,0.0002106796,0.001068191,0.0005253204,0.00003984779],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001722913,"about_ca_system_score_gemma":0.00009209537,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008831013,"about_ca_topic_score_gemma":0.000001492332,"domain_scores_codex":[0.9984034,0.00007261909,0.0002275713,0.0007776878,0.0001298965,0.0003888627],"domain_scores_gemma":[0.9971136,0.001091566,0.0001514175,0.001410364,0.0001299357,0.0001031216],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000006861645,0.00002235875,0.000003202488,0.00005749069,0.00002897218,0.00001276778,0.0002361379,0.4904868,0.000005124967,0.5089451,0.0001223534,0.00007285705],"study_design_scores_gemma":[0.0001314732,0.00003435673,0.000006859781,0.0001009641,0.00001468768,0.000001574984,0.00004534939,0.6240771,0.0001144184,0.3750381,0.0001868084,0.000248304],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1159476,0.00003996952,0.8813366,0.0001504143,0.0004320696,0.0004543685,0.00001289514,0.0003603407,0.001265774],"genre_scores_gemma":[0.9642857,0.0001111943,0.03385457,0.0002181642,0.00009033991,0.000008986075,0.000004174033,0.00003631604,0.001390563],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8483381,"threshold_uncertainty_score":0.9999506,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1361429278773144,"score_gpt":0.2093906717822086,"score_spread":0.07324774390489427,"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."}}