{"id":"W2021737601","doi":"10.1155/ijmms.2005.1555","title":"Simplicity and stability of the first eigenvalue of a nonlinear elliptic system","year":2005,"lang":"en","type":"article","venue":"International Journal of Mathematics and Mathematical Sciences","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Polytechnique Montréal","funders":"","keywords":"Mathematics; Simplicity; Eigenvalues and eigenvectors; Nonlinear system; Stability (learning theory); Mathematical analysis; Applied mathematics; Pure mathematics; Computer science","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":[],"consensus_categories":[],"category_scores_codex":[0.001536231,0.0001224358,0.0004038352,0.00009063446,0.000088452,0.0000466383,0.00052923,0.00005181214,0.00005328213],"category_scores_gemma":[0.001411569,0.0000705568,0.0001363133,0.0001401352,0.0005888453,0.0001530133,0.0001887436,0.0001151114,0.000001553169],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003627754,"about_ca_system_score_gemma":0.00007739157,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005758686,"about_ca_topic_score_gemma":0.00002037959,"domain_scores_codex":[0.9977494,0.00004426793,0.001080125,0.0001138751,0.0008846894,0.0001276505],"domain_scores_gemma":[0.9972342,0.001176435,0.0009349101,0.0001640509,0.0004163321,0.00007403195],"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":[0.00002049047,0.001171123,0.001306959,0.001223063,0.0001645877,0.000001585929,0.003347394,0.00004416301,0.005534585,0.9856306,0.0000379582,0.001517439],"study_design_scores_gemma":[0.001422286,0.0004586436,0.001875682,0.002810797,0.0004371726,0.0006558379,0.004477718,0.1844167,0.07058951,0.73229,0.0002010326,0.0003646382],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9806677,0.00006956563,0.01733135,0.0009263257,0.0001067851,0.0001831487,0.00002096166,0.00000655021,0.0006875987],"genre_scores_gemma":[0.893046,0.00001648388,0.1068152,0.00001502968,0.00009112247,0.000001837725,1.170277e-7,0.000006788253,0.000007414204],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2533407,"threshold_uncertainty_score":0.2877223,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06070580964211534,"score_gpt":0.336199521408471,"score_spread":0.2754937117663557,"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."}}