{"id":"W2133532825","doi":"10.1515/ans-2009-0109","title":"On a Fourth Order Elliptic Problem with a Singular Nonlinearity","year":2009,"lang":"en","type":"article","venue":"Advanced Nonlinear Studies","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":58,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Division of Mathematical Sciences; University of British Columbia; Conselho Nacional de Desenvolvimento Científico e Tecnológico; Pacific Institute for the Mathematical Sciences","keywords":"Biharmonic equation; Mathematics; Dirichlet boundary condition; Nonlinear system; Order (exchange); Ball (mathematics); Mathematical analysis; Pure mathematics; Space (punctuation); Dirichlet problem; Boundary value problem; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0002498481,0.0004466801,0.0006486249,0.0001381078,0.0003308878,0.00004548737,0.00022266,0.00008775335,0.00001774772],"category_scores_gemma":[0.001540446,0.0003305496,0.0001133963,0.0006040201,0.0001591955,0.0001810774,0.00006414811,0.0003645117,0.000097072],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009242065,"about_ca_system_score_gemma":0.00009044803,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004684004,"about_ca_topic_score_gemma":0.0001336848,"domain_scores_codex":[0.997664,0.00008977841,0.0005752281,0.0005848748,0.0005349895,0.0005510711],"domain_scores_gemma":[0.9977102,0.000692037,0.0002631013,0.0006354676,0.0005731146,0.0001260717],"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":[0.01182274,0.02614589,0.0008215407,0.001774191,0.006357504,0.0009517323,0.02203573,0.04476921,0.02124389,0.6326439,0.006053737,0.2253799],"study_design_scores_gemma":[0.02096363,0.01592056,0.001097256,0.002887527,0.001611233,0.0001090642,0.002179545,0.05801799,0.0238608,0.8452517,0.02334432,0.004756384],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.8940325,0.0008745268,0.08494014,0.006585049,0.0004420784,0.002896176,0.0001808363,0.001312899,0.008735816],"genre_scores_gemma":[0.1359711,0.0001418799,0.8615872,0.0004607212,0.0003663302,0.00005991789,0.00005411588,0.0000781543,0.001280657],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.776647,"threshold_uncertainty_score":0.9999146,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05686379812046233,"score_gpt":0.3664253226572164,"score_spread":0.3095615245367541,"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."}}