{"id":"W256609995","doi":"10.1016/j.jfa.2015.10.015","title":"Solutions without any symmetry for semilinear elliptic problems","year":2015,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Comisión Nacional de Investigación Científica y Tecnológica; National Natural Science Foundation of China; Fondo Nacional de Desarrollo Científico y Tecnológico; Agence Nationale de la Recherche","keywords":"Mathematics; Symmetry (geometry); Identity (music); Nonlinear system; Energy (signal processing); Symmetry group; Mathematical physics; Elliptic curve; Mathematical analysis; Pure mathematics; Geometry; Quantum mechanics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002281682,0.001373264,0.001579933,0.00176371,0.001698573,0.002982974,0.002021478,0.00286959,0.007094494],"category_scores_gemma":[0.008511681,0.0008079758,0.002000124,0.0007343192,0.003956302,0.006256102,0.004023036,0.004363434,0.0009863987],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001262529,"about_ca_system_score_gemma":0.001812184,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0013852,"about_ca_topic_score_gemma":0.0009717682,"domain_scores_codex":[0.9990784,0.0003278692,0.00006864291,0.0001194163,0.000251288,0.0001544121],"domain_scores_gemma":[0.9976659,0.0006482243,0.0003829845,0.0003206224,0.0003504246,0.0006319492],"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":[0.00003582917,0.00003984914,0.00008203591,0.00003567801,0.00001042741,0.00005494457,0.00007750311,0.001555129,0.0008045346,0.9942625,0.001137779,0.001903628],"study_design_scores_gemma":[0.00004681173,0.00002143508,0.0001053984,0.00001170306,0.000005719836,0.00005662502,0.00005465685,0.02545663,0.0001536981,0.9733748,0.0006985789,0.00001395582],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3684088,0.00256376,0.4806863,0.01068868,0.00257884,0.0002776889,0.0006409314,0.0004861315,0.1336688],"genre_scores_gemma":[0.8544857,0.001551799,0.06389352,0.002159218,0.002075632,0.0004294278,0.0009812185,0.0006168787,0.07380658],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007094494,"threshold_uncertainty_score":0.0237335,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1816682088969008,"score_gpt":0.3476527253620159,"score_spread":0.1659845164651151,"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."}}