{"id":"W4404702788","doi":"10.4153/s0008439524000572","title":"Asymptotic estimate of solutions in a 4th-order parabolic equation with the Frobenius norm of a Hessian matrix","year":2024,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Science Foundation of Shandong Province; National Natural Science Foundation of China","keywords":"Mathematics; Hessian matrix; Hessian equation; Norm (philosophy); Mathematical analysis; Matrix norm; Matrix (chemical analysis); Neumann boundary condition; Order (exchange); Boundary value problem; Applied mathematics; Partial differential equation; Eigenvalues and eigenvectors","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005486211,0.0001967139,0.0003989961,0.0003068078,0.00008555256,0.00005313385,0.0002481293,0.0001099323,0.002807049],"category_scores_gemma":[0.0007688749,0.0001362165,0.00009523726,0.0006654561,0.0002288202,0.00004348042,0.00003540721,0.0002419845,0.0007218171],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000127259,"about_ca_system_score_gemma":0.0005575391,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002320507,"about_ca_topic_score_gemma":0.0217346,"domain_scores_codex":[0.9982924,0.0001153684,0.0006124297,0.0002233738,0.0003194622,0.0004369494],"domain_scores_gemma":[0.998198,0.0009496572,0.0001189198,0.00041242,0.0001228047,0.0001982538],"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":[0.00001551787,0.0001749966,0.00005011214,0.0009073784,0.00009244231,0.00002280775,0.001636374,0.000417304,0.0002937772,0.9936524,0.00216745,0.0005694333],"study_design_scores_gemma":[0.001277479,0.0002901114,0.001269877,0.003292323,0.0006910747,0.0000802646,0.0009794686,0.2248459,0.001044571,0.7606322,0.004790286,0.0008065046],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6222146,0.0007710832,0.3210615,0.03208122,0.0002157,0.002934134,0.000391639,0.0002174746,0.02011276],"genre_scores_gemma":[0.9841507,0.000003315678,0.01489679,0.00003934781,0.00004314477,0.00009171198,0.00001617802,0.00004786618,0.0007109122],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3619362,"threshold_uncertainty_score":0.9981045,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03989293382536217,"score_gpt":0.3109809596660617,"score_spread":0.2710880258406995,"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."}}