{"id":"W2100238519","doi":"10.1098/rspa.2005.1560","title":"Weyl transforms and a degenerate elliptic partial differential equation","year":2005,"lang":"en","type":"article","venue":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Degenerate energy levels; Partial differential equation; Differential operator; Orthonormal basis; Hypoelliptic operator; Inverse; Parametrix; Fourier integral operator; Symbol of a differential operator; Fourier transform; Pure mathematics; Hermite polynomials; First-order partial differential equation; Mathematical analysis; Elliptic operator; Elliptic partial differential equation; Differential equation; Semi-elliptic operator; Operator theory; Physics; Ordinary differential equation; Quantum mechanics","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":[0.0005317847,0.0001924449,0.000390877,0.00001927246,0.000198247,0.00009513943,0.0002030819,0.0000610834,0.00001955339],"category_scores_gemma":[0.0001531618,0.0001042444,0.0002451673,0.0002260392,0.0003591725,0.0001673897,0.00006917562,0.0001589749,0.000001419368],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001159274,"about_ca_system_score_gemma":0.000007952205,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001525326,"about_ca_topic_score_gemma":1.266827e-7,"domain_scores_codex":[0.998731,0.000005977528,0.0003286233,0.0002404229,0.0004163733,0.0002776237],"domain_scores_gemma":[0.9994077,0.0002995369,0.0000836641,0.00005833014,0.00004336186,0.0001074201],"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":[0.000004420626,0.0002315592,0.00003453386,0.001014245,0.00007061171,2.565683e-8,0.002462526,0.0002438742,0.0106806,0.9836833,0.00002988613,0.001544396],"study_design_scores_gemma":[0.0001650976,0.00004970978,0.00008297661,0.0001124014,0.0001372428,0.000001835831,0.0001107377,0.74464,0.01695641,0.2375851,0.00001975199,0.000138769],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9397978,0.00003805805,0.05874202,0.0006458123,0.00001671027,0.0001708674,0.000001892198,0.00004431577,0.0005425472],"genre_scores_gemma":[0.9570657,0.000010452,0.04264837,0.00001571904,0.0001290024,0.00001965464,1.063639e-7,0.00001095256,0.0001000296],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7460983,"threshold_uncertainty_score":0.4250963,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02968274623099941,"score_gpt":0.2688618338386055,"score_spread":0.2391790876076061,"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."}}