{"id":"W200474756","doi":"10.1007/978-3-0348-0585-8_3","title":"The Heat Kernel and Green Function of the Sub-Laplacian on the Heisenberg Group","year":2013,"lang":"en","type":"book-chapter","venue":"","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Heisenberg group; Heat kernel; Laplace operator; Hypoelliptic operator; Mathematics; Differential operator; Kernel (algebra); Operator (biology); Pure mathematics; Group (periodic table); Fourier transform; Mathematical physics; Type (biology); Function (biology); Mathematical analysis; Physics; Quantum mechanics; Chemistry","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":[0.0004167594,0.0008155378,0.000770751,0.001321674,0.0006919918,0.001633578,0.0008497864,0.001032474,0.003883502],"category_scores_gemma":[0.0008488048,0.000337911,0.0005820101,0.001174461,0.003108334,0.002601715,0.0007820212,0.002322646,0.001281567],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00105484,"about_ca_system_score_gemma":0.0007894295,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001235285,"about_ca_topic_score_gemma":0.0008156248,"domain_scores_codex":[0.9998136,0.00004655043,0.000008450053,0.00003108433,0.00007820714,0.00002216968],"domain_scores_gemma":[0.9997974,0.00008620344,0.00001445858,0.00003353804,0.00004324647,0.00002517262],"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":[0.000005733116,0.000006701925,0.00002120255,0.00003435145,0.000003477105,0.00002048692,0.0001256952,0.0007058639,0.0005175627,0.9893651,0.0030376,0.006156217],"study_design_scores_gemma":[0.00000149122,0.000004364696,0.00006308284,0.000008908939,0.00000163543,0.00003639174,0.00002029504,0.001908187,0.00014988,0.9888793,0.008921195,0.000005235522],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.08626256,0.04620782,0.2344504,0.006148465,0.005217786,0.00008140251,0.000493916,0.0005360703,0.6206015],"genre_scores_gemma":[0.5658466,0.02975219,0.06212048,0.001651468,0.006490364,0.0001810593,0.0003778306,0.0006489785,0.332931],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003883502,"threshold_uncertainty_score":0.01299167,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04744442863454727,"score_gpt":0.2630172718367912,"score_spread":0.215572843202244,"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."}}