{"id":"W4416192305","doi":"10.3934/dcds.2025181","title":"A special concavity property for positive Hessian quotient operators","year":2025,"lang":"","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Hessian matrix; Quotient; Hessian equation; Property (philosophy); Tensor (intrinsic definition)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000668725,0.0004382477,0.0003596924,0.0007310936,0.0007423682,0.0009263738,0.0006014947,0.000538771,0.003847871],"category_scores_gemma":[0.002002281,0.0002262606,0.0005386929,0.0002940121,0.002186879,0.001963023,0.001556236,0.001177144,0.0003761047],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006092936,"about_ca_system_score_gemma":0.0005927538,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001232014,"about_ca_topic_score_gemma":0.001164317,"domain_scores_codex":[0.9995562,0.00007298026,0.00002113099,0.00009846358,0.0001625875,0.0000886827],"domain_scores_gemma":[0.9989018,0.0002461793,0.0001484747,0.0001050343,0.0003900916,0.0002083755],"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":[0.00001824815,0.00001516072,0.0004898565,0.00003725066,0.000008193786,0.0002051117,0.000161731,0.001239007,0.009409474,0.9831444,0.001155621,0.004116038],"study_design_scores_gemma":[0.00001977132,0.00008327166,0.001692839,0.00002126748,0.00001726458,0.0008611507,0.0001415321,0.1002113,0.009222913,0.881548,0.006143535,0.00003722683],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3783601,0.0005971941,0.5324244,0.00189485,0.00029332,0.00008687879,0.000216796,0.0002852046,0.08584126],"genre_scores_gemma":[0.9572868,0.0002850374,0.0261352,0.000328351,0.0002034915,0.00005138765,0.00009838311,0.0001115233,0.01549982],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003847871,"threshold_uncertainty_score":0.0128724,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0124673428987518,"score_gpt":0.2675442049688279,"score_spread":0.2550768620700761,"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."}}