{"id":"W2035677629","doi":"10.1142/s0218348x0900451x","title":"GAPS IN THE RATIOS OF THE SPECTRA OF LAPLACIANS ON FRACTALS","year":2009,"lang":"en","type":"article","venue":"Fractals","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Sierpinski triangle; Fractal; Mathematics; Eigenvalues and eigenvectors; Limit (mathematics); Laplace operator; Pure mathematics; Series (stratigraphy); Convergence (economics); Property (philosophy); Spectrum (functional analysis); Fourier series; Mathematical analysis; Physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00100988,0.0004836798,0.0005125453,0.002517209,0.0007656807,0.001731327,0.0007312622,0.0008122858,0.003791744],"category_scores_gemma":[0.006621933,0.0003549236,0.0004019482,0.0005752635,0.002585154,0.003094923,0.001362812,0.000991829,0.0004089641],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005402839,"about_ca_system_score_gemma":0.0001648616,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002016446,"about_ca_topic_score_gemma":0.0001318579,"domain_scores_codex":[0.9992709,0.0001484153,0.00005385024,0.0001342364,0.0002754894,0.0001170821],"domain_scores_gemma":[0.996494,0.001989069,0.0005272895,0.0002983829,0.0002875467,0.0004036408],"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":[0.0001047997,0.00004124701,0.001320439,0.00010215,0.000009688778,0.0005476972,0.0005274307,0.003767186,0.01656337,0.9671669,0.001009039,0.008840013],"study_design_scores_gemma":[0.00003824614,0.00007328998,0.002738015,0.0000448987,0.00001215311,0.001571863,0.000433429,0.04247567,0.006407349,0.9440879,0.002072254,0.00004490247],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9248677,0.0009259278,0.04841213,0.000634705,0.00008291518,0.00001873748,0.0001171535,0.0003152294,0.02462554],"genre_scores_gemma":[0.9923239,0.0002651537,0.005599675,0.00006928395,0.00009495658,0.00001978424,0.00006377551,0.00006782915,0.001495588],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003791744,"threshold_uncertainty_score":0.01268464,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02450041174306317,"score_gpt":0.3030368799229133,"score_spread":0.2785364681798502,"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."}}