{"id":"W2912296057","doi":"10.5539/jmr.v11n1p102","title":"Mathematical Details on Singular Integral Equation Method for Solving Crack Problems","year":2019,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Numerical methods in engineering","field":"Engineering","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Science Foundation","keywords":"Mathematics; Integral equation; Fredholm integral equation; Singular integral; Limit (mathematics); Mathematical analysis; Point (geometry); Summation equation; Electric-field integral equation; Singular solution; Integro-differential equation; Partial differential equation; Calculus (dental); Applied mathematics; Geometry; First-order partial differential equation","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":[],"consensus_categories":[],"category_scores_codex":[0.008495702,0.0001905515,0.0005413767,0.0005061329,0.0000560146,0.0001197959,0.0004479931,0.0001399234,0.0001240163],"category_scores_gemma":[0.003737793,0.0001503513,0.0002052013,0.0003534131,0.00003367016,0.000200542,0.00005516618,0.0009805205,0.0001087348],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002740152,"about_ca_system_score_gemma":0.00004429948,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.527438e-7,"about_ca_topic_score_gemma":1.192056e-7,"domain_scores_codex":[0.9973016,0.0001250203,0.0008559089,0.0001406158,0.001054969,0.0005218324],"domain_scores_gemma":[0.9939123,0.004960914,0.0001466385,0.0003376438,0.0004826669,0.0001598033],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00006929995,0.0006570371,0.00003959952,0.009297417,0.0004958584,0.00002516667,0.004240242,0.5489727,0.2894764,0.07617473,0.001477151,0.06907438],"study_design_scores_gemma":[0.000386882,0.0003638633,0.000006442726,0.0008421539,0.00002011472,0.00005534994,0.0003796121,0.8486782,0.02160678,0.1267335,0.0007736586,0.0001535275],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02977689,0.0001232707,0.9669764,0.0001028366,0.000338452,0.0005643517,0.00000148101,0.00005509888,0.002061213],"genre_scores_gemma":[0.06302643,0.00002331976,0.9364349,0.000007856431,0.0001890116,0.00002654202,5.328088e-7,0.00009337623,0.0001980592],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2997054,"threshold_uncertainty_score":0.6131149,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1393817858206299,"score_gpt":0.423884740260653,"score_spread":0.2845029544400232,"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."}}