{"id":"W4417434969","doi":"10.5539/jmr.v17n5p32","title":"Existence of Solutions of a Periodic Problem With a Function Φ Continuous on Dom(φ) ⊂ R","year":2025,"lang":"","type":"article","venue":"Journal of Mathematics Research","topic":"Nonlinear Differential Equations Analysis","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Sign (mathematics); Function (biology); Continuous function (set theory); Boundary value problem; Upper and lower bounds; Periodic boundary conditions","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001014526,0.001237619,0.000683573,0.001072207,0.000875786,0.001278236,0.001179967,0.002048768,0.002684892],"category_scores_gemma":[0.005023833,0.000473378,0.0009754123,0.0004648569,0.00175342,0.001503324,0.002068542,0.00148685,0.0002659763],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006682491,"about_ca_system_score_gemma":0.0008830341,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001350729,"about_ca_topic_score_gemma":0.0006768539,"domain_scores_codex":[0.9996712,0.0001024016,0.00001642437,0.00008328311,0.00004836869,0.0000782898],"domain_scores_gemma":[0.998399,0.0009464945,0.0002671416,0.00005685277,0.0001777635,0.0001526642],"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":[0.001039981,0.0004435272,0.008344191,0.001626936,0.000340713,0.004944552,0.002240346,0.1946934,0.06896355,0.6798034,0.005397411,0.03216187],"study_design_scores_gemma":[0.0001474766,0.0006010007,0.002659148,0.0002738337,0.00009199376,0.001041465,0.001240235,0.8331642,0.01267794,0.1421955,0.005796308,0.0001109342],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5816374,0.002402875,0.3804256,0.002891336,0.0002905945,0.0001503029,0.0002831167,0.000139839,0.03177888],"genre_scores_gemma":[0.925123,0.001203093,0.05206553,0.0001825679,0.000172932,0.0003078409,0.0003069963,0.0001098585,0.02052828],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002684892,"threshold_uncertainty_score":0.008981884,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1347188485970912,"score_gpt":0.4103933839775096,"score_spread":0.2756745353804183,"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."}}