{"id":"W2039603470","doi":"10.1155/2013/162769","title":"Convolution Theorems for Quaternion Fourier Transform: Properties and Applications","year":2013,"lang":"en","type":"article","venue":"Abstract and Applied Analysis","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":47,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"Japan Society for the Promotion of Science; Natural Sciences and Engineering Research Council of Canada; Universitas Hasanuddin","keywords":"Mathematics; Quaternion; Convolution (computer science); Convolution theorem; Fourier transform; Algebra over a field; Convolution power; Fourier inversion theorem; Pure mathematics; Mathematical analysis; Fourier analysis; Fractional Fourier transform; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002712363,0.0001564962,0.0003556255,0.0002739033,0.000243146,0.00008738364,0.00007335116,0.00009279157,0.0001436919],"category_scores_gemma":[0.0000193726,0.0001136464,0.000151982,0.0005726133,0.0001122646,0.0001177408,0.00001510589,0.00007012623,0.00001628194],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001260764,"about_ca_system_score_gemma":0.000008680364,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001165039,"about_ca_topic_score_gemma":0.00003688262,"domain_scores_codex":[0.999073,0.000007366068,0.0003075537,0.0002689573,0.0001464772,0.0001966854],"domain_scores_gemma":[0.9993834,0.0001441585,0.00012255,0.0001847117,0.00007561027,0.00008951632],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00008851883,0.000429547,0.005349705,0.000575256,0.00757258,3.428095e-7,0.002491456,0.0001327612,0.003432175,0.4086868,0.001191241,0.5700496],"study_design_scores_gemma":[0.001389709,0.00007143174,0.0225946,0.00001848674,0.009951657,0.000003082003,0.005323866,0.01894726,0.002082112,0.9344981,0.004202973,0.000916783],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.650205,0.0004265243,0.3444729,0.0004858002,0.000007185716,0.001060279,0.0000153829,0.0000761803,0.00325078],"genre_scores_gemma":[0.9959415,0.0001227271,0.002448689,0.00004641869,0.0000656656,0.0005917049,0.0000387935,0.00001333907,0.0007311628],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5691329,"threshold_uncertainty_score":0.4634366,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03598714728844969,"score_gpt":0.2575474131230461,"score_spread":0.2215602658345964,"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."}}