{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T05:29:34Z","timestamp":1791091774623,"version":"4.1.0"},"reference-count":12,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1953,1,1]],"date-time":"1953-01-01T00:00:00Z","timestamp":-536457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1953,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>The irreproducibility of some chemical reactions is due either to (A) the inherent mechanism of the process or (B) extraneous factors (e.g., impurities). The purpose of this paper is to show that mathematical techniques developed in recent years permit the quantitative calculation of statistical properties of reactions of the type (A). An exposition of some general methods is given; their application to some typical chain mechanisms shows that conditions for the experimental observation of inherent fluctuations can occur. The distinction between the two types of irreproducibility is briefly discussed.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1953.tb00129.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T07:03:15Z","timestamp":1544166195000},"page":"92-106","source":"Crossref","is-referenced-by-count":40,"title":["Application of the Theory of Stochastic Processes to the Study of Irreproducible Chemical Reactions and Nucleation Processes"],"prefix":"10.1093","volume":"15","author":[{"given":"K.","family":"Singer","sequence":"first","affiliation":[{"name":"Royal Holloway College."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920090675100_cit1","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1039\/tf9464200140","volume":"42","author":"Bacon","year":"1946","journal-title":"Trans. Faraday Soc."},{"key":"2024090920090675100_cit2","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.2517-6161.1949.tb00031.x","article-title":"Symposium on stochastic processes","volume":"11","author":"Bartlett","year":"1949","journal-title":"J. R. Statist. Soc., B"},{"key":"2024090920090675100_cit3","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1039\/df9490500103","article-title":"Crystal growth","volume":"5","author":"Davies","year":"1949","journal-title":"Disc., Faraday Soc."},{"key":"2024090920090675100_cit4","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1063\/1.1750549","volume":"8","author":"Delbr\u00fcck","year":"1940","journal-title":"J. Chem. Physics"},{"key":"2024090920090675100_cit5","volume-title":"An Introduction to Probability Theory and its Applications","author":"Feller","year":"1950"},{"key":"2024090920090675100_cit6","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1039\/TF9383400940","volume":"34","author":"Garner","year":"1938","journal-title":"Trans. Faraday Soc."},{"key":"2024090920090675100_cit7","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1039\/tf9383400985","volume":"34","author":"Garner","year":"1938","journal-title":"Trans. Faraday Soc."},{"key":"2024090920090675100_cit8","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1111\/j.2517-6161.1949.tb00032.x","article-title":"Symposium on stochastic processes","volume":"11","author":"Kendall","year":"1949","journal-title":"J. R. Statist. Soc., B"},{"key":"2024090920090675100_cit9","first-page":"5","article-title":"C.r. (Doklady)","volume":"56","author":"Kolmogoroff","year":"1947","journal-title":"Acad. Sci. U.S.S.R."},{"key":"2024090920090675100_cit10","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1111\/j.2517-6161.1949.tb00030.x","article-title":"Symposium on stochastic processes","volume":"11","author":"Moyal","year":"1949","journal-title":"J. R. Statist. Soc., B"},{"key":"2024090920090675100_cit11","first-page":"345","volume":"53","author":"Quartaroli","year":"1923","journal-title":"Gazz. chim. ital."},{"key":"2024090920090675100_cit12","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1039\/df9490500112","article-title":"Crystal growth","volume":"5","author":"van Hook","year":"1949","journal-title":"Disc., Faraday Soc."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1953.tb00129.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/15\/1\/92\/49093784\/jrsssb_15_1_92.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/15\/1\/92\/49093784\/jrsssb_15_1_92.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T20:16:15Z","timestamp":1725912975000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/15\/1\/92\/7026622"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1953,1,1]]},"references-count":12,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1953,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1953.tb00129.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1953,1]]},"published":{"date-parts":[[1953,1,1]]}}}