{"title":"A note on a functional equation model of decay processes: analysis and consequences","authors":"Ronald E. Mickens, Sandra A. Rucker","doi":"10.1080/10236198.2023.2260891","DOIUrl":null,"url":null,"abstract":"AbstractIt is known that many physical systems undergoing (nuclear, atomic, etc.) decay do not obey the standard decreasing exponential formula which corresponds to the solution of a first-order, linear ODE having constant coefficients. We propose and solve a new functional equation mathematical model whose solutions are consistent with current experimental data. The basis of our functional representation is centred on the critical role played by the concept of the decay half-life.Keywords: Exponential decaynon-exponential decaylinear functional equationsquantum mechanicsMathematics Subject Classification: 34-06 AcknowledgmentsDr. Ronald E. Mickens (REM) wishes to thank Dr. Pedro Jordan, Stennis Space Center, MI, for many useful discussions on mathematical modelling. Both REM and SAR acknowledge the critical help of Imani Beverly and Bryan Briones, Atlanta University Center, Robert W. Woodruff Library, in locating and reproducing various publications required for this investigation.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10236198.2023.2260891","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractIt is known that many physical systems undergoing (nuclear, atomic, etc.) decay do not obey the standard decreasing exponential formula which corresponds to the solution of a first-order, linear ODE having constant coefficients. We propose and solve a new functional equation mathematical model whose solutions are consistent with current experimental data. The basis of our functional representation is centred on the critical role played by the concept of the decay half-life.Keywords: Exponential decaynon-exponential decaylinear functional equationsquantum mechanicsMathematics Subject Classification: 34-06 AcknowledgmentsDr. Ronald E. Mickens (REM) wishes to thank Dr. Pedro Jordan, Stennis Space Center, MI, for many useful discussions on mathematical modelling. Both REM and SAR acknowledge the critical help of Imani Beverly and Bryan Briones, Atlanta University Center, Robert W. Woodruff Library, in locating and reproducing various publications required for this investigation.Disclosure statementNo potential conflict of interest was reported by the author(s).
摘要:众所周知，许多物理系统(核、原子等)的衰变不符合标准的指数递减公式，该公式对应于一阶常系数线性ODE的解。我们提出并求解了一个新的泛函方程数学模型，其解与现有实验数据一致。我们的功能表示的基础集中在衰变半衰期概念所起的关键作用上。关键词:指数衰减非指数衰减线性泛函方程量子力学数学学科分类:34-06Ronald E. Mickens (REM)谨感谢密歇根州斯坦尼斯航天中心的Pedro Jordan博士就数学建模进行了许多有益的讨论。REM和SAR都感谢亚特兰大大学中心、Robert W. Woodruff图书馆的Imani Beverly和Bryan Briones在定位和复制本研究所需的各种出版物方面提供的重要帮助。披露声明作者未报告潜在的利益冲突。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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