Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.
{"title":"Theory of Impulsive Differential Equations","authors":"V. Lakshmikantham, D. Bainov, P. Simeonov","doi":"10.1142/0906","DOIUrl":"https://doi.org/10.1142/0906","url":null,"abstract":"Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.","PeriodicalId":277853,"journal":{"name":"Series in Modern Applied Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115026101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stochastic System Reliability Modelling","authors":"S. Osaki","doi":"10.1142/0164","DOIUrl":"https://doi.org/10.1142/0164","url":null,"abstract":"","PeriodicalId":277853,"journal":{"name":"Series in Modern Applied Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130198941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quasilinearization and the Identification Problem","authors":"R. Bellman, R. Roth","doi":"10.1142/0029","DOIUrl":"https://doi.org/10.1142/0029","url":null,"abstract":"","PeriodicalId":277853,"journal":{"name":"Series in Modern Applied Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1983-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122430316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mathematical Methods in Medicine","authors":"R. Bellman","doi":"10.1142/0028","DOIUrl":"https://doi.org/10.1142/0028","url":null,"abstract":"","PeriodicalId":277853,"journal":{"name":"Series in Modern Applied Mathematics","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1983-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127179747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Introducing a new hobby for other people may inspire them to join with you. Reading, as one of mutual hobby, is considered as the very easy hobby to do. But, many people are not interested in this hobby. Why? Boring is the reason of why. However, this feel actually can deal with the book and time of you reading. Yeah, one that we will refer to break the boredom in reading is choosing selective computation as the reading material.
{"title":"Selective Computation","authors":"R. Bellman","doi":"10.1142/0122","DOIUrl":"https://doi.org/10.1142/0122","url":null,"abstract":"Introducing a new hobby for other people may inspire them to join with you. Reading, as one of mutual hobby, is considered as the very easy hobby to do. But, many people are not interested in this hobby. Why? Boring is the reason of why. However, this feel actually can deal with the book and time of you reading. Yeah, one that we will refer to break the boredom in reading is choosing selective computation as the reading material.","PeriodicalId":277853,"journal":{"name":"Series in Modern Applied Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130839845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.
{"title":"The Laplace Transform","authors":"R. Bellman, R. Roth","doi":"10.1142/0107","DOIUrl":"https://doi.org/10.1142/0107","url":null,"abstract":"The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.","PeriodicalId":277853,"journal":{"name":"Series in Modern Applied Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114319643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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