A. Alpatov, V. Kravets, D. Kolosov, V. Kravets, E. Lapkhanov
{"title":"齐次函数中物理过程相似准则集形成的算法","authors":"A. Alpatov, V. Kravets, D. Kolosov, V. Kravets, E. Lapkhanov","doi":"10.14738/tmlai.96.11295","DOIUrl":null,"url":null,"abstract":"The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions\",\"authors\":\"A. Alpatov, V. Kravets, D. Kolosov, V. Kravets, E. Lapkhanov\",\"doi\":\"10.14738/tmlai.96.11295\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.\",\"PeriodicalId\":119801,\"journal\":{\"name\":\"Transactions on Machine Learning and Artificial Intelligence\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Machine Learning and Artificial Intelligence\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14738/tmlai.96.11295\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Machine Learning and Artificial Intelligence","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14738/tmlai.96.11295","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Algorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions
The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.
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