{"title":"Ray Transforms of the Moments of Planar Tensor Fields","authors":"E. Yu. Derevtsov","doi":"10.1134/S1990478923030067","DOIUrl":null,"url":null,"abstract":"<p> The paper considers ray transforms of the moments of symmetric tensor fields of arbitrary\nrank given in the unit disk. The basic geometric and differential properties of mixed ray\ntransforms of tensor fields and mixed ray transforms of the moments of tensor fields are\nestablished. A simple algorithm for reconstructing a low-rank tensor field from known mixed ray\ntransforms of its moments is proposed and justified.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"521 - 534"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The paper considers ray transforms of the moments of symmetric tensor fields of arbitrary
rank given in the unit disk. The basic geometric and differential properties of mixed ray
transforms of tensor fields and mixed ray transforms of the moments of tensor fields are
established. A simple algorithm for reconstructing a low-rank tensor field from known mixed ray
transforms of its moments is proposed and justified.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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