平面张量场矩的射线变换

IF 0.58 Q3 Engineering Journal of Applied and Industrial Mathematics Pub Date : 2023-11-04 DOI:10.1134/S1990478923030067

E. Yu. Derevtsov

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引用次数: 0

摘要

本文研究了单位圆盘上任意阶对称张量场矩的射线变换。建立了张量场混合射线变换和张量场矩混合射线变换的基本几何性质和微分性质。提出了一种由已知矩的混合射线变换重构低阶张量场的简单算法，并证明了该算法的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Ray Transforms of the Moments of Planar Tensor Fields

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.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

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.