Reconstruction of a Vector Field in a Ball from its Normal Radon Transform

2015 ◽  
Vol 205 (3) ◽  
pp. 418-439 ◽  
Author(s):  
A. P. Polyakova
Keyword(s):  
Vector Field ◽  
Radon Transform

The Modulo Radon Transform and its Inversion

2021 ◽  
Author(s):  
Ayush Bhandari ◽  
Matthias Beckmann ◽  
Felix Krahmer
Keyword(s):  
Radon Transform

Mathematical Model of Flat Surface Machining Inaccuracies due to Elastic Strains of Technological System

2018 ◽  
pp. 1-14 ◽  
Author(s):  
I. I. Kravchenko
Keyword(s):  
Mathematical Model ◽  
Vector Field ◽  
Model Development ◽  
Technological System ◽  
Mutual Arrangement ◽  
Real Surface ◽  
Main Bearing ◽  
Flat Surfaces ◽  
Internal Surfaces ◽  
Elastic Strains

The paper considers the mathematical model development technique to build a vector field of the shape deviations when machining flat surfaces of shell parts on multi-operational machines under conditions of anisotropic rigidity in technological system (TS). The technological system has an anisotropic rigidity, as its elastic strains do not obey the accepted concepts, i.e. the rigidity towards the coordinate axes of the machine is the same, and they occur only towards the external force. The record shows that the diagrams of elastic strains of machine units are substantially different from the circumference. The issues to ensure the specified accuracy require that there should be mathematical models describing kinematic models and physical processes of mechanical machining under conditions of the specific TS. There are such models for external and internal surfaces of rotation [2,3], which are successfully implemented in practice. Flat surfaces (FS) of shell parts (SP) are both assembly and processing datum surfaces. Therefore, on them special stipulations are made regarding deviations of shape and mutual arrangement. The axes of the main bearing holes are coordinated with respect to them. The joints that ensure leak tightness and distributed load on the product part are closed on these surfaces. The paper deals with the analytical construction of the vector field F, which describes with appropriate approximation the real surface obtained as a result of modeling the process of machining flat surfaces (MFS) through face milling under conditions of anisotropic properties.

On the geometry of Killing vector field

2019 ◽  
Vol 2019 (2) ◽  
pp. 62-67
Author(s):  
R.A. Ilyasova
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Killing Vector Field
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