scholarly journals Integral geometry on discrete matrices

2021 ◽  
Vol 7 (3) ◽  
pp. 364-374
Author(s):  
Abdelbaki Attioui
Keyword(s):  
Radon Transform ◽  
Integral Geometry ◽  
Inversion Formula ◽  
Diophantine Equations ◽  
Support Theorem ◽  
Linear Diophantine Equations ◽  
Infinite Sets

Abstract In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.

Coordination sequences and layer-by-layer growth of periodic structures

2019 ◽  
Vol 234 (5) ◽  
pp. 291-299
Author(s):  
Anton Shutov ◽  
Andrey Maleev
Keyword(s):  
Generating Functions ◽  
Diophantine Equations ◽  
Periodic Structures ◽  
Layer Growth ◽  
Layer By Layer ◽  
Explicit Formulas ◽  
New Approach ◽  
Coordination Numbers ◽  
Linear Diophantine Equations ◽  
Recurrent Relations

Abstract A new approach to the problem of coordination sequences of periodic structures is proposed. It is based on the concept of layer-by-layer growth and on the study of geodesics in periodic graphs. We represent coordination numbers as sums of so called sector coordination numbers arising from the growth polygon of the graph. In each sector we obtain a canonical form of the geodesic chains and reduce the calculation of the sector coordination numbers to solution of the linear Diophantine equations. The approach is illustrated by the example of the 2-homogeneous kra graph. We obtain three alternative descriptions of the coordination sequences: explicit formulas, generating functions and recurrent relations.

scholarly journals On the Non-Linear Diophantine Equations 31x + 41y = z2 and 61x + 71y = z2

2018 ◽  
Vol 18 (2) ◽  
pp. 185-188
Author(s):  
Satish Kumar ◽  
◽  
Deepak Gupta ◽  
Hari Kishan
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations ◽  
Non Linear

The d-plane radon transform on the torus $$ \mathbb{T}^n $$

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Ahmed Abouelaz
Keyword(s):  
Radon Transform ◽  
Inversion Formula ◽  
Flat Torus ◽  
Smooth Functions ◽  
Suitable Function

AbstractWe define and study the d-plane Radon transform, namely R, on the n-dimensional (flat) torus. The transformation R is obtained by integrating a suitable function f over all d-dimensional geodesics (d-planes in the torus). We specially establish an explicit inversion formula of R and we give a characterization of the image, under the d-plane Radon transform, of the space of smooth functions on the torus.

Few Non-Linear Diophantine Equations

2021 ◽  
pp. 295-306
Author(s):  
Satyabrota Kundu ◽  
Sypriyo Mazumder
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations ◽  
Non Linear
Sign in / Sign up

Export Citation Format

Share Document