Presentation of (min,+) Algebra and Analysis, a powerful tool for Non-linear Mathematics. Examples of applications to Mathematical Physics and Signal Processing
Dr A. Kenoufi (SCORE, France), Dr M. GONDRAN, Dr A. GONDRAN, and Dr T. LEHNER.
(min,+)-algebra and analysis are particular and interesting fields of the so-called tropical and idempotent mathematics, and find their roots in theoretical informatics and computer sciences, particularly in operations research and automation. This has been, and is still a very productive and rich approach in pure and applied mathematics, in physics, informatics and engineering sciences.
One proposes to introduce this mathematical framework and to exhibit a new class of non-linear wavelets, very efficient to perform multi-resolution analysis, to handle fractal and multi-fractal phenomena such as turbulence, and which is a promising tool to improve image processing for instance. %In a second step, one shows a complex variational calculus based on (min,+) analysis and apply it on the well-known Born-Infeld problem in electrodynamics.