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Presentation of (min,+) Algebra and Analysis, a powerful tool for Nonlinear 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.
Abstract:
(min,+)algebra and analysis are particular and interesting fields of the socalled 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 nonlinear wavelets, very efficient to perform multiresolution analysis, to handle fractal and multifractal 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 wellknown BornInfeld problem in electrodynamics.
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