The Maslov dequantization, idempotent and tropical mathematics: A brief introduction
arXiv:math/0507014
Abstract
This paper is a brief introduction to idempotent and tropical mathematics. Tropical mathematics can be treated as a result of the so-called Maslov dequantization of the traditional mathematics over numerical fields as the Planck constant tends to zero taking imaginary values.
English and Russian versions. This article, a result of a very considerable expansion of math.GM/0501038, is to appear in Journal of Mathematical Sciences (Notes of Scientific Seminars of the V.A. Steklov Mathematical Institute), see <http://tinyurl.com/a3ahc>. Dedicated to Anatoly Vershik with admiration and gratitude. Russian version to be published in "Zapiski Nauchnykh Seminarov POMI"
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Cited by in corpus (15)
- Tropical Arithmetic and Tropical Matrix Algebra
- Erlangen Program at Large--2: Inventing a wheel. The parabolic one
- Tropical optimization problems
- Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
- Idempotence of finitely generated commutative semifields
- Generators of modules in tropical geometry
- Explicit solution of a tropical optimization problem with application to project scheduling
- Idempotent probability measures, I
- Exact Sequences in Non-Exact Categories (An Application to Semimodules)
- On uniform metrizability of the functor of idempotent probability measures
- Geometry in the tropical limit
- The Fréchet Contingency Array Problem is Max-Plus Linear
- A note on tropical triangles in the plane
- On infinite iterations of the functor of idempotent probability measures
- Idempotent and tropical mathematics. Complexity of algorithms and interval analysis