Duality and separation theorems in idempotent semimodules
TLDR
In this article, a nonlinear projection on subsemimodules is introduced, where the projection of a point is the maximal approximation from below of the point in the sub-semimmodule.About:
This article is published in Linear Algebra and its Applications.The article was published on 2004-03-01 and is currently open access. It has received 273 citations till now. The article focuses on the topics: Idempotent matrix & Projection (mathematics).read more
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Introduction to Tropical Geometry
Diane Maclagan,Bernd Sturmfels +1 more
TL;DR: Tropical islands Building blocks Tropical varieties Tropical rain forest Tropical garden Toric connections Bibliography Index Bibliography as mentioned in this paper, Section 5.1.1] and Bibliography 2.2.
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Max-linear Systems: Theory and Algorithms
TL;DR: Max-algebra: Two Special Features.- One-sided Max-linear Systems and Max- algebraic Subspaces.
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First steps in tropical geometry
TL;DR: Tropical algebraic geometry is the geometry of the tropical semiring as mentioned in this paper, where the objects are polyhedral cell complexes which behave like complex algebraic varieties and have a complete description of the families of quadrics through four points in the tropical projective plane and a counterexample to the incidence version of Pappus' Theorem.
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Maslov dequantization, idempotent and tropical mathematics: A brief introduction
TL;DR: In this article, a brief introduction to idempotent and tropical mathematics is given, which can be seen as the result of the so-called Maslov dequantization of the traditional mathematics over numerical fields as the Planck constant tends to zero taking imaginary values.
References
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Infinite Dimensional Analysis: A Hitchhiker's Guide
TL;DR: In this paper, Riesz spaces are used to represent the topology of the space of sequences of sequences and correspondences of correspondences in Markov transitions, where the correspondences correspond to Markov transition.
Book
A Compendium of Continuous Lattices
TL;DR: In this article, the authors present a primer of complete lattices and complete topology of continuous lattices, including the Scott topology and meet-continuous lattices.
Journal ArticleDOI
Synchronization and Linearity: An Algebra for Discrete Event Systems
TL;DR: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints, which is shown to parallel the classical linear system theory in several ways.