This volume is a collection of papers from the International Conference on Tropical and Idempotent Mathematics, held in Moscow, Russia in August 2007. This is a relatively new branch of mathematical sciences that has been rapidly developing and gaining popularity over the last decade. Tropical mathematics can be viewed as a result of the Maslov dequantization applied to ``traditional'' mathematics over fields. Importantly, applications in econophysics and statistical mechanics lead to an explanation of the nature of financial crises. Another original application provides an analysis of instabilities in electrical power networks. Idempotent analysis, tropical algebra, and tropical geometry are the building blocks of the subject. Contributions to idempotent analysis are focused on the Hamilton-Jacobi semigroup, the max-plus finite element method, and on the representations of eigenfunctions of idempotent linear operators. Tropical algebras, consisting of plurisubharmonic functions and their germs, are examined. The volume also contains important surveys and research papers on tropical linear algebra and tropical convex geometry.International Workshop Tropical-07, Tropical and Idempotent Mathematics, August 25-30, 2007, Independent University of Moscow and ... in the former case, and of the form f(x+1i+1j)+f(x+1j)ay f(x+1i)+f(x+2Am1j) in the latter case, where 1q denotes q-th unit base vector in Zn. It turns out that ... In Section 2 we give necessary definitions and preliminary facts about TP-functions on boxes and truncated boxes.

Title | : | Tropical and Idempotent Mathematics |

Author | : | Grigoriĭ Lazarevich Litvinov, S. N. Sergeev |

Publisher | : | American Mathematical Soc. - 2009 |

Continue