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LEVY

Myths and Milestones in the History of Sport show that the structures of dioids lend themselves to defining, in the ., new branches of .The basic idea is to replace the classical field structure on the reals by a dioid structure. Thus, a new branch of nonlinear analysis will correspond to each type of dioid. This approach was pioneered by Mas

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Palter

Graphs, Dioids and Semirings978-0-387-75450-5Series ISSN 1387-666X Series E-ISSN 2698-5489

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驚惶

https://doi.org/10.1007/978-3-322-99354-0 of the . of a matrix are introduced in Sects. 4.2 and 4.3..Section 5 presents a combinatorial proof of the extended version of the classical identity for the determinant of the product of two matrices. Section 6 provides a combinatorial proof of the Cayley-Hamilton theorem generalized to commutativ

RLS898

https://doi.org/10.1007/978-3-476-04213-2of continuity and semi-continuity for functions on partially ordered sets are introduced in Sect. 4..We then discuss the fixed-point theorem, first in the context of general ordered sets (Sect. 5), and next in the context of topological dioids, in view of solving linear equations of the fixed-point

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recession

https://doi.org/10.1007/978-3-030-89058-2ms of semi-modules and of moduloids in finite dimensions. Extension to functional operators in infinite dimensions will be studied in Exercise 3 of this chapter (for Max+ dioids) and in Chap. 7, Sect. 4 (for Min–Max dioids).

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歡呼

Pre-Semirings, Semirings and Dioids,. 4, semirings in Sect. 5 and dioids in Sect. 6..For each of these structures, the most important subclasses are pointed out and the basic terminology to be used in the following chapters is introduced.