zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An introduction to idempotency. (English) Zbl 0898.16032
Gunawardena, Jeremy (ed.), Idempotency. Based on a workshop, Bristol, UK, October 3--7, 1994, Cambridge: Cambridge University Press. 1-49 (1998).
This paper is an excellent survey article about semirings with commutative and idempotent addition which have an absorbing zero and an identity. Such semirings are sometimes also called dioids. After introducing some basic concepts and general results for (semirings and) dioids, the author discusses their main application areas in detail: automata and idempotency (Kleene’s theorem, the tropical dioid), discrete event systems (mathematical models, topical functions, periodicity, cycle times), nonlinear partial differential equations (viscosity solutions, functional analysis over dioids), optimisation and large deviations (idempotent measures and integration, topical functions and asymptotics). In each section the basic ideas are explained and main results (some of them with proofs) and open problems are stated. A detailed reference list of more than 100 items is also contained. (Also submitted to MR). For the entire collection see [Zbl 0882.00035].

MSC:
16Y60Semirings
35A99General theory of PDE
46S99Nonclassical functional analysis