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Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

Let a_1=1 and define a_(n+1) to be the least integer greater than a_n which cannot be written as the sum of at most h>=2 addends among the terms a_1, a_2, ..., a_n. This ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

The Tutte 12-cage, also called the Benson graph (Exoo and Jajcay 2008), is the unique 12-cage graph, equivalent to the generalized hexagon GH(2,2) and alternately called the ...

There are at least two graphs associated with H. Walther. A graph on 25 vertices which appears somewhat similar to Tutte's fragment is implemented without discussion or ...

About Eric Weisstein's World of Mathematics

A generalization of an Ulam sequence in which each term is the sum of two earlier terms in exactly s ways. (s,t)-additive sequences are a further generalization in which each ...

An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...