Ads
related to: finite and infinite sequence ppt project management presentation
Search results
Results From The WOW.Com Content Network
If I and J are finite sets, then the presentation is called a finite presentation; a module is called finitely presented if it admits a finite presentation. Since f is a module homomorphism between free modules , it can be visualized as an (infinite) matrix with entries in R and M as its cokernel .
If both are finite it is said to be a finite presentation. A group is finitely generated (respectively finitely related, finitely presented) if it has a presentation that is finitely generated (respectively finitely related, a finite presentation). A group which has a finite presentation with a single relation is called a one-relator group.
The infinite words, or ω-words, can likewise be viewed as functions from to Σ. The set of all infinite words over Σ is denoted Σ ω. The set of all finite and infinite words over Σ is sometimes written Σ ∞ or Σ ≤ω. Thus an ω-language L over Σ is a subset of Σ ω.
A renewal system is defined to be the set of all infinite concatenations of some fixed finite collection of finite words. Subshifts of finite type are identical to free (non-interacting) one-dimensional Potts models ( n -letter generalizations of Ising models ), with certain nearest-neighbor configurations excluded.
An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type ...
For a finite binary string w we let C w denote the cylinder generated by w. This is the set of all infinite sequences beginning with w, which is a basic open set in Cantor space. The product measure μ(C w) of the cylinder generated by w is defined to be 2 −|w|. Every open subset of Cantor space is the union of a countable sequence of ...
The non-negativity of the covariance for the infinite sequence can then be obtained as a limiting result from this finite sequence result. Equality of the lower bound for finite sequences is achieved in a simple urn model: An urn contains 1 red marble and n − 1 green marbles, and these are sampled without replacement until the urn is empty.
The ordinary generating function of a sequence can be expressed as a rational function (the ratio of two finite-degree polynomials) if and only if the sequence is a linear recursive sequence with constant coefficients; this generalizes the examples above. Conversely, every sequence generated by a fraction of polynomials satisfies a linear ...