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The Infinite sites model (ISM) is a mathematical model of molecular evolution first proposed by Motoo Kimura in 1969. [1] Like other mutation models, the ISM provides a basis for understanding how mutation develops new alleles in DNA sequences.
This definition covers several different uses of the word "sequence", including one-sided infinite sequences, bi-infinite sequences, and finite sequences (see below for definitions of these kinds of sequences). However, many authors use a narrower definition by requiring the domain of a sequence to be the set of natural numbers. This narrower ...
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
The infinite sequence of additions expressed by a series cannot be explicitly performed in sequence in a finite amount of time. However, if the terms and their finite sums belong to a set that has limits , it may be possible to assign a value to a series, called the sum of the series .
In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers.
The sequence is called exact if it is exact at each for all <, i.e., if the image of each homomorphism is equal to the kernel of the next. The sequence of groups and homomorphisms may be either finite or infinite. A similar definition can be made for other algebraic structures.
A sequence could be a finite sequence from a data source or an infinite sequence from a discrete dynamical system. Such a discrete function could be defined explicitly by a list (if its domain is finite), or by a formula for its general term, or it could be given implicitly by a recurrence relation or difference equation.
A sequence in biology is the one-dimensional ordering of monomers, covalently linked within a biopolymer; it is also referred to as the primary structure of a biological macromolecule. While it can refer to many different molecules, the term sequence is most often used to refer to a DNA sequence or a protein sequence .