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the String group can be thought of as a "higher" complex spin group extension, in the sense of higher group theory since the space (,) is an example of a higher group. It can be thought of the topological realization of the groupoid B U ( 1 ) {\displaystyle \mathbf {B} U(1)} whose object is a single point and whose morphisms are the group U ( 1 ...
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]
First array of four aggregates (numbered 1–4 at bottom), each vertical line (four trichords labeled a–d) is an aggregate while each horizontal line (four trichords labeled a-d) is also an aggregate. [1] Composition for Four Instruments (1948) is an early serial music composition written by American composer Milton Babbitt.
[64] Bartók employs both diatonic and chromatic clusters in his Fourth String Quartet (1928). [65] The sound mass technique in such works as Ruth Crawford Seeger's String Quartet (1931) and Iannis Xenakis's Metastaseis (1955) is an elaboration of the tone cluster. "Unlike most tonal and non-tonal linear dissonances, tone clusters are ...
It differs from the longest common substring: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The problem of computing longest common subsequences is a classic computer science problem, the basis of data comparison programs such as the diff utility , and has applications in ...
All-interval tetrachords (Play ⓘ).An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. [1] There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form.
Let be a group, written multiplicatively, and let be a ring. The group ring of over , which we will denote by [], or simply , is the set of mappings : of finite support (() is nonzero for only finitely many elements ), where the module scalar product of a scalar in and a mapping is defined as the mapping (), and the module group sum of two mappings and is defined as the mapping () + ().
A string-searching algorithm, sometimes called string-matching algorithm, is an algorithm that searches a body of text for portions that match by pattern. A basic example of string searching is when the pattern and the searched text are arrays of elements of an alphabet ( finite set ) Σ.