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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 ...
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.
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]
In mathematics, the classification of finite simple groups (popularly called the enormous theorem [1] [2]) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group ...
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.
where T is the total sum of squares and products (SSP) matrix, W is the within-samples SSP matrix and B is the between-samples SSP matrix. Similar terminology may also be used in linear discriminant analysis , where W and B are respectively referred to as the within-groups and between-groups SSP matrices.
For a Lie group of rank R, one can choose at most R orthogonal circles that do not twist around each other, and so form a maximal torus within the Lie group, corresponding to a collection of R mutually-commuting Lie algebra generators, spanning a Cartan subalgebra. Each elementary particle state can be thought of as a different orthogonal ...
A large body of research in meaningful 'real-world' contexts lends support to the applicability of the common ingroup identity model. In a diverse range of intergroup situations, it has been demonstrated that the conditions specified by the contact hypothesis (i.e. cooperative interaction) reduce intergroup bias through transforming members' representations of separate group memberships to one ...