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A quasigroup (Q, ∗) is a non-empty set Q with a binary operation ∗ (that is, a magma, indicating that a quasigroup has to satisfy closure property), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both. a ∗ x = b. y ∗ a = b.
Objects studied in discrete mathematics include integers, graphs, and statements in logic. [1][2][3] By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized ...
Examples of the use of groups in physics include the Standard Model, gauge theory, the Lorentz group, and the Poincaré group. Group theory can be used to resolve the incompleteness of the statistical interpretations of mechanics developed by Willard Gibbs , relating to the summing of an infinite number of probabilities to yield a meaningful ...
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.
e. In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. [1]
The Shannon–Weaver model is one of the first and most influential models of communication. It was initially published in the 1948 paper "A Mathematical Theory of Communication" and explains communication in terms of five basic components: a source, a transmitter, a channel, a receiver, and a destination. The source produces the original message.
This group is isomorphic to SO(3), the group of rotations in 3-dimensional space. The automorphism group of the octonions (O) is the exceptional Lie group G 2. In graph theory an automorphism of a graph is a permutation of the nodes that preserves edges and non-edges. In particular, if two nodes are joined by an edge, so are their images under ...
Tuckman's stages of group development. The forming–storming–norming–performing model of group development was first proposed by Bruce Tuckman in 1965, [1] who said that these phases are all necessary and inevitable in order for a team to grow, face up to challenges, tackle problems, find solutions, plan work, and deliver results.