Computational group theoryIn mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups. The subject has attracted interest because for many interesting groups (including most of the sporadic groups) it is impractical to perform calculations by hand.
Space groupIn mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions.
Additive inverseIn mathematics, the additive inverse of a number a (sometimes called the opposite of a) is the number that, when added to a, yields zero. The operation taking a number to its additive inverse is known as sign change or negation. For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself. The additive inverse of a is denoted by unary minus: −a (see also below).
In-group favoritismIn-group favoritism, sometimes known as in-group–out-group bias, in-group bias, intergroup bias, or in-group preference, is a pattern of favoring members of one's in-group over out-group members. This can be expressed in evaluation of others, in allocation of resources, and in many other ways. This effect has been researched by many psychologists and linked to many theories related to group conflict and prejudice. The phenomenon is primarily viewed from a social psychology standpoint.
Social identity theorySocial identity is the portion of an individual's self-concept derived from perceived membership in a relevant social group. As originally formulated by social psychologists Henri Tajfel and John Turner in the 1970s and the 1980s, social identity theory introduced the concept of a social identity as a way in which to explain intergroup behaviour.
Schur decompositionIn the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily equivalent to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix. The Schur decomposition reads as follows: if A is an n × n square matrix with complex entries, then A can be expressed as where Q is a unitary matrix (so that its inverse Q−1 is also the conjugate transpose Q* of Q), and U is an upper triangular matrix, which is called a Schur form of A.
Galois theoryIn mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying roots of polynomials.
Grand Unified TheoryIn particle physics, a Grand Unified Theory (GUT) is a model in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this unified force has not been directly observed, many GUT models theorize its existence. If the unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.
String theoryIn physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string.
TacticityTacticity (from taktikos, "relating to arrangement or order") is the relative stereochemistry of adjacent chiral centers within a macromolecule. The practical significance of tacticity rests on the effects on the physical properties of the polymer. The regularity of the macromolecular structure influences the degree to which it has rigid, crystalline long range order or flexible, amorphous long range disorder. Precise knowledge of tacticity of a polymer also helps understanding at what temperature a polymer melts, how soluble it is in a solvent and its mechanical properties.
The Big Bang TheoryThe Big Bang Theory is an American television sitcom created by Chuck Lorre and Bill Prady, both of whom served as executive producers on the series, along with Steven Molaro. The three of them also served as head writers. It aired on CBS from September 24, 2007 to May 16, 2019, running for 12 seasons and 279 episodes.
Dyad (music)In music, a dyad (less commonly, diad) is a set of two notes or pitches that, in particular contexts, may imply a chord. Dyads can be classified by the interval between the notes. For example, the interval between C and E is a major third, which can imply a C major chord, made up of the notes C, E and G. When the pitches of a dyad occur in succession, they form a melodic interval. When they occur simultaneously, they form a harmonic interval. The harmonic series is built over a fundamental pitch, and the rest of the partials in the series are called overtones.
