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Duality Theories
Duality may refer to: Mathematics * Duality (mathematics), a mathematical concept ** Dual (category theory), a formalization of mathematical duality ** Duality (optimization) ** Duality (order theory), a concept regarding binary relations ** Duality (projective geometry), general principle of projective geometry ** Duality principle (Boolean algebra), the extension of order-theoretic duality to Boolean algebras ** S-duality (homotopy theory) * Philosophy, logic, and psychology * Dualistic cosmology, a twofold division in several spiritual and religious worldviews * Dualism (philosophy of mind), where the body and mind are considered to be irreducibly distinct * De Morgan's laws, specifically the ability to generate the dual of any logical expression * Complementary duality of Carl Jung's functions and types in Socionics * Duality (CoPs), refers to the notion of a duality in a Community of Practice Science Electrical and mechanical * Duality (electrical circuits), regarding isomo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (mathematics)
In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is , then the dual of is . In other cases the dual of the dual – the double dual or bidual – is not necessarily identical to the original (also called ''primal''). Such involutions sometimes have fixed points, so that the dual of is itself. For example, Desargues' theorem is self-dual in this sense under the ''standard duality in projective geometry''. In mathematical contexts, ''duality'' has numerous meanings. It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics". Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (Set It Off Album)
Duality may refer to: Mathematics * Duality (mathematics), a mathematical concept ** Dual (category theory), a formalization of mathematical duality ** Duality (optimization) ** Duality (order theory), a concept regarding binary relations ** Duality (projective geometry), general principle of projective geometry ** Duality principle (Boolean algebra), the extension of order-theoretic duality to Boolean algebras ** S-duality (homotopy theory) * Philosophy, logic, and psychology * Dualistic cosmology, a twofold division in several spiritual and religious worldviews * Dualism (philosophy of mind), where the body and mind are considered to be irreducibly distinct * De Morgan's laws, specifically the ability to generate the dual of any logical expression * Complementary duality of Carl Jung's functions and types in Socionics * Duality (CoPs), refers to the notion of a duality in a Community of Practice Science Electrical and mechanical * Duality (electrical circuits), re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (Lisa Gerrard And Pieter Bourke Album)
''Duality'' is a collaborative album by Lisa Gerrard and Pieter Bourke released in 1998. It was Lisa Gerrard's second post- Dead Can Dance album after '' The Mirror Pool'' from 1995. Lisa Gerrard and Brendan Perry released their last album in 1996 and had officially disbanded Dead Can Dance earlier in 1998. At the ARIA Music Awards of 1998, the album was nominated for ARIA Award for Best World Music Album.ARIA Award previous winners. Overview The beginning of the song "Shadow Magnet" influenced, in part, the music at the beginning of the ''Gladiator'' soundtrack (music by Hans Zimmer Hans Florian Zimmer (; born 12 September 1957) is a German film score composer and music producer. He has won two Academy Awards, a BAFTA Award, five Grammy Awards, and has been nominated for three Primetime Emmy Awards, Emmy Awards and a Tony ... and Lisa Gerrard). The track "Nadir (Synchronicity)" was initially intended for use at the end of that film. However, due to copyright issues, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (Peter Leitch And John Hicks Album)
''Duality'' is an album by guitarist Peter Leitch and pianist John Hicks that was recorded in 1994. Recording and music The album was recorded at Rudy Van Gelder Studio, Englewood Cliffs, New Jersey, on June 1 and 2, 1994."RSR CD 134" Reservoir Music. Retrieved July 31, 2017. It is a duet album played by guitarist Peter Leitch and pianist . The material is a mix of standards, relatively unknown compositions, and pieces written by each of the musicians. Release and reception ''Duality'' was released by[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave–particle Duality
Wave–particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave (physics), wave properties according to the experimental circumstances. It expresses the inability of the Classical physics, classical concepts such as particle or wave to fully describe the behavior of quantum objects. During the 19th and early 20th centuries, light was found to behave as a wave then later was discovered to have a particle-like behavior, whereas electrons behaved like particles in early experiments then were later discovered to have wave-like behavior. The concept of duality arose to name these seeming contradictions. History Wave-particle duality of light In the late 17th century, Sir Isaac Newton had advocated that light was Corpuscular theory of light, corpuscular (particulate), but Christiaan Huygens took an opposing wave description. While Newton had favored a particle approach, he was the first to at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
U-duality
In physics, U-duality (short for unified duality)S. Mizoguchi,On discrete U-duality in M-theory, 2000. is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the "U-duality (symmetry) group" of M-theory as defined on a particular background space (topological manifold In topology, a topological manifold is a topological space that locally resembles real ''n''- dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds ...). This is the union of all the S-duality and T-duality available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong coupling of another theory, for example. References String theory {{string-th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-duality
T-duality (short for target-space duality) in theoretical physics is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in a spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius proportional to 1/R. The idea of T-duality was first noted by Bala Sathiapalan in an obscure paper in 1987. The two T-dual theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description. The idea of T-duality can be extended to more complicated theories, including superstring theories. The existence of these dualities implies tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-duality
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult to a theory in which they are easier. In quantum field theory, S-duality generalizes a well established fact from classical electrodynamics, namely the invariance of Maxwell's equations under the interchange of electric and magnetic fields. One of the earliest known examples of S-duality in quantum field theory is Montonen–Olive duality which relates two versions of a quantum field theory called ''N'' = 4 supersymmetric Yang–Mills theory. Recent work of Anton Kapustin and Edward Witten suggests that Montonen–Olive duality is closely related to a research program in mathematics called the geometric Langlands program. Another realization of S-duality i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Duality
String duality is a class of symmetries in physics that link different string theories, theories which assume that the fundamental building blocks of the universe are strings instead of point particles. Overview Before the so-called "duality revolution" there were believed to be five distinct versions of string theory, plus the (unstable) bosonic and gluonic theories. Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the ''bulk''), while open strings have their ends attached to D-branes, which are membranes of lower dimensionality (their dimension is odd - 1,3,5,7 or 9 - in type IIA and even - 0,2,4,6 or 8 - in type IIB, including the time direction). Before the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories ( SO(32) and ''E''8×''E''8). The thinking was that out of these fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mysterious Duality
In physics, M-theory is a theory that unifies all Consistency, consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories initially appeared to be very different, work by many physicists showed that the theories were related in intricate and nontrivial ways. Physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Witten's conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory (physics), field theory called eleven-dimensional supergravity. Although a complete formulation o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montonen–Olive Duality
Montonen–Olive duality or electric–magnetic duality is the oldest known example of strong–weak duality or S-duality according to current terminology. It generalizes the electro-magnetic symmetry of Maxwell's equations by stating that magnetic monopoles, which are usually viewed as emergent quasiparticles that are "composite" (i.e. they are solitons or topological defects), can in fact be viewed as "elementary" quantized particles with electrons playing the reverse role of "composite" topological solitons; the viewpoints are equivalent and the situation dependent on the duality. It was later proven to hold true when dealing with a ''N'' = 4 supersymmetric Yang–Mills theory. It is named after Finnish physicist Claus Montonen and British physicist David Olive after they proposed the idea in their academic paper '' Magnetic monopoles as gauge particles?'' where they state: S-duality is now a basic ingredient in topological quantum field theories and string theori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
