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Duality Of Structure
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 Science Electrical and mechanical * Duality (electrical circuits), regarding isomorphism of electrical circuits * Duality (mechanical engineering), regarding is ... [...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 . 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 the second type to some family of scalars. For instance, ''linear algebra duality'' corresponds in this way to bilinear maps from pairs of vecto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holographic Duality
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence. The ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (Ra Album)
''Duality'' is the second studio album by American alternative metal band Ra. This is the band's first album with bassist/backing vocalist P.J. Farley and drummer Andy Ryan. The style from this album has noticeably changed since Ra's debut album of ''From One''. The album boasts a hard rock and melodic vibe whereas their first album had more of a nu metal feel. The middle-eastern influences in the CD are still present, but are noticeably pushed back. Akin to their former album, ''Duality'' only claimed one charting single, which was the song "Fallen Angels", a song that was inspired by the Kevin Smith film Dogma. The tenth track "Got Me Going" was played on the radio in the background of the movie ''Hot Rod''. Early pressings of the album were immediately recalled from stores because of a manufacturing glitch, as skipping could be heard on track 2. The problem has since been corrected, and latest pressings of the album feature a sticker on the front of the case stating it to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (Set It Off Album)
''Duality'' is the second studio album by American band Set It Off. The album was released on October 14, 2014 through record labels Equal Vision Records and Rude Records. The album was announced on August 13, 2014, alongside the announcement of a tour with rock bands Black Veil Brides and Falling in Reverse. Track listing All tracks are produced by Brandon Paddock Brandon Paddock is an American Pop and Rock musician and producer and member of Electronic Pop/Dance duo Fancy Cars. Commercial success Paddock has received two RIAA Platinum Records (awarded for the shipment of 1,000,000 units) for his work on ..., except where noted. Charts References 2014 albums Set It Off (band) albums Equal Vision Records albums {{2010s-album-stub ... [...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 and Lisa Gerrard). The track "Nadir (Synchronicity)" was initially intended for use at the end of that film. However, due to copyright issues, a song 'influenced' by this track was used instead. "Tempest" and "Sacrifice" were used for the ''Insider ''Insider'', previously named ''Business Insider'' (''BI''), is an American financial and business news website founded in 2007. Since 2015, a maj ... [...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 |
Wave–particle Duality
Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote: Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger and many others, current scientific theory holds that all particles exhibit a wave nature and vice versa. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected. Although the use of the wave–particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved; see interpretations of quantum mechanics. Bohr regarded the "duality ... [...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 branch of mathematics, 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 mathe ...). 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-theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-duality
In theoretical physics, T-duality (short for target-space duality) 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 that ... [...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 in quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Duality
String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian animated short * ''Strings'' (2004 film), a film directed by Anders Rønnow Klarlund * ''Strings'' (2011 film), an American dramatic thriller film * ''Strings'' (2012 film), a British film by Rob Savage * ''Bravetown'' (2015 film), an American drama film originally titled ''Strings'' * ''The String'' (2009), a French film Music Instruments * String (music), the flexible element that produces vibrations and sound in string instruments * String instrument, a musical instrument that produces sound through vibrating strings ** List of string instruments * String piano, a pianistic extended technique in which sound is produced by direct manipulation of the strings, rather than striking the piano's keys Types of groups * String band, musical ens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mysterious Duality
M-theory is a theory in physics that unifies all 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 called eleven-dimensional supergravity. Although a complete formulation of M-theory is not known, such a fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
