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Duality
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 iso ... [...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] |
Duality (mixtape)
''Duality'' (stylized as ''DU∆LITY'') is the debut mixtape from Captain Murphy, the animated rapper alter-ego of experimental musician Flying Lotus. It was initially released as a 34-minute short film featuring songs performed by Murphy as well as archived cult footage (including footage involving Heaven's Gate co-founder Marshall Applewhite), pornography, cartoons and 1980s films. A deluxe edition was released for download on November 28, 2012, with tracks separated, as well as bonus tracks and instrumentals. Background Captain Murphy first appeared over the summer of 2012 on the Flying Lotus-produced track "Between Friends" for the 2012 Adult Swim Singles Program. The track also featured Odd Future's Earl Sweatshirt trading verses with Murphy. Speculation began to arise that Murphy was either Tyler, The Creator, Earl Sweatshirt, Flying Lotus, or a combination of the three due to the frequent pitch shifts in vocals. Between July and September 2012, Murphy released several musi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (optimization)
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem. Therefore, the solution to the primal is an upper bound to the solution of the dual, and the solution of the dual is a lower bound to the solution of the primal. This fact is called weak duality. In general, the optimal values of the primal and dual problems need not be equal. Their difference is called the duality gap. For convex optimization problems, the duality gap is zero under a constraint qualification condition. This fact is called strong duality. Dual problem Usually the term "dual problem" refers to the ''Lagrangian dual problem'' but other ... [...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] |
Dual (category Theory)
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category ''C'' and the dual properties of the opposite category ''C''op. Given a statement regarding the category ''C'', by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite category ''C''op. Duality, as such, is the assertion that truth is invariant under this operation on statements. In other words, if a statement is true about ''C'', then its dual statement is true about ''C''op. Also, if a statement is false about ''C'', then its dual has to be false about ''C''op. Given a concrete category ''C'', it is often the case that the opposite category ''C''op per se is abstract. ''C''op need not be a category that arises from mathematical practice. In this case, another category ''D'' is also termed to be in duality with ''C'' if ''D'' and ''C''op are e ... [...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 theories, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Duality (projective Geometry)
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language () and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a ''duality''. Such a map can be constructed in many ways. The concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry. Principle of duality A projective plane may be defined axiomatically as an incidence structure, in terms of a set of ''points'', a set of ''lines'', and an incidence relation that determines which points lie on which lines. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality Principle (Boolean Algebra)
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean algebra" ... [...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 |
