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Duality - Wikipedia, the free encyclopedia In alchemy, duality is a dynamic principle of opposing or complementary elements or spirits. Duality is an album of Lisa Gerrard and Pieter Bourke. Duality is a CD (2005) released by US rock band, Ra. en.wikipedia.org /wiki/Duality   (285 words)

Jean-Pierre Serre - Wikipedia, the free encyclopedia Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the Ecole Normale Supérieure in Paris. Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003. en.wikipedia.org /wiki/Jean-Pierre_Serre   (552 words)

Duality (mathematics) - Wikipedia, the free encyclopedia Using a duality of this type, every statement in the first theory can be translated into a "dual" statement in the second theory, where the direction of all arrows has to be reversed. In another group of dualities, the objects of one theory are translated into objects of another theory and the morphisms between objects in the first theory are translated into morphisms in the second theory, but with direction reversed. Dual graph is a concept in graph theory. en.wikipedia.org /wiki/Duality_(mathematics)   (315 words)

Equivalence of categories - Wikipedia, the free encyclopedia One of the central themes of algebraic geometry is the duality of the category of affine schemes and the category of commutative rings. In pointless topology the category of spatial locales is known to be equivalent to the dual of the category of sober spaces. An equivalence of categories consists of a functor between the involved categories, which is required to have an "inverse" functor. en.wikipedia.org /wiki/Equivalence_of_categories   (1435 words)

Duality In alchemy, duality is a dynamic principle of opposing or complementary elements or spirits. In electronics, duality is the relationship between two devices or circuits that have mathematical descriptions that are identical except that voltages in one correspond to currents in the other, and vice versa. In analytical psychology, duality is an archetype, that is to say, one of the deep powerful symbols of the functioning of the psyche. www.brainyencyclopedia.com /encyclopedia/d/du/duality.html   (233 words)

Duality (mathematics) - Wikipedia, the free encyclopedia Using a duality of this type, every statement in the first theory can be translated into a "dual" statement in the second theory, where the direction of all arrows has to be reversed. In another group of dualities, the objects of one theory are translated into objects of another theory and the morphisms between objects in the first theory are translated into morphisms in the second theory, but with direction reversed. Dual graph is a concept in graph theory. en.wikipedia.org /wiki/Duality_%28mathematics%29   (314 words)

Coherent sheaf - Wikipedia, the free encyclopedia The duality theory in scheme theory that extends Serre duality is called coherent duality (sometimes Grothendieck duality). The role played by coherent sheaves is as a class of sheaves, say on an algebraic variety or complex manifold, that is more general than the locally free sheaf — such as invertible sheaf, or sheaf of sections of a (holomorphic) vector bundle — but still with manageable properties. In mathematics, especially in algebraic geometry and the theory of complex manifolds, a coherent sheaf F on a locally ringed space X is a sheaf isomorphic with the cokernel of a morphism of O en.wikipedia.org /wiki/Coherent_sheaf   (690 words)

Stone Duality for Lattices - Dunn, Hartonas (ResearchIndex) Stone Duality for Lattices- Dunn, Hartonas (ResearchIndex) 75.4% : Stone Duality for Lattices- Hartonas, Dunn (1997) Duality for Lattices with Operators: a modal logic approach. citeseer.ist.psu.edu /513797.html   (690 words)

Serre duality - Wikipedia, the free encyclopedia In algebraic geometry, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality) for vector bundles and the more general coherent sheaves. While the role of K above in general Serre duality is played by the determinant line bundle of the cotangent bundle, when V is a manifold, in full generality K cannot just be a single sheaf in the absence of some hypothesis of non-singularity on V. Serre duality of curves is therefore something very classical; but it has interesting light to cast. en.wikipedia.org /wiki/Serre_duality   (413 words)

S-duality - Wikipedia, the free encyclopedia In theoretical physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory. An S-duality transformation maps the states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1 / g in the dual theory. In 4 dimensions, a lattice gauge model with G as the gauge group would be dual to a lattice gauge model with G' as the gauge group (with the electric and magnetic fields interchanged). en.wikipedia.org /wiki/Strong-weak_duality   (413 words)

Dualism - Wikipedia, the free encyclopedia In philosophy of mind, dualism is any of a narrow variety of views about the relationship between mind and matter, which are seen as totally different kinds of things. In philosophy of science, dualism often refers to the dichotomy between the "subject" (the observer) and the "object" (the observed). In theology, dualism can refer to ditheism : the belief that there are two basic principles in the universe, usually personified as deities, that work in polar opposition to each other. en.wikipedia.org /wiki/Dualism   (413 words)

Pontryagin duality - Wikipedia, the free encyclopedia In mathematics, in particular in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform. There are analogues of duality theory for noncommutative groups, some of which are formulated in the language of C*- algebras. The group operation on the dual group is given by pointwise multiplication of characters, the inverse of a character is its complex conjugate and the topology on the space of characters is that of uniform convergence on compact sets (i.e., the compact-open topology). en.wikipedia.org /wiki/Pontryagin_duality   (1942 words)

Wave-particle duality - Wikipedia, the free encyclopedia In quantum mechanics, the wave-particle duality is explained as follows: every system and particle is described by state functions which encode the probability distributions of all measurable variables. An intriguingly simple experiment, the double-slit experiment, summarizes the duality: aim an electron gun at a screen with two slits and record their positions of detection at a detector behind the screen. In physics, wave-particle duality holds that light and matter can exhibit properties of both waves and of particles. en.wikipedia.org /wiki/Duality_(physics)   (1942 words)

Duality (mathematics) - Wikipedia, the free encyclopedia Using a duality of this type, every statement in the first theory can be translated into a "dual" statement in the second theory, where the direction of all arrows has to be reversed. In another group of dualities, the objects of one theory are translated into objects of another theory and the morphisms between objects in the first theory are translated into morphisms in the second theory, but with direction reversed. Dual graph is a concept in graph theory. en.wikipedia.org /wiki/Duality_(mathematics)   (315 words)

Alexander Grothendieck - Wikipedia, the free encyclopedia Perhaps Grothendieck's deepest single accomplishment is the invention of the étale and l-adic cohomology theories, which explain an observation of André Weil's, that there is a deep connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. Alexander Grothendieck (born March 28, 1928, Berlin) was one of the most important mathematicians active in the 20th century. Grothendieck's radical left-wing and pacifist politics were doubtless born of his wartime experiences. en.wikipedia.org /wiki/Alexander_Grothendieck   (315 words)

categories: symmetry vs. duality The categorical notion of duality is captured precisely by adjointness, or the unity and identity of opposites. In the vernacular, symmetry and duality are sometimes used interchangeably, both referring to 2-ness: the quality, character or condition of being two or twofold - a dichotomy. Both symmetry and duality should be seen as sources of beauty in mathematics also, however, in order to be addressed mathematically. north.ecc.edu /alsani/ct01(5-8)/msg00048.html   (425 words)

Xuanzang (Hsüan-tsang) [Internet Encyclopedia of Philosophy] The store consciousness must be purified of its subject-object duality and notions of false existence, and restored to its pure state tantamount to buddhahood, the Absolute Suchness, and the undifferentiated. So illusive a force determines the world of difference and belongs to human nature, sprouting the erroneous notions of an I and a non-I. That duality can only be conquered by enlightenment, which effects the transformation of an ordinary person into a Buddha. Its appearance although objective and external is in fact the transcendental illusion, because of which consciousness is bifurcated into the subject-object duality. www.iep.utm.edu /x/xuanzang.htm   (425 words)

Wave-particle duality - Wikipedia, the free encyclopedia In quantum mechanics, the wave-particle duality is explained as follows: every system and particle is described by state functions which encode the probability distributions of all measurable variables. This is still a controversial subject because these experimenters have assumed arguments of wave-particle duality and have assumed the validity of deBroglie's equation in their argument. In quantum electrodynamics, Richard Feynman shows the wave-particle duality of photons and electrons is an illusion. en.wikipedia.org /wiki/Wave_theory_of_light   (1371 words)

Pontryagin Duality Encyclopedia Article, Definition, History, Biography There are analogues of duality theory for noncommutative groups, some of which are formulated in the language of C*- algebras. As a consequence of this, the dual of T is canonically isomorphic with Z. The group operation on the dual group is given by pointwise multiplication of characters, the inverse of character is its complex conjugate and the topology on the space of characters is that of uniform convergence on compact sets (i.e., the compact-open topology). www.artisticnudity.com /encyclopedia/Pontryagin_duality   (2102 words)

PlanetMath: Serre duality While Serre duality is not in a strict sense a generalization of Poincaré duality, they are philosophically similar, and both fit into a larger pattern on duality results. This is version 5 of Serre duality, born on 2003-08-15, modified 2005-03-10. Cross-references: Poincaré duality, strict, pairing, locally free, nonsingular, sheaf, coherent sheaf, perfect, field, algebraically closed, projective varieties, dimension, schemes, states planetmath.org /encyclopedia/DualizingSheaf.html   (134 words)

Wave-particle duality - Wikipedia, the free encyclopedia In quantum mechanics, the wave-particle duality is explained as follows: every system and particle is described by state functions which encode the probability distributions of all measurable variables. An intriguingly simple experiment, the double-slit experiment, summarizes the duality: aim an electron gun at a screen with two slits and record their positions of detection at a detector behind the screen. Wave-particle duality of C60, M. Arndt, O. Nairz, J. Voss-Andreae, C. Keller, G. van der Zouw, A. Zeilinger, Nature 401, 680-682, 14 October 1999 en.wikipedia.org /wiki/Wave-particle_duality   (134 words)

Talk:Pontryagin duality - Wikipedia, the free encyclopedia If a merge was to happen, dual group suffers from not having any reasons for wanting duality (which yours covers from a couple of angles) and Pontryagin duality suffers from not actually saying what the dual group is (in terms that an undergrad maths student can handle). Pontryagin duality looks good, but I wondered why you created this instead of adding to and/or rewriting dual group. The best solution may be a merged page under Pontryagin duality (a more accurate title) with dual group redirecting. en.wikipedia.org /wiki/Talk:Pontryagin_duality   (631 words)

Learn more about Particle physics in the online encyclopedia. The 20th century explorations of nuclear physics and quantum physics, culminating with proofs of nuclear fission and nuclear fusion, gave rise to an active industry of generating one atom from another, even rendering possible (although not feasible economically) the transmutation of lead into gold. Within physics itself, there are some objections to the extreme reductionist approach of attempting to explain everything in terms of elementary particles and their interaction. Particle physics is a branch of physics that studies the elementary constituents of matter and radiations, and the interactions between them. www.onlineencyclopedia.org /p/pa/particle_physics.html   (631 words)

Prophet's Manual - 2012 End of time - Fractality Each gravitational shell is duality of two equal and opposite spatial and time shells that rotate in opposite directions and their coherence at ¼ curvature is quantum leap from one to another coherent quantum state – regardless if it’s small space of an atom or large space of the universe. Duality of inversely proportional fractalities is total randomness in between. It’s geometry of 3 equal opposites – 2 in horizontal and one in angular direction, hence 3D, which is coherence of duality with its singular source. www.prophetsmanual.com /content/index.cfm?navID=21&itemID=24   (3579 words)

U-duality - Wikipedia, the free encyclopedia 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. This page was last modified 11:04, 4 Dec 2004. en.wikipedia.org /wiki/U-duality   (3579 words)

Abstract Stone Duality Abstract Stone Duality is a re-axiomatisation based on the monadic adjunction between the dual categories of `frames' and `spaces', rather than on finite intersections and arbitrary unions. Abstract Stone Duality (ASD) is a type theory in which the topology on a space is an exponential with a l -calculus, not an infinitary lattice. Identifying the need for Scott domains to be overt (open) objects in intuitionistic locale theory, we re-work Scott's informations systems construction from first principles, to obtain a cartesian closed full subcategory in abstract Stone duality. www.cs.man.ac.uk /~pt/ASD   (3579 words)

DUALITY What it is abstracting may not be clear; when it is compared to other contemporary works, however, there may be some suggestion of the Duality, a concept that began this early in Mesoamerican culture. The Duality consists of two seemingly opposite aspects that in fact can only exist by the presence of the other. Named the Priest of Naranjo, this stone sculpture carries many of the motifs associated with Huaxtec sculpture: the conical headpiece, the particular design on the tunic, and the hook-shaped epcololli earrings. members.aol.com /maroic/dual.htm   (3579 words)

Stone duality - Wikipedia, the free encyclopedia Stone's representation for distributive lattices can be extended via an equivalence of coherent spaces and Stone-type dualities also provide the foundation for pointless topology and are exploited in theoretical computer science for the study of formal semantics. Many other Stone-type dualities could be added to these basic dualities. en.wikipedia.org /wiki/Stone_duality   (3579 words)

Serre Duality Serre duality on complex supermanifolds, Carl Haske, R. Wells, Jr.... On Generalizing a Theorem of Serre: A Case Study in the Duality Between Algebra... N = 1 dualities and the dynamics of brane... www.scienceoxygen.com /math/735.html   (133 words)

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