Mathematics

• Alexander duality
  Alexander duality
  In mathematics, Alexander duality refers to a duality theory presaged by a result of 1915 by J. W. Alexander, and subsequently further developed, particularly by P. S. Alexandrov and Lev Pontryagin...
  
  
• Alvis–Curtis duality
  Alvis–Curtis duality
  In mathematics, Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by and studied by his student...
  
  
• Araki duality
• Beta-dual space
  Beta-dual space
  In functional analysis and related areas of mathematics, the beta-dual or \beta-dual is a certain linear subspace of the algebraic dual of a sequence space.- Definition :...
  
  
• Coherent duality
  Coherent duality
  In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory....
  
  
• De Groot dual
  De Groot dual
  In mathematics, in particular in topology, the de Groot dual of a topology τ on a set X is the topology τ* whose closed sets are generated by compact saturated subsets of .- References :...
  
  
• Dual abelian variety
  Dual abelian variety
  In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field K.-Definition:To an abelian variety A over a field k, one associates a dual abelian variety Av , which is the solution to the following moduli problem...
  
  
• Dual basis in a field extension
  Dual basis in a field extension
  In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite extension L/K, by using the field trace. This requires the property that the field trace TrL/K provides a non-degenerate quadratic form over K...
  
  
• Dual bundle
  Dual bundle
  In mathematics, the dual bundle of a vector bundle π : E → X is a vector bundle π* : E* → X whose fibers are the dual spaces to the fibers of E...
  
  
• Dual curve
  Dual curve
  In projective geometry, a dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to its dual, sending each point to the point dual to its tangent line. If C is algebraic then so is its dual and the degree...
  
  
• Dual (category theory)
  Dual (category theory)
  In category theory, a branch of mathematics, duality is a correspondence between properties of a category C and so-called dual properties of the opposite category Cop...
  
  
• Dual graph
  Dual graph
  In mathematics, the dual graph of a given planar graph G is a graph which has a vertex for each plane region of G, and an edge for each edge in G joining two neighboring regions, for a certain embedding of G. The term "dual" is used because this property is symmetric, meaning that if H is a dual...
  
  
• Dual group
  Dual group
  In mathematics, the dual group may be:* The Pontryagin dual of a locally compact abelian group* The Langlands dual of a reductive algebraic group* The Deligne-Lusztig dual of a reductive group over a finite field....
  
  
• Dual object
  Dual object
  In category theory, a branch of mathematics, it is possible to define a concept of dual object generalizing the concept of dual space in linear algebra.A category in which each object has a dual is called autonomous or rigid.-Definition:...
  
  
• Dual pair
  Dual pair
  In functional analysis and related areas of mathematics a dual pair or dual system is a pair of vector spaces with an associated bilinear form....
  
  
• Dual polygon
  Dual polygon
  In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.-Properties:Regular polygons are self-dual....
  
  
• Dual polyhedron
  Dual polyhedron
  In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...
  
  
• Dual problem
  Dual problem
  In constrained optimization, it is often possible to convert the primal problem to a dual form, which is termed a dual problem. Usually dual problem refers to the Lagrangian dual problem but other dual problems are used, for example, the Wolfe dual problem and the Fenchel dual problem...
  
  
• Dual representation
  Dual representation
  In mathematics, if G is a group and ρ is a linear representation of it on the vector space V, then the dual representation is defined over the dual vector space as follows:...
  
  
• Dual q-Hahn polynomials
  Dual q-Hahn polynomials
  In mathematics, the dual q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.-Definition:...
  
  
• Dual q-Krawtchouk polynomials
  Dual q-Krawtchouk polynomials
  In mathematics, the dual q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.-Definition:...
  
  
• Dual space
  Dual space
  In mathematics, any vector space, V, has a corresponding dual vector space consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors which are studied in tensor algebra...
  
  
• Dual topology
  Dual topology
  In functional analysis and related areas of mathematics a dual topology is a locally convex topology on a dual pair, two vector spaces with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space....
  
  
• Dual wavelet
  Dual wavelet
  In mathematics, a dual wavelet is the dual to a wavelet. In general, the wavelet series generated by a square integrable function will have a dual series, in the sense of the Riesz representation theorem...
  
  
• Duality (order theory)
  Duality (order theory)
  In the mathematical area of order theory, every partially ordered set P gives rise to a dual partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the set with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P...
  
  
• Duality (projective geometry)
  Duality (projective geometry)
  A striking feature of projective planes is the "symmetry" of the roles played by points and lines in the definitions and theorems, and duality is the formalization of this metamathematical concept. There are two approaches to the subject of duality, one through language and the other a more...
  
  
• Duality theory for distributive lattices
  Duality theory for distributive lattices
  In mathematics, duality theory for distributive lattices provides three different representations of bounded distributive lattices via Priestley spaces, spectral spaces, and pairwise Stone spaces...
  
  
• Dualizing complex
• Dualizing sheaf
• Eckmann–Hilton duality
  Eckmann–Hilton duality
  In the mathematical disciplines of algebraic topology and homotopy theory, Eckmann–Hilton duality in its most basic form, consists of taking a given diagram for a particular concept and reversing the direction of all arrows, much as in category theory with the idea of the opposite category.It...
  
  
• Esakia duality
  Esakia duality
  In mathematics, Esakia duality is the dual equivalence between the category of Heyting algebras and the category of Esakia spaces. Esakia duality provides an order-topological representation of Heyting algebras via Esakia spaces....
  
  
• Fenchel's duality theorem
  Fenchel's duality theorem
  In mathematics, Fenchel's duality theorem is a result in the theory of convex functions named after Werner Fenchel.Let ƒ be a proper convex function on Rn and let g be a proper concave function on Rn...
  
  
• Haag duality
• Hodge dual
  Hodge dual
  In mathematics, the Hodge star operator or Hodge dual is a significant linear map introduced in general by W. V. D. Hodge. It is defined on the exterior algebra of a finite-dimensional oriented inner product space.-Dimensions and algebra:...
  
  
• Jónsson–Tarski duality
• Lagrange duality
• Langlands dual
• Lefschetz duality
  Lefschetz duality
  In mathematics, Lefschetz duality is a version of Poincaré duality in geometric topology, applying to a manifold with boundary. Such a formulation was introduced by Solomon Lefschetz in the 1920s, at the same time introducing relative homology, for application to the Lefschetz fixed-point theorem...
  
  
• Local Tate duality
  Local Tate duality
  In Galois cohomology, local Tate duality is a duality for Galois modules for the absolute Galois group of a non-archimedean local field. It is named after John Tate who first proved it. It shows that the dual of such a Galois module is the Tate twist of usual linear dual...
  
  
• Opposite category
  Opposite category
  In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite...
  
  
• Poincaré duality
  Poincaré duality
  In mathematics, the Poincaré duality theorem named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds...
  
  
  • Twisted Poincaré duality
    Twisted Poincaré duality
    In mathematics, the twisted Poincaré duality is a theorem removing the restriction on Poincaré duality to oriented manifolds. The existence of a global orientation is replaced by carrying along local information, by means of a local coefficient system....
    
    
• Poitou–Tate duality
• Pontryagin duality
  Pontryagin duality
  In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact groups, such as R, the circle or finite cyclic groups.-Introduction:...
  
  
• S-duality (homotopy theory)
• Schur–Weyl duality
  Schur–Weyl duality
  Schur–Weyl duality is a mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear and symmetric groups...
  
  
• Serre duality
  Serre duality
  In algebraic geometry, a branch of mathematics, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n . It shows that a cohomology group Hi is the dual space of another one, Hn−i...
  
  
• Spanier–Whitehead duality
• Stone's duality
• Tannaka–Krein duality
• Verdier duality
  Verdier duality
  In mathematics, Verdier duality is a generalization of the Poincaré duality of manifolds to locally compact spaces with singularities. Verdier duality was introduced by , as an analog for locally compact spaces of the coherent duality for schemes due to Grothendieck...
  
  

Science: Engineering

• Duality (electrical circuits)
• Duality (mechanical engineering)
  Duality (mechanical engineering)
  In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force and deformation in an expression.Here is a partial list of mechanical dualities:...
  
  

Science: Physics

• Complementarity (physics)
  Complementarity (physics)
  In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality...
  
  
• Dual resonance model
  Dual resonance model
  In theoretical physics, a dual resonance model arose the early investigation of string theory as an S-matrix theory of the strong interaction....
  
  
• Duality (electricity and magnetism)
• Englert–Greenberger duality relation
• Holographic duality
• Kramers–Wannier duality
• Mirror symmetry
  Mirror symmetry
  In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden...
  
  
• Montonen–Olive duality
• Mysterious duality
• String duality
  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....
  
  
• S-duality
  S-duality
  In theoretical physics, S-duality is an equivalence of two quantum field theories or string theories. An S-duality transformation maps states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory...
  
  
• T-duality
  T-duality
  T-duality is a symmetry of quantum field theories with differing classical descriptions, of which the relationship between small and large distances in various string theories is a special case. Discussion of the subject originated in a paper by T. S. Buscher and was further developed by Martin...
  
  
• U-duality
  U-duality
  In physics, U-duality 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 group" of M-theory as defined on a particular background space . This is the union of all the S- and T-dualities...
  
  
• Wave-particle duality