List of dualities
Mathematics
In mathematics, a duality, generally speaking, 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 A is B, then the dual of B is A.
- Alexander duality
- Alvis–Curtis duality
- Artin–Verdier duality
- Beta-dual space
- Coherent duality
- Conjugate hyperbola
- De Groot dual
- Dual abelian variety
- Dual basis in a field extension
- Dual bundle
- Dual curve
- Dual (category theory)
- Dual graph
- Dual group
- Dual object
- Dual pair
- Dual polygon
- Dual polyhedron
- Dual problem
- Dual representation
- Dual q-Hahn polynomials
- Dual q-Krawtchouk polynomials
- Dual space
- Dual topology
- Dual wavelet
- Duality (optimization)
- Duality (order theory)
- Duality of stereotype spaces
- Duality (projective geometry)
- Duality theory for distributive lattices
- Dualizing complex
- Dualizing sheaf
- Eckmann–Hilton duality
- Esakia duality
- Fenchel's duality theorem
- Hodge dual
- Isbell duality
- Jónsson–Tarski duality
- Lagrange duality
- Langlands dual
- Lefschetz duality
- Local Tate duality
- Opposite category
- Poincaré duality
- Poitou–Tate duality
- Pontryagin duality
- S-duality (homotopy theory)
- Schur–Weyl duality
- Series-parallel duality[1][2]
- Serre duality
- Spanier–Whitehead duality
- Stone's duality
- Tannaka–Krein duality
- Verdier duality
- Grothendieck local duality
Philosophy and religion
Engineering
- Duality (electrical circuits)
- Duality (mechanical engineering)
- Observability/Controllability in control theory
Physics
- Complementarity (physics)
- Dual resonance model
- Duality (electricity and magnetism)
- Englert–Greenberger duality relation
- Holographic duality
- Kramers–Wannier duality
- Mirror symmetry
- Montonen–Olive duality
- Mysterious duality (M-theory)
- Seiberg duality
- String duality
- Wave–particle duality
Economics and finance
See also
References
- ^ a b Ellerman, David Patterson (1995-03-21). "Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics". Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics (PDF). G - Reference, Information and Interdisciplinary Subjects Series (illustrated ed.). Rowman & Littlefield Publishers, Inc. pp. 237–268. ISBN 0-8476-7932-2. Archived (PDF) from the original on 2016-03-05. Retrieved 2019-08-09.
[…] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the series sum) of the resistances a + b. If the resistances are placed in parallel, their compound resistance is the parallel sum of the resistances, which is denoted by the full colon […]
{{cite book}}:|work=ignored (help) [1] (271 pages) - ^ a b Ellerman, David Patterson (May 2004) [1995-03-21]. Introduction to Series-Parallel Duality (PDF). University of California at Riverside. CiteSeerX 10.1.1.90.3666. Archived from the original on 2019-08-10. Retrieved 2019-08-09.
The parallel sum of two positive real numbers x:y = [(1/x) + (1/y)]−1 arises in electrical circuit theory as the resistance resulting from hooking two resistances x and y in parallel. There is a duality between the usual (series) sum and the parallel sum. […]
[2] (24 pages)