List of dualities
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{{About|a listing of dualities in mathematics, philosophy and science|other uses|Duality (disambiguation)}}
{{Use dmy dates|date=January 2020|cs1-dates=y}}
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Mathematics
{{main|Duality (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
- Twisted Poincaré duality
- Poitou–Tate duality
- Pontryagin duality
- S-duality (homotopy theory)
- Schur–Weyl duality
- Series-parallel duality
- Serre duality
- Spanier–Whitehead duality
- Stone's duality
- Tannaka–Krein duality
- Verdier duality
- Grothendieck local duality
Philosophy and religion
{{See also|Dualism (disambiguation)}}
Engineering
Physics
- Complementarity (physics)
- Dual resonance model
- Duality (electricity and magnetism)
- Babinet's principle (electromagnetism)
- Englert–Greenberger duality relation
- Holographic duality
- AdS/CFT correspondence
- Kramers–Wannier duality
- Mirror symmetry
- 3D mirror symmetry
- Montonen–Olive duality
- Mysterious duality (M-theory)
- Seiberg duality
- String duality
- S-duality
- T-duality
- U-duality
- Wave–particle duality
Economics and finance
See also
References
{{Reflist|refs=
{{cite book |title=Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics |chapter=Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics |series=G - Reference, Information and Interdisciplinary Subjects Series |work=The worldly philosophy: studies in intersection of philosophy and economics |author-first=David Patterson |author-last=Ellerman |author-link=David Patterson Ellerman |edition=illustrated |publisher=Rowman & Littlefield Publishers, Inc. |date=1995-03-21 |isbn=0-8476-7932-2 |pages=237–268 |url=http://www.ellerman.org/wp-content/uploads/2012/12/IntellectualTrespassingBook.pdf |chapter-url=https://books.google.com/books?id=NgJqXXk7zAAC&pg=PA237 |access-date=2019-08-09 |url-status=live |archive-url=https://web.archive.org/web/20160305012729/http://www.ellerman.org/wp-content/uploads/2012/12/IntellectualTrespassingBook.pdf |archive-date=2016-03-05 |quote=[…] 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 […]}} [https://web.archive.org/web/20150917191423/http://www.ellerman.org/Davids-Stuff/Maths/sp_math.doc] (271 pages)
{{cite book |title=Introduction to Series-Parallel Duality |author-first=David Patterson |author-last=Ellerman |author-link=David Patterson Ellerman |publisher=University of California at Riverside |date=May 2004 |orig-year=1995-03-21 |citeseerx=10.1.1.90.3666 |url=http://www.ellerman.org/wp-content/uploads/2012/12/Series-Parallel-Duality.CV_.pdf |access-date=2019-08-09 |url-status=live |archive-url=https://web.archive.org/web/20190810011716/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf |archive-date=2019-08-10 |quote=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. […]}} [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf] (24 pages)
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