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Theorems showing that certain objects of interest are the dual spaces (in the sense of linear algebra) of other objects of interest are often called dualities. Many of these dualities are given by a bilinear pairing of two K-vector spaces A ⊗ B → K. For perfect pairings, there is, therefore, an isomorphism of A to the dual of B.
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.
The designed–emergent duality focuses on time and captures the tension between pre-planned and emergent activities. Designers can plan an activity that is designed to achieve a particular purpose however, some activities emerge through interaction and participation of the community; these are unplanned and may be contrary to what the designers intended.
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.
Here is a partial list of electrical dualities: voltage – current; parallel – series (circuits) resistance – conductance; voltage division – current division; impedance – admittance; capacitance – inductance; reactance – susceptance; short circuit – open circuit; Kirchhoff's current law – Kirchhoff's voltage law. KVL and KCL
Seiberg duality is an equivalence of the IR fixed points in an N=1 theory with SU(N c) as the gauge group and N f flavors of fundamental chiral multiplets and N f flavors of antifundamental chiral multiplets in the chiral limit (no bare masses) and an N=1 chiral QCD with N f-N c colors and N f flavors, where N c and N f are positive integers satisfying
John Frank Adams (1981), Spin(8), Triality, F 4 and all that, in "Superspace and supergravity", edited by Stephen Hawking and Martin Roček, Cambridge University Press, pages 435–445. John Frank Adams (1996), Lectures on Exceptional Lie Groups (Chicago Lectures in Mathematics), edited by Zafer Mahmud and Mamora Mimura, University of Chicago ...
Dualism most commonly refers to: . Mind–body dualism, a philosophical view which holds that mental phenomena are, at least in certain respects, not physical phenomena, or that the mind and the body are distinct and separable from one another