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On “contour apparent”, “courbe de contact” and ramification curves: Duality between a principle and a tool
As has already been described in the literature, it was Julius Plucker who solved the “paradox” of the duality principle in the 1830s – that is, the...
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From duality in mathematical programming to Fenchel duality and convex analysis: Duality as a force of inspiration in the creation of new mathematics
“Duality” is an intriguing notion in the history of mathematics that refers to a variety of phenomena in many different areas and sub-disciplines of...
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Duality à la Bourbaki
In this chapter, we will investigate an aspect in the post-1930 history of duality which deserves special attention, namely the influence of...
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Legendre duality: from thermodynamics to information geometry
This paper reviews the role of convex duality in Information Geometry. It clarifies the notion of bi-orthogonal coordinates associated with Legendre...
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Philosophical and mathematical duality in Albert Lautman’s work
The terms “duality” and “dual” appear repeatedly in the writings of the mathematical philosopher and World War II French Resistance fighter Albert...
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The historical development of Pontrjagin duality
This chapter has several aims. The first aim is a historical description of two parts of Lev Pontrjagin’s scientific work, namely his work on...
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Duality in optimal consumption–investment problems with alternative data
This study investigates an optimal consumption–investment problem in which the unobserved stock trend is modulated by a hidden Markov chain that...
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The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only
Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing...
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From Grassmann complements to Hodge-duality
Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical...
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Duality in the problems of optimal control described by Darboux-type differential inclusions
This paper is devoted to the optimization of the Mayer problem with hyperbolic differential inclusions of the Darboux type and duality. We use the...
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Interpreting systems of continuity equations in spaces of probability measures through PDE duality
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the...
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Duality for Poincaré series of surfaces and delta invariant of curves
In this article we study the delta invariant of reduced curve germs via topological techniques. We describe an explicit connection between the delta...
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On the Lagrange Duality of Stochastic and Deterministic Minimax Control and Filtering Problems
AbstractAs shown below, the linear operator norms in the deterministic and stochastic cases are optimal values of the Lagrange-dual problems. For...
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De Morgan’s De Morgan’s Laws Duality in the Emergence of Formal Logic
The first idea that comes to our minds when we think about duality in logic is, without any doubt, the duality expressed by the so-called De Morgan’s...
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De Groot Duality for Represented Spaces
We explore de Groot duality in the setting of represented spaces. The de Groot dual of a space is the space of closures of its singletons, with the...
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The emergence of duality in 19th-century algebra of logic
A Boolean algebra is a paradigmatic example of a structure that exhibits a particular kind of duality. Such an algebra can be defined as a set of...
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Discrete duality finite volume scheme for a generalized Joule heating problem
In this paper we conceive and analyze a discrete duality finite volume (DDFV) scheme for the unsteady generalized thermistor problem, including a p -La...
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Tannakian Duality
In order to gain more insight into the structure of the compact quantum groups, in general and for the concrete examples too, and to effectively...
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Classes of meromorphic harmonic functions and duality principle
We introduce new classes of meromorphic harmonic univalent functions. Using the duality principle, we obtain the duals of such classes of functions...
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A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent
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