Related papers: Synopsis of Duality
We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify…
Dualities and duality transformations form a well established methodology in various aspects of quantum many body physics and quantum field theories, allowing one to exploit equivalence between models which may naively seem completely…
This paper is the second part of a two-part paper investigating the structure and properties of dyadic polygons. A dyadic polygon is the intersection of the dyadic subplane $D^2$ of the real plane $R^2$ and a real convex polygon with…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
We give new examples of plane curves with two or more Galois points as a family, and describe the number of Galois points for these curves, by using finite fields.
It is well known that in a two-slit interference experiment, acquiring which-path information about the particle, leads to a degrading of the interference. It is argued that path-information has a meaning only when one can umabiguously tell…
The strong interaction between electrons reveals the duality of the itinerancy and the localization of quasiparticles. The physical phenomena corresponding to each component of the duality could be realized and coexist within the category…
We study the generalization of $R\to 1/R$ duality to arbitrary conformally invariant sigma models with an isometry. We show that any pair of dual sigma models can be represented as quotients of a self-dual sigma model obtained by gauging…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its…
We define a class of maps between holomorphically embedded null curves which generalize conformal transformations, and can be defined in any complex dimension. In four dimensions, we can also define a similar map between self-dual surfaces,…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
This paper studies convex sets categorically, namely as algebras of a distribution monad. It is shown that convex sets occur in two dual adjunctions, namely one with preframes via the Boolean truth values {0,1} as dualising object, and one…
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…
We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold's problems.
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding…
This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical…