A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are formulated over these structures. Quantum equivalence is shown between dual theories. A global constraint is proven to be needed to achieve well defined bundles. T...

A contact representation by triangles of a graph is a set of triangles in the plane such that two triangles intersect on at most one point, each triangle represents a vertex of the graph and two triangles intersects if and only if their corresponding vertices are adjacent. De Fraysseix, Ossona de Mendez and Rosenstiehl proved that every planar graph admits a contact representation by triangles....

Christian Weiß and Jens Berkmann Institute for Communications Engineering (LNT) Munich University of Technology (TUM) e-mail: Christian.Weiss,Jens.Berkmann @ei.tum.de The trellis of a finite abelian group code is locally (i.e., trellis section by trellis section) related to the trellis of the corresponding dual group code. This allows to express the update rules of the BCJR algorithm operating ...

This paper presents a tree-based framework for producing self-dual morphological operators, based on a tree-representation complete inf-semilattice (CISL). The idea is to use a self-dual tree transform to map a given image into the above CISL, perform one or more morphological operations there, and map the result back to the image domain using the inverse tree transform. We also present a parti...

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...

We consider the three forms of self-duality that can be exhibited by a planar graph G, map self-duality, graph self-duality and matroid self-duality. We show how these concepts are related with each other and with the connectivity of G. We use the geometry of self-dual polyhedra together with the structure of the cycle matroid to construct all self-dual graphs. 1.1. Forms of Self-duality. Given...

MAP kinases are a family of enzymes that coordinate diverse cellular programs in response to signals relayed from the extracellular milieu. They are components of signalling pathways that have a common architecture, in which the MAP kinases themselves are the terminal members of a three-component linear kinase cascade. The MAP kinases are activated by dual phosphorylation on a conserved Thr-Xxx...