This paper is a continuation of the paper [4]. In [4] it was shown that there exists a duality Ψa between the category DSkeLC (introduced there) and the category SkeLC of locally compact Hausdorff spaces and continuous skeletal maps. We describe here the subcategories of the category DSkeLC which are dually equivalent to the following eight categories: all of them have as objects the locally co...

Let R be a commutative ring. For two (left) R-modules M and N , the set HomR(M,N) of allR-linear maps fromM toN is anR-module under natural addition and scaling operations on linear maps. (If R were non-commutative then the definition (r · f)(m) = r · (f(m)) would yield a function r · f from M to N which is usually not R-linear. Try it!) In the special case where N = R we get the R-module M∨ = ...

[email protected] We show that tree level superstring theories on certain supersymmetric backgrounds admit a symmetry which we call “fermionic T-duality”. This is a nonlocal redefinition of the fermionic worldsheet fields similar to the redefinition we perform on bosonic variables when we do an ordinary T-duality. This duality maps a supersymmetric background to another supersymmetric background wi...

We give an elementary description of the maps in the linear strand of the minimal free resolution of a square-free monomial ideal, that is, the Stanley-Reisner ideal associated to a simplicial complex. The description is in terms of the homology of the canonical Alexander dual complex. As applications we are able to prove for monomial ideals and j = 1 a conjecture of J. Herzog giving lower boun...

The aim of this paper is to characterize in terms of classical (quasi)convexity of extended real-valued functions the set-valued maps which are K-(quasi)convex with respect to a convex cone K. In particular, we recover some known characterizations of K-(quasi)convex vector-valued functions, given by means of the polar cone of K.

We show that the duality between the self-dual and Maxwell-Chern-Simons theories in 2+1dimensions survives when the space-time becomes noncommutative. Existence of the SeibergWitten map is crucial in the present analysis. It should be noted that the above models, being manifestly gauge variant and invariant respectively, transform differently under the SeibergWitten map. We also discuss this du...

The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect product Diff sF , where F denotes the space of scalar functions. This paper generalizes the second construction to consider geodesic motion on Dif...

A polyhedral map is called {p, q}-equivelar if each face has p edges and each vertex belongs to q faces. In [12], it was shown that there exist infinitely many geometrically realizable {p, q}-equivelar polyhedral maps if q > p = 4, p > q = 4 or q − 3 > p = 3. It was shown in [6] that there exist infinitely many {4, 4}and {3, 6}-equivelar polyhedral maps. In [1], it was shown that {5, 5}and {6, ...

v Fq and their Gray images, where v 3 = v. We define the Lee weight of the elements of R, we give a Gray map from R to F 3n q and we give the relation between the dual and the Gray image of a code. This allows us to investigate the structure and properties of self-dual cyclic, formally self-dual and the Gray image of formally self-dual codes over R. Further, we give several constructions of for...

Abstract. This paper concerns the structure of the space C of real valued cocycles for a flow (X,Zm). We show that C is always larger than the set of cocycles cohomologous to the linear maps if the flow has a free dense orbit. By considering appropriate dual spaces for C, we obtain the concept of an invariant cocycle integral. The extreme points of the set of invariant cocycle integrals paralle...