In this work we study the Capacitated p-Center Problem (CpCP ) and we propose an exact algorithm to solve it. We study two auxiliary problems and their relation to CpCP , and we propose two different Lagrangean duals based on each of the auxiliary problems. The lower and upper bounds provided by each of the Lagrangean duals reduce notably the set of candidate radii and allow to solve the proble...

We derive the gravity duals of noncommutative gauge theories from the YangBaxter sigma model description of the AdS5×S superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4) abelian. Hence these should be called abelian Jordanian deformations. As a result, the gravity dua...

In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...

In the first part of this study we have introduced six different multiobjective dual problems to a general multiobjective optimization problem, for which we presented weak as well as strong duality assertions. Afterwards, we derived some inclusion results for the image sets of three of these problems. The aim of this second part is to complete our investigations by studying the relations betwee...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

A class of non-canonical duals for the multiwindow Gabor scheme, incorporating both rational and integer oversampling of the Gaborian combined time-frequency space, is considered. Using properties of Gabor frame matrices, block Discrete Fourier transforms, and results from number theory, we establish existence conditions for the noncanonical duals for both integer and rational oversampling rate...

Coupling constant renormalization is investigated in 2 dimensional σ models related by non Abelian duality transformations. In this respect it is shown that already in the one loop order of perturbation theory the duals of a one parameter family of models, interpolating between the SU (2) principal model and the O(3) sigma model, behave differently from the original models. In particular we fin...

We investigate a number of Presburger liveness problems for nondeterministic reversal-bounded multicounter machines with a free counter (NCMFs). We show the following: – The -Presburger-i.o. problem and the -Presburger-eventual problem are both decidable. So are their duals, the -Presburger-almost-always problem and the -Presburger-always problem. – The -Presburger-i.o. problem and the -Presbur...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

ABSTRAC"T A construction method for semiregular group divisible designs is given. This method can be applied to yield many classes of (in general, non-symmetric) semiregular group divisible designs whose duals are semiregular group divisible. In particular, the method can be used to construct many classes of transversal designs whose duals are serniregular group divisible designs, but not trans...