2,807 research outputs found
Dynamical systems of type (m,n) and their C*-algebras
Given positive integers n and m, we consider dynamical systems in which n
copies of a topological space is homeomorphic to m copies of that same space.
The universal such system is shown to arise naturally from the study of a
C*-algebra we denote by O_{mn}, which in turn is obtained as a quotient of the
well known Leavitt C*-algebra L_{mn}, a process meant to transform the
generating set of partial isometries of L{mn} into a tame set. Describing
O_{mn} as the crossed-product of the universal (m,n)-dynamical system by a
partial action of the free group F_{m+n}, we show that O_{mn} is not exact when
n and m are both greater than or equal to 2, but the corresponding reduced
crossed-product, denoted O_{mn}^r, is shown to be exact and non-nuclear. Still
under the assumption that m,n>=2, we prove that the partial action of F_{m+n}
is topologically free and that O_{mn}^r satisfies property (SP) (small
projections). We also show that O_{mn}^r admits no finite dimensional
representations. The techniques developed to treat this system include several
new results pertaining to the theory of Fell bundles over discrete groups.Comment: 38 page
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains
We continue our systematic construction of Baxter Q-operators for spin
chains, which is based on certain degenerate solutions of the Yang-Baxter
equation. Here we generalize our approach from the fundamental representation
of gl(n) to generic finite-dimensional representations in quantum space. The
results equally apply to non-compact representations of highest or lowest
weight type. We furthermore fill an apparent gap in the literature, and provide
the nearest-neighbor Hamiltonians of the spin chains in question for all cases
where the gl(n) representations are described by rectangular Young diagrams, as
well as for their infinite-dimensional generalizations. They take the form of
digamma functions depending on operator-valued shifted weights.Comment: 26 pages, 1 figur
An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories
We provide a simple non-perturbative formulation for non-commutative
four-dimensional N = 2 supersymmetric Yang-Mills theories. The formulation is
constructed by a combination of deconstruction (orbifold projection), momentum
cut-off and matrix model techniques. We also propose a moduli fixing term that
preserves lattice supersymmetry on the deconstruction formulation. Although the
analogous formulation for four-dimensional N = 2 supersymmetric Yang-Mills
theories is proposed also in Nucl.Phys.B857(2012), our action is simpler and
better suited for computer simulations. Moreover, not only for the
non-commutative theories, our formulation has a potential to be a
non-perturbative tool also for the commutative four-dimensional N = 2
supersymmetric Yang-Mills theories.Comment: 32 pages, final version accepted in JHE
A Semantic Similarity Measure for Expressive Description Logics
A totally semantic measure is presented which is able to calculate a
similarity value between concept descriptions and also between concept
description and individual or between individuals expressed in an expressive
description logic. It is applicable on symbolic descriptions although it uses a
numeric approach for the calculus. Considering that Description Logics stand as
the theoretic framework for the ontological knowledge representation and
reasoning, the proposed measure can be effectively used for agglomerative and
divisional clustering task applied to the semantic web domain.Comment: 13 pages, Appeared at CILC 2005, Convegno Italiano di Logica
Computazionale also available at
http://www.disp.uniroma2.it/CILC2005/downloads/papers/15.dAmato_CILC05.pd
Logical operators for ontological modeling
We show that logic has more to offer to ontologists than standard first order
and modal operators. We first describe some operators of linear logic which we
believe are particularly suitable for ontological modeling, and suggest how to interpret
them within an ontological framework. After showing how they can coexist
with those of classical logic, we analyze three notions of artifact from the literature
to conclude that these linear operators allow for reducing the ontological commitment
needed for their formalization, and even simplify their logical formulation
Geometric Reasoning with polymake
The mathematical software system polymake provides a wide range of functions
for convex polytopes, simplicial complexes, and other objects. A large part of
this paper is dedicated to a tutorial which exemplifies the usage. Later
sections include a survey of research results obtained with the help of
polymake so far and a short description of the technical background
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