Search results for " DOM"

Varieties of Codes and Kraft Inequality

2005

Decipherability conditions for codes are investigated by using the approach of Guzman, who introduced in [7] the notion of variety of codes and established a connection between classes of codes and varieties of monoids. The class of Uniquely Decipherable (UD) codes is a special case of variety of codes, corresponding to the variety of all monoids. It is well known that the Kraft inequality is a necessary condition for UD codes, but it is not sufficient, in the sense that there exist codes that are not UD and that satisfy the Kraft inequality. The main result of the present paper states that, given a variety $\mathcal{V}$ of codes, if all the elements of $\mathcal{V}$ satisfy the Kraft inequ…

Decidability of bisimulation equivalences for parallel timer processes

1993

In this paper an abstract model of parallel timer processes (PTPs), allowing specification of temporal quantitative constraints on the behaviour of real time systems, is introduced. The parallel timer processes are defined in a dense time domain and are able to model both concurrent (with delay intervals overlapping on the time axis) and infinite behaviour. Both the strong and weak (abstracted from internal actions) bisimulation equivalence problems for PTPs are proved decidable. It is proved also that, if one provides the PTP model additionally with memory cells for moving timer value information along the time axis, the bisimulation equivalence (and even the vertex reachability) problems …

Dirichlet Forms, Poincaré Inequalities, and the Sobolev Spaces of Korevaar and Schoen

2004

We answer a question of Jost on the validity of Poincare inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen.

A Pedagogical Proof of Arrow's Impossibility Theorem

1999

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students. This special case conveys the nature of Arrow's result. It is well known that the restriction to three options is not really limiting (any larger se…

Sobolev embeddings, extensions and measure density condition

2008

AbstractThere are two main results in the paper. In the first one, Theorem 1, we prove that if the Sobolev embedding theorem holds in Ω, in any of all the possible cases, then Ω satisfies the measure density condition. The second main result, Theorem 5, provides several characterizations of the Wm,p-extension domains for 1<p<∞. As a corollary we prove that the property of being a W1,p-extension domain, 1<p⩽∞, is invariant under bi-Lipschitz mappings, Theorem 8.

Lipschitz conditions,b-arcwise connectedness and conformal mappings

1982

Generalized quasidisks and conformality II

2015

We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced in [12], sufficient to guarantee the extendability of a conformal map f from the unit disk onto a domain to the entire plane as a homeomorphism of locally exponentially integrable distortion. Sufficient conditions for extendability to a homeomorphism of locally p-integrable distortion are also given.

On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian

2012

Abstract This paper concerns the best Lipschitz extension problem for a discrete distance that counts the number of steps. We relate this absolutely minimizing Lipschitz extension with a discrete ∞-Laplacian problem, which arises as the dynamic programming formula for the value function of some e -tug-of-war games. As in the classical case, we obtain the absolutely minimizing Lipschitz extension of a datum f by taking the limit as p → ∞ in a nonlocal p -Laplacian problem.

Factorization of absolutely continuous polynomials

2013

In this paper we study the ideal of dominated (p,s)-continuous polynomials, that extend the nowadays well known ideal of p-dominated polynomials to the more general setting of the interpolated ideals of polynomials. We give the polynomial version of Pietsch s factorization Theorem for this new ideal. Our factorization theorem requires new techniques inspired in the theory of Banach lattices.

A unified Pietsch domination theorem

2008

In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.