5 resultados para Convex Duality

em Aston University Research Archive


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The title of Juana Castro’s poetry book publshed in 1978, Cóncava mujer — Concave woman — expresses the hollow nature of the social female subject. From Juana Castro’s point of view, this female social concavity is only allowed to transformed itself into its opposite, the convex women which clearly represents the reproductive role of the female body. These two extreme roles assigned to women, hollowness or maternity, are the poetic paradigms for Juana Castro’s two poetry books analised in this article. As if we were presented with the two sides of a coin, Cóncava mujer and Del dolor y las alas – On anguish and wings--(1982) reflect the author´s concious realisation of the above-mentioned female duality as a defined and percieved subject by male society. Each poetry book, however, respond to two different personal moments, and each result in two different ways of conceiving poetic language. On one hand, the poetic subject of Cóncava mujer emerges with all its force as a feminist voice whose goal is the attack of all aspects of the patriarchal society as the cause of the female concavity. On the other hand, in Del dolor y las alas the poetic voice unfolds her motherhood as both loss and creation: the death of Juana Castro’s son makes the poetic subject incomplete, and therefore a concave one; whereas the poetic discourse appears as the perfect way to occupy the empty space left by the son’s death.

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This paper draws attention for the fact that traditional Data Envelopment Analysis (DEA) models do not provide the closest possible targets (or peers) to inefficient units, and presents a procedure to obtain such targets. It focuses on non-oriented efficiency measures (which assume that production units are able to control, and thus change, inputs and outputs simultaneously) both measured in relation to a Free Disposal Hull (FDH) technology and in relation to a convex technology. The approaches developed for finding close targets are applied to a sample of Portuguese bank branches.

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We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ?WS?WL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.

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We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

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We have devised a general scheme that reveals multiple duality relations valid for all multi-channel Luttinger Liquids. The relations are universal and should be used for establishing phase diagrams and searching for new non-trivial phases in low-dimensional strongly correlated systems. The technique developed provides universal correspondence between scaling dimensions of local perturbations in different phases. These multiple relations between scaling dimensions lead to a connection between different inter-phase boundaries on the phase diagram. The dualities, in particular, constrain phase diagram and allow predictions of emergence and observation of new phases without explicit model-dependent calculations. As an example, we demonstrate the impossibility of non-trivial phase existence for fermions coupled to phonons in one dimension. © 2013 EPLA.