Superresolution and number of degrees of freedom in inverse diffraction with subwavelength sources

info:eu-repo/semantics/published

Number of degrees of freedom in inverse diffraction

The problem of inverse diffraction from plane to plane is considered in the case where a finite aperture exists in the boundary plane. Singular values and singular functions for the problem are introduced, and the number of degrees of freedom is defined in terms of the distribution of the singular values. Numerical computations are presented for the one-dimensional problem, and it is shown that the effect of evanescent waves disappears at a distance of approximately one wavelength from the boundary plane, even when the dimension of the slit is comparable with the wavelength of the diffracted field. © 1983 Taylor & Francis Group, LLC.

Consistent couplings between fields with a gauge freedom and deformations of the master equation

The antibracket in the antifield-BRST formalism is known to define a map Hp × Hq → Hp + q + 1 associating with two equivalence classes of BRST invariant observables of respective ghost number p and q an equivalence class of BRST invariant observables of ghost number p + q + 1. It is shown that this map is trivial in the space of all functionals, i.e. that its image contains only the zeroth class. However, it is generically non-trivial in the space of local functionals. Implications of this result for the problem of consistent interactions among fields with a gauge freedom are then drawn. It is shown that the obstructions to constructing non-trivial such interactions lie precisely in the image of the antibracket map and are accordingly non-existent if one does not insist on locality. However consistent local interactions are severely constrained. The example of the Chern-Simons theory is considered. It is proved that the only consistent, local, Lorentz covariant interactions for the abelian models are exhausted by the non-abelian Chern-Simons extensions. © 1993.

Symmetrical freedom quilts: the ethnomathematics of ways of communication, liberation, and art

Symmetrical Freedom Quilts may be considered as links between mathematics, history, ethnomathematics, and the art of quilting. A quilt theme is a pedagogical way to integrate mathematics, art, and history in an interdisciplinary approach. This article combines an ethnomathematical-historical perspective by elaborating a history project related to the Underground Railroad. This work will allow teachers to develop classroom projects that help students to better understand geometry, especially concepts of symmetry and transformations. One of the objectives of this project is to stimulate student’s creativity and interest, because quilts may be considered as cultural and mathematical expressions of student’s daily life.

The Equalization of Effective Communicative Freedom: Democratic Justice in the Constitutional State and Beyond

Jurgen Habermas takes the realization of rights through the democratic self-organization of legal communities to be the normative core of emancipatory politics. In this article I explore the implications of this claim in relation to the requirements of justice. I argue that Habermas's discourse theory of democratic legitimacy presupposes a substantive principle of justice that demands the equalization of effective communicative freedom for all structurally constituted social groups in any constitutional state. This involves the elimination of a range of structural injustices rooted in the complex interrelationships between political, economic and cultural orders. In the final section I sketch briefly the implications of this analysis in the context of ongoing globalization processes. It is suggested that the most effective way to establish a just system of global governance is to equalize effective communicative freedom among nation-states.