Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

Which executive functioning deficits are associated with AD/HD, ODD/CD and comorbid AD/HD+ODD/CD?

Item does not contain fulltextThis study investigated (1) whether attention deficit/hyperactivity disorder (AD/HD) is associated with executive functioning (EF) deficits while controlling for oppositional defiant disorder/conduct disorder (ODD/CD), (2) whether ODD/CD is associated with EF deficits while controlling for AD/HD, and (3)~whether a combination of AD/HD and ODD/CD is associated with EF deficits (and the possibility that there is no association between EF deficits and AD/HD or ODD/CD in isolation). Subjects were 99~children ages 6–12 years. Three putative domains of EF were investigated using well-validated tests: verbal fluency, working memory, and planning. Independent of ODD/CD, AD/HD was associated with deficits in planning and working memory, but not in verbal fluency. Only teacher rated AD/HD, but not parent rated AD/HD, significantly contributed to the prediction of EF task performance. No EF deficits were associated with ODD/CD. The presence of comorbid AD/HD accounts for the EF deficits in children with comorbid AD/HD+ODD/CD. These results suggest that EF deficits are unique to AD/HD and support the model proposed by R. A. Barkley (1997).17 p

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea