We present a rigorous, detailed study of the generic, quantitative properties of gravitational lensing near cusp catastrophes. Concentrating on the case when the individual images are unresolved, we derive explicit formulas for the total magnification and centroid of the images created for sources outside, on, and inside the cusped caustic. We obtain new results on how the image magnifications ...

The phase diagrams of some cholesterol-lipid mixtures exhibit two immiscibility regions along with a sharp cusp, pointing to a particular stoichiometry for possible lipid/cholesterol complex formation. It has been hypothesized that reactive cholesterol monomers are present in mixtures with cholesterol content greater than that at the cusp. To test this hypothesis, we have examined how the prese...

Let k be a global function field with field of constants Fr, r = p m, and let ∞ be a fixed place of k. In his habilitation thesis [Boc2], Gebhard Böckle attaches abelian Galois representations to characteristic p valued cusp eigenforms and double cusp eigenforms [Go1] such that Hecke eigenvalues correspond to the image of Frobenius elements. In the case where k = Fr(T ) and ∞ corresponds to the...

The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which m...

The term talon cusp refers to a relatively rare dental anomaly in which an accessory cusplike structure projects from the cingulum area or cement-enamel junction. The condition can occur in either maxillary or mandibular anterior teeth in both the primary and permanent dentitions. This article reports 2 cases of talon cusp affecting consanguineous first cousins: a case of bilateral talon cusps ...

We study the distribution of zeros of holomorphic Hecke cusp forms in several “thin” sets as the weight, k, tends to infinity. We obtain unconditional results for slowly shrinking (with k) hyperbolic balls. This relies on a new, effective, proof of Rudnick’s theorem and on an effective version of Quantum Unique Ergodicity for holomorphic forms, which we obtain in this paper. In addition, assumi...

OBJECTIVE The underlying neurophysiologic mechanism responsible for secondary paroxysmal kinesigenic dyskinesia (PKD) is still unclear. Here, we study the pathogenesis of PKD in two patients with a demyelinating lesion in the spinal cord. METHODS Electromyogram recordings from affected arms of two patients with spinal cord lesions presenting PKD were compared with our laboratory standards. Th...

The aortic root of a 30-year-old man was replaced with a Freestyle stentless aortic bioprosthesis for aortic regurgitation associated with annuloaortic ectasia. His clinical course was uneventful, and he was discharged without complications. Three years and six months after surgery, he presented with a high fever. Four years after surgery, transthoracic echocardiography revealed severe aortic r...

This paper studies the Fourier expansion of Hecke-Maass eigenforms for GL(2,Q) of arbitrary weight, level, and character at various cusps. It is shown that the Fourier coefficients at a cusp satisfy certain very explicit multiplicativity relations. As an application, it is proved that a local representation of GL(2,Qp) which is isomorphic to a local factor of a global cuspidal automorphic repre...

In this paper we study the fluxes of energetic protons (30–4000 keV) and electrons (20–400 keV) in the exterior cusp and in the adjacent high-latitude dayside plasma sheet (HLPS) with the Cluster/RAPID instrument. Using two sample orbits we demonstrate that the Cluster observations at high latitudes can be dramatically different because the satellite orbit traverses different plasma regions for...