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...

A case study is presented to test the role several different sources may play in populating the exterior cusp with energetic (E> 40 keV) electrons. The properties of the electrons measured in the exterior cusp are compared with the expected signatures of three sources in order to weigh the role each source may contribute in populating this region. The potential sources probed are: (1) solar ene...

The cusp singularity—a point at which two curves of fold points meet—is a prototypical example in Takens’ classification of singularities in constrained equations, which also includes folds, folded saddles, folded nodes, among others. In this article, we study cusp singularities in singularly perturbed systems for sufficiently small values of the perturbation parameter, in the regime in which t...

A talon cusp is a rare form of developmental anomaly characterized by a well-delineated additional cusp like projection located on the surface of an anterior tooth and extends at least half the distance from the cementoenamel junction to the incisal edge. It usually occurs on palatal and lingual surface of the anterior teeth. On rare occasions the cusp may project from the facial surface or fro...

This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel manipulators was shown to be associated with the existence of cusp points. At each of th...

This paper investigates the cuspidal configurations of 3-RPR parallel manipulators that may appear on their singular surfaces in the joint space. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a non-singular change of assembly mode. In previous works, the cusp points were calculated in sections of the joint space by solving a 24th-...

The e ect of arti cial di usion on discrete shock structures is examined for a family of schemes which includes scalar di usion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the di usive ux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets th...

Two-point observations by the INTERBALL satellite pair unveiled a presence of a large vortex-like structure filled by slow and heated plasma in the outer cusp during periods of the positive BZ interplanetary magnetic field (IMF) component. We have found the rotation of the magnetic field and the decrease of its magnitude connected with the presence of a hot plasma population inside the vortex. ...

It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere, the logarithmic cusp slope γ of the tracers must be given exactly by γ = 2β where β is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster...