Stable Determination of the Electromagnetic Coefficients by Boundary Measurements

The goal of this paper is to prove a stable determination of the coefficients for the time-harmonic Maxwell equations, in a Lipschitz domain, by boundary measurements

Linear instability criteria for ideal fluid flows subject to two subclasses of perturbations

In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and those in the corresponding factor space. This classification of perturbations arises naturally from the geometric structure of hydrodynamics; our first class of perturbations is the tangent space to the co-adjoint orbit. Instability criteria for equilibrium solutions are established in the form of lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbation.Comment: 29 page

Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam

The velocity of a ~3 GeV neutrino beam is measured by comparing detection times at the near and far detectors of the MINOS experiment, separated by 734 km. A total of 473 far detector neutrino events was used to measure (v-c)/c=5.12.910-5 (at 68% C.L.). By correlating the measured energies of 258 charged-current neutrino events to their arrival times at the far detector, a limit is imposed on the neutrino mass of mnu<50 MeV/c2 (99% C.L.)

Spline Collocation For Convolutional Parabolic Boundary Integral Equations

. We consider spline collocation methods for a class of parabolic pseudodifferential operators. We show optimal order convergence results in a large scale of anisotropic Sobolev spaces. The results cover for example the case of the single layer heat operator equation when the spatial domain is a disc. 1. Introduction. The integral equation method for the solution of parabolic problems is known already for a long time, for the early literature see [23],[21],[28,29,30]. The reasons which recommend this method instead of the domain methods are similar as in the elliptic case. The main arguments are: In the level of the numerical implementation there is a reduction in the dimension of the matrix equation to be solved. The method is very suitable for exterior problems. Moreover, by using the direct method the unknown function is a quantity of physical interest. In contrast to the elliptic case, there does not exist any general theory for the numerical solution of the parabolic boundary int..