A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly determined from the data itself. To our knowledge, in the most existing stability results, the boundary conditions are assumed to be close to a set of CGO sol...

This paper is devoted to the problem of recovering a potential q in a domain in R for d ≥ 3 from the Dirichlet to Neumann map. This problem is related to the inverse Calderón conductivity problem via the Liouville transformation. It is known from the work of Haberman and Tataru [11] and Nachman and Lavine [17] that uniqueness holds for the class of conductivities of one derivative and the class...

The pair (K, ρ) consisting of a knotK ⊂ S and a surjective map ρ from the knot group onto a dihedral group is said to be a p-colored knot. In [Mos], D. Moskovich conjectures that for any odd prime p there are exactly p equivalence classes of p-colored knots up to surgery along unknots in the kernel of the coloring. We show that there are at most 2p equivalence classes. This is an improvement up...

Due to high retention rates, small private online course (SPOC) has become increasingly popular among universities. However, existing analyses of learning behavioral patterns in SPOC remain extremely lacking. This present study conducts an empirical analysis on the behavioral patterns of 12,517 undergraduates engaging in a college’s SPOC platform, called StarC. In this study, the authors collec...

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photoacoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the lite...

The Universidad Carlos III de Madrid has been offering several face-to-face remedial courses for freshmen to review or learn concepts and practical skills that they should know before starting their degree program. During the last two years our University has adopted MOOC-like technologies to support some of these courses so that a “flipping the classroom” methodology can be applied in a partic...

I will present a uniqueness result for an inverse boundary value problem (IBVP) for time harmonic Maxwell’s equations. We assume that the unknown electromagnetic properties of the medium, namely the magnetic permeability, the electric permittivity and the conductivity, are described by continuously differentiable functions. The IBVP is a nonlinear problem to determine these parameters using the...