We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper ...
The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
We present an automated approach to verify the correctness of programming assignments, such as the ones that arise in a functional programming course. Our approach takes as input student submissions and reference solutions, and uses equivalence checking to ...
The adsorption of molecules on surfaces affects the surface dipole and thus changes in the work function may be expected. The effect in change of work function is particularly strong if charge between substrate and adsorbate is involved. Here we report the ...
We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...
A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...
The Weil-Barner explicit formula is applied to the prime counting function and to the problem of numerical partial verification of the Riemann hypothesis. ...
This thesis study investigates the architectural potential of digital information, using case studies and prototypes to explore the integration of dynamic information in the architectural environment. Responsive architecture, a design field that has arisen ...
We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...
