Normal vectors are of primary importance in reconstructing the surface of the left ventricle from MR images of the heart. They are fundamental for accurate measurement of wall thickness, which is a very important parameter in assessing ventricular function. In this work, we present a novel technique for computing accurate normal vectors. This technique is based on variational calculus. It expli...

The paper deals with the ground and the first excited state of the polaron in the one dimensional Holstein model. Various variational methods are used to investigate both the weak coupling and strong coupling cases, as well as the crossover regime between them. Two of the methods, which are presented here for the first time, introduce new elements to the understanding of the nature of the polar...

The proof is exceedingly innovative and relies upon a closure theorem for Dirichlet series. Lecture 2 deals with a variational problem for product measures which is used to solve a non-linear Cauchy problem introduced by Schrödinger to describe phenomena in quantum physics. Lecture 3 gives an exposition about Beurling’s studies of free boundary problems for the Laplace operator related to Helmh...

For homogeneous lossless 3D periodic slabs of fixed arbitrary geometry, we characterize guided modes by means of the eigenvalues associated to a variational formulation. We treat robust modes, which exist for frequencies and wavevectors that admit no propagating Bragg harmonics and therefore persist under perturbations, as well as nonrobust modes, which can disappear under perturbations due to ...