The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.

For Markov processes and Hamiltonians given by energy forms, singular drift coefficients and potentials, more general than distributions, are allowed. We show that the forms can be regularized in… Expand

We prove that the solution of Nelson's stochastic mechanics equation associated with any stationary solution ψ of the Schrodinger equation is the homogeneous Markov process of the heat equation with… Expand

Using a computer, the Fermi surface for the one‐electron model of an infinite crystal in three dimensions with zero range interactions, i.e., with so‐called point interactions, is studied. A computer… Expand

We present a simple numerical analysis of the di$usion on a curved surface given by the equation � (r)=0 in a 4nite domain D ⊂ R 3 . The 4rst non-vanishing eigenvalue of the Beltrami– Laplace… Expand

We expand the scattering amplitude and the scattering matrix around the zero‐range limit, i.e., with point interactions, in the case when the potential has a finite number of wells. The lower‐order… Expand