Penrose presents a version of the theorem in which the true but unprovable sentence is an assertion that a certain computer program runs on forever.Expand

Studies a nonlinear heat equation in a finite interval of space subject to a white noise forcing term. The equation without the forcing term exhibits several equilibrium configurations, two of which… Expand

This example indicates that there is more than one way to look at the role of pictures in proof. The weakest claim is that a picture can serve as an aid to inspire a proof. The mathematician… Expand

A time dependent approach to self-adjointness is presented and it is applied to quantum mechanical Hamiltonians which are not semi-bounded. Sufficient conditions are given for self-adjointness of… Expand

Sobolev inequalities give lower bounds for quantum mechanical Hamiltonians. These inequalities are derived from commutator inequalities related to the Heisenberg uncertainty principle.

A perturbation theory is developed for self‐adjoint operators whose resolvents leave a cone invariant. The Perron‐Frobenius theory may be applied to the perturbed operator to conclude that its lowest… Expand

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also… Expand