The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.

In 1940 Naimark showed that if a set of quantum observables are positive semi-definite and sum to the identity then, on a larger space, they have a joint resolution as commuting projectors. In 1955 Sz.-Nagy showed that any set of observables could be so resolved, with the resolution respecting all linear sums. Crucially, both resolutions return the correct Born probabilities for the original ob...

Assume that, in the near future, someone can prove resolution of singularities in arbitrary characteristic and dimension. Then one may want to know why the case of positive characteristic is so much harder than the classical characteristic zero case. Our intention here is to provide this piece of information for people who are not necessarily working in the field. A singularity of an algebraic ...

An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like algebra. It makes possible to define a coherent state associated with the shape-invariant potentials. For a large class of such potentials, it is shown that the in...

Abstract. We verify a recent conjecture of Kenyon/Szendrői by computing the generating function for pyramid partitions. Pyramid partitions are closely related to Aztec Diamonds; their generating function turns out to be the partition function for the Donaldson–Thomas theory of a non-commutative resolution of the conifold singularity {x1x2 −x3x4 = 0} ⊂ C. The proof does not require algebraic geo...