A note on closed ideals in rings of smooth functions

We prove that if finitely many smooth functions on a manifoldM generate a closed ideal inC (M), then they generate a closed ideal inC (M×N).     

Multiple periodic solutions for a nonlinear suspension bridge equation

We investigate nonlinear oscillations in a fourth-order partialdifferential equation which models a suspension bridge. Previouswork establishes multiple periodic solutions when a parameterexceeds a certain eigenvalue. In this paper, we use Leray-Schauderdegree theory to prove that if the parameter is increased further,beyond a second eigenvalue, then additional solutions are created.     

Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees

We prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.     

Edgeworth versus Gram-Charlier series: x-Cumulant and probability density tests

Edgeworth series are often considered the same as Gram-Charlier series in systematic expansions of nongaussian probability distributions. Testing direct approximations of the probability itself as well as of cumulants in coordinate space as functions of measured cumulants in momentum space, we show how the former far outperforms the latter.