For n<105 all coefficients of Fn(x) are ±1 or 0. For n = 10S, the coefficient 2 occurs for the first time. Denote by A w the greatest coefficient of Fn(x) (in absolute value). Schur proved that lim sup -4n= °°. Emma Lehmer proved that An>cn l,z for infinitely many n. In fact she proved that infinitely many such w's are of the form pqr with p, q, and r prime. In the present note we are going to ...

In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter l. This nonlinear dependence on l is allowed both in the leading coefficient and in the potential. We extend the traditional notions of eigenvalues and eigenfunctions to this more general setting. Our main result generalizes the re...

We propose a generalisation of the Pomeranchuk theorem which argues that elastic cross-sections should show universal energy dependence: difference integrated any pair initial channels has to disappear at high enough energy.

Erratum to " The Clark-Ocone formula for vector valued random variables in abstract Wiener space " , Jour. In this paper we considered the extension of the Clark-Ocone formula for a random variable defined on an abstract Wiener space (W, H, µ) and taking values in a Banach space (denoted there either B or Y). The main result appears in Theorem 3.4. Unfortunately, as first pointed out to us by J...

This paper presents a useful theorem for non-linear transformations of the sum of independent, zeromean, Gaussian random variables. It is proved that the linear regression coefficient of the non-linear transformation output with respect to the overall input is identical to the linear regression coefficient with respect to any Gaussian random variable that is part of the input. As a side-result,...