The weak energy condition and the expansion history of the Universe

We examine flat models containing a dark matter component and an arbitrary dark energy component, subject only to the constraint that the dark energy satisfies the weak energy condition. We determine the constraints that these conditions place on the evolution of the Hubble parameter with redshift, H(z)$H(z)$, and on the scaling of the coordinate distance with redshift, r(z)$r(z)$. Observational constraints on H(z)$H(z)$ are used to derive an upper bound on the current matter density. We demonstrate how the weak energy condition constrains fitting functions for r(z)$r(z)$.     

Asymptotic form of the high energy photoionization cross section of fullerenes

We show that the theoretical predictions on high energy behavior of the photoionization cross section of fullerenes depend crucially on the form of the function $V(r)$ which approximates the fullerene field. The shape of the high energy cross section is obtained without solving the wave equation. The cross section energy dependence is determined by the analytical properties of the function $V(r)$.