We investigate 3-adic valuations of generalized harmonic numbers H n . These valuations are completely determined by the 3-adic expansion of n. Moreover, we also give 3-adic valuations of generalized alternating harmonic numbers.

Valuations were introduced in De Bruyn andVandecasteele (Valuations of near polygons, preprint, 2004) as a very important tool for classifying near polygons. In the present paperwe study valuations of dual polar spaces.Wewill introduce the class of theSDPS-valuations and characterize these valuations. We will show that a valuation of a finite thick dual polar space is the extension of an SDPS-v...

The graceful exit transition from a dilaton-driven inflationary phase to a decelerated Friedmann−Robertson−Walker era requires certain classical and quantum corrections to the string effective action. Classical corrections can stabilize a high curvature string phase while the evolution is still in the weakly coupled regime, and quantum corrections can induce violation of the null energy conditi...

We discuss the possibility of a smooth transition from the pre-to the post-big bang regime, in the context of the lowest-order string eeective action (without higher-derivative corrections), taking into account with a phenomenological model of source the repulsive gravitational eeects due to the back-reaction of the quantum uctuations outside the horizon. We determine a set of necessary conditi...

We propose the model of Chain Inflation, in which a sequential chain of coupled scalar fields drives inflation. Motivated by the stringy landscape, we allow the number of fields to be very large, ranging from hundreds to many more; we note that the model is quite general and applies to any multidimensional potential, in string theory or otherwise. Each stage of inflation (which can be thought o...