Multiplicative relations among singular moduli

We consider some Diophantine problems of mixed modular-multiplicative type associated with the Zilber-Pink conjecture. In particular, we prove a finiteness statement for the number of multiplicative relations between singular moduli (j-invariants of elliptic curves with complex multiplication.)Comment: Comments Welcome

Water Quality Monitoring of the Indiana Dunes National Lakeshore Great Marsh Complex

The Great Marsh complex of the Indiana Dunes National Lakeshore was drained extensively by humans, beginning in the late 1800’s to provide land for farming and residences. Since 1998, 500 acres of the Great Marsh complex have been undergoing restoration in an attempt to return them to their pre-developed conditions. To assess the success of the ongoing restoration on water quality, 15 different parameters used to assess water quality are being measured. Data collected from June 2007 through July 2011 indicates that the water quality is typical of that for a wetlands in this region, and that the Great Marsh complex is functioning properly as a wetlands. For example, total phosphorous analyses indicate that the Great Marsh complex is consuming substantial amounts of phosphorus present in water entering the wetland, that the average conductivity in the Great Marsh complex is ≈270µS/cm, and that the amount of nitrogen in the water generall y decreases as the water passes through the marsh. The restored Great Marsh complex also experiences seasonal changes that are characteristic of a wetlands. This includes fluctuating water temperatures, water levels, pH levels, and dissolved oxygen levels

Weighted multiple interpolation and the control of perturbed semigroup systems

In this paper the controllabillity and admissibility of perturbed semigroup systems are studied, using tools from the theory of interpolation and Carleson measures. In addition, there are new results on the perturbation of Carleson measures and on the weighted interpolation of functions and their derivatives in Hardy spaces, which are of interest in their own right

Infrastructure for Engineered Emergence on Sensor/Actuator Networks

The ability to control emergent phenomena depends on decomposingthem into aspects susceptible to independent engineering. Forspatial self-managing systems, the amorphous-medium abstraction lets youseparate the systemÂs specification from its implementation