No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas on (4 r 1) dimensional manifolds. As an application, we derive some results on divisibilities of the index of Toeplitz operators on (4 r 1) dimensional spin manifolds and some congruent formulas on characteristic number for (4 r 1) dimensional spin c manifolds.

We consider a one-dimensional model biodegradation system consisting of two reactionadvection equations for nutrient and pollutant concentrations and a rate equation for biomass. The hydrodynamic dispersion is ignored. Under an explicit condition on the decay and growth rates of biomass, the system can be approximated by two component models by setting biomass kinetics to equilibrium. We derive closed form solutions for constant speed traveling fronts for the reduced two component models and compare their profiles in homogeneous media. For a spatially random velocity field, we introduce travel time and study statistics of degradation fronts via representations in terms of the travel time probability density function (<i>pdf</i>) and the traveling front profiles. The travel time <i>pdf</i> does not vary with the nutrient and pollutant concentrations and only depends on the random water velocity. The traveling front profiles