Heavy tailed durations of regional rainfall

Durations of rain events and drought events over a given region provide important information about the water resources of the region. Of particular interest is the shape of upper tails of the probability distributions of such durations. Recent research suggests that the underlying probability distributions of such durations have heavy tails of hyperbolic type, across a wide range of spatial scales from 2 km to 120 km. These findings are based on radar measurements of spatially averaged rain rate (SARR) over a tropical oceanic region. The present work performs a nonparametric inference on the Pareto tail-index of wet and dry durations at each of those spatial scales, based on the same data, and compares it with conclusions based on the classical Hill estimator. The results are compared and discussed. The authors express sincere thanks to the Mathematisches Forschungsinstitut Oberwolfach (MFO) for facilitating their collaboration under a “Research in Pairs” project hosted at MFO during March 5–25, 2006. The research of the second and third authors was supported by the project LC06024.     

An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations

We present an algebraic multigrid algorithm for fully coupled implicit Runge–Kutta and Boundary Value Method time-discretizations of the div-grad and curl-curl equations. The algorithm uses a blocksmoother and a multigrid hierarchy derived from the hierarchy built by any algebraic multigrid algorithm for the stationary version of the problem. By a theoretical analysis and numerical experiments, we show that the convergence is similar to or better than the convergence of the scalar algebraic multigrid algorithm on which it is based. The algorithm benefits from several possibilities for implementation optimization. This results in a computational complexity which, for a modest number of stages, scales almost linearly as a function of the number of variables.     

An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs

Adaptive tensor product wavelet methods are applied for solving Poisson’s equation, as well as anisotropic generalizations, in high space dimensions. It will be demonstrated that the resulting approximations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that we may lose is independent of the space dimension n. The cost of producing these approximations will be proportional to their length with a constant factor that may grow with n, but only linearly.     

Hydrophilic Carotenoids: Surface Properties and Aggregation Behavior of the Potassium Salt of the Highly Unsaturated Diacid Norbixin

The oft‐claimed ‘good’ water solubility of the food color norbixin ( 3 ) could not be confirmed. In contrast, the potassium salt 5 of norbixin formed suitable dispersions. The surface and aggregation properties of salt 5 were investigated and compared with other naturally occurring and synthetic hydrophilic carotenoids (Table).