Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces

We study the asymptotic Dirichlet problem for p-harmonic functions in a very general setting of Gromov hyperbolic metric measure spaces.     

Evaluation and Optimization of the Oxidation efficiency of a UV-Persulphate-Oxidation Toc-Analyzer for the Determination of Oil Contamination from Forestry in Ground Water

Different chain oils (tall, rape seed and mineral oils) have been used as model compounds to evaluate and optimize the applicability of UV-persulphate TOC-analyzer for quantitative determination of forestry oils and to follow the progress of their biodegradability. It was shown, that K 2 S 2 O 8 -UV-oxidation method is not sufficient to oxidize chain oils completely. There were differences in oxidation efficiency between different oils, changing from about 46% measured for tall oil to about 25% observed for rape seed chain oil. The addition of Triton X-100 surfactant up to 2% (w/w) was observed to increase the oxidation efficiency, e.g. to 75% for tall oil. The observations can be explained by assuming that in the presence of surfactant the emulsions are more homogeneous and stable. Optimization using two-level full factorial design (temperature of the oxidation chamber and the amount of persulphate) was studied. The results show that the UV-persulphate-oxidation TOC-analyzer is not suitable method to monitor biodegradability of chain oils.     

Large deviations of infinite intersections of events in Gaussian processes

Consider events of the form {_Zs≥ζ(s),s∈S}$\{Z_s\ge \zeta \left(s\right),s\in S\}$, where Z$Z$ is a continuous Gaussian process with stationary increments, ζ$\zeta$ is a function that belongs to the reproducing kernel Hilbert space R$R$ of process Z$Z$, and S⊂R$S\subset \mathbb{R}$ is compact. The main problem considered in this paper is identifying the function β^∗∈R${\beta }^{\ast }\in R$ satisfying β^∗(s)≥ζ(s)${\beta }^{\ast }\left(s\right)\ge \zeta \left(s\right)$ on S$S$ and having minimal R$R$-norm. The smoothness (mean square differentiability) of Z$Z$ turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s$\zeta \left(s\right)=s$ for s∈[0,1]$s\in [0,1]$ and Z$Z$ is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process.