The Riemann mapping theorem from Riemann's viewpoint

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.Comment: 14 pages, 2 figure

The Effect of Heat Treatment on Nanoparticle Size and ORRActivity for Carbon-supported Pd–Fe Alloy Electrocatalysts

The synthesized carbon-supported Pd-Fealloy electrocatalysts were characterized for the purpose of the fuel cell cathode oxygen reduction reaction (ORR). The synthesized catalysts were characterized in terms of structural morphology and catalytic activity by XRD and electrochemical measurements. Surface cyclic voltammetry was used to confirm the formation of the Pd–Fe alloy. The catalysts were heat-treated at temperatures ranging from 300 ◦C to 700 ◦C for different ageing times, in order to improve activity and stability. The average particle size of 10.16 nm, and the highest ORR catalytic activity were obtained at the optimal heat-treatment temperature 300 ◦C for 3h. Electrocatalytic ORR activity was also examined in an acidic solution containing methanol. The results showed that the synthesized Pd–Fe/C catalyst has methanol tolerant capabilities

Turbulent Mixing in Clusters of Galaxies

We present a spherically-symmetric, steady-state model of galaxy clusters in which radiative cooling from the hot gas is balanced by heat transport through turbulent mixing. We assume that the gas is in hydrostatic equilibrium, and describe the turbulent heat diffusion by means of a mixing length prescription with a dimensionless parameter alpha_mix. Models with alpha_mix ~ 0.01-0.03 yield reasonably good fits to the observed density and temperature profiles of cooling core clusters. Making the strong simplification that alpha_mix is time-independent and that it is roughly the same in all clusters, the model reproduces remarkably well the observed scalings of X-ray luminosity, gas mass fraction and entropy with temperature. The break in the scaling relations at kT \~ 1-2 keV is explained by the break in the cooling function at around this temperature, and the entropy floor observed in galaxy groups is reproduced naturally.Comment: Accepted for publication in ApJ

Pattern Formation in a Two-Dimensional Array of Oscillators with Phase-Shifted Coupling

We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike pinwheels, (anti)spirals with phase-randomized cores, and antiferro patterns embedded in (anti)spirals. We consider the symmetry properties of the system to explain the observed behaviors, and estimate the wavelengths of the patterns by linear analysis. Finally, we point out the implications of our work for biological neural networks