On the lower bound of the discrepancy of (t; s) sequences: I

We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.Comment: Minor change

On the lower bound of the discrepancy of Halton's sequence

Let $(H_s(n))_{n \geq 1}$ be an $s-$dimensional Halton's sequence. Let $D_N$ be the discrepancy of the sequence $(H_s(n))_{n = 1}^{N}$. It is known that $ND_N =O(\ln^s N)$ as $N \to \infty$. In this paper we prove that this estimate is exact: $$ \overline{\lim}_{ N \to \infty} N \ln^{-s}(N) D_N >0. $

Diameter and density of Neptune

Diameter, density, and atmospheric data calculated for Neptune from 7 Apr. 1968 occultatio

Thermal reactor

A thermal reactor apparatus and method of pyrolyticaly decomposing silane gas into liquid silicon product and hydrogen by-product gas is disclosed. The thermal reactor has a reaction chamber which is heated well above the decomposition temperature of silane. An injector probe introduces the silane gas tangentially into the reaction chamber to form a first, outer, forwardly moving vortex containing the liquid silicon product and a second, inner, rewardly moving vortex containing the by-product hydrogen gas. The liquid silicon in the first outer vortex deposits onto the interior walls of the reaction chamber to form an equilibrium skull layer which flows to the forward or bottom end of the reaction chamber where it is removed. The by-product hydrogen gas in the second inner vortex is removed from the top or rear of the reaction chamber by a vortex finder. The injector probe which introduces the silane gas into the reaction chamber is continually cooled by a cooling jacket

Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results

Recently a local mean field theory for both eqilibrium and transport properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77, 165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to the results of dynamic Monte Carlo simulations. In a thermal equilibrium state we compare the density of states and the occupation probabilities. We also study the transition rates between different states and find that the mean field rates underestimate a certain class of important transitions. We propose modified rates to be used in the mean field approach which take into account correlations at the minimal level in the sense that transitions are only to take place from an occupied to an empty site. We show that this modification accounts for most of the difference between the mean field and Monte Carlo rates. The linear response conductance is shown to exhibit the Efros-Shklovskii behaviour in both the mean field and Monte Carlo approaches, but the mean field method strongly underestimates the current at low temperatures. When using the modified rates better agreement is achieved