A law of the iterated logarithm for discrepancies: non-constant limsup

We prove the existence of a sequence {n _k x} whose discrepancies obey a bounded law of the iterated logarithm with a non-constant limsup.     

Application of an electrochemical membrane reactor to the thermochemical water splitting IS process for hydrogen production

The Bunsen reaction (SO₂ + I₂ + 2H₂O = H₂SO₄ + 2HI) in the thermochemical IS process to produce hydrogen was successfully employed using an electrochemical membrane reactor. H₂SO₄ and HI were concentrated in the anode side and the cathode side of the reactor, respectively. I₂ is the dominant bulk of the recycling chemicals in this process, and I₂ concentration at the outlet of the reactor was reduced ca. 93% by using this technique. The electric energy consumption for the reaction was about 50% smaller by reducing the concentration of I₂ indicating that the IS process can be operate efficiently at low I₂ concentration. The reaction was carried out for 4 h, and the HI concentration was increased by 26%. This amount was the same within 10% as the values calculated from the total loaded electricity. In order to decrease the overpotential at the anode side, small amount of HI was added to the anode side solution. The total voltage was reduced by 0.03 V by the addition of HI.     

Noise-induced critical breakdown of phase lockings in a forced van der Pol oscillator

The effect of noise on the period of the van der Pol oscillator forced by a sinusoidal signal is analyzed in detail. The dynamics of the forced nonlinear oscillator with noise is described by the evolution of probability densities by a Markov operator. The oscillator shows a 1 : 1 phase-locked oscillation whose period is equal to the period of the sinusoidal forcing when the forcing is sufficiently strong. Noise modulates the oscillator's period as expected, but we show that this modulation is not uniform; the period of the oscillator changes drastically at a certain strength of noise. Thus this noise-induced breakdown of the phase locking can be considered as a stochastic bifurcation. The breakdown of stochastic phase-locking or the stochastic bifurcation is also analyzed from the viewpoint of the spectra of the Markov operator.     

Quantum state of muon and proton in crystalline silicon

Quantum state and dynamics of muon and proton in crystalline silicon have been studied by solving one‐particle Schrödinger equations for the impurities. The ground state wavefunctions and energies are determined as a function of local distortion of the host Si lattice, where the Si–H interaction we used is that parameterized by Ramírez and Herrero following the results of earlier pseudopotential‐density‐functional calculation. It is shown that quantum zero‐point motion of muon induces an effective potential barrier between the tetrahedral‐symmetry (T) site and the bond‐center (BC) site, which ensures bistability of muonium states observed in experiments. It is also shown that, if we fully consider the quantum effect with the present model potential, the BC site becomes less stable than the T site on the contrary to the experiments and former theoretical calculations.     

Luminescence of rare-earth ions in perovskite-type oxides: from basic research to applications

Luminescence of a rare-earth ion in SrTiO₃ or other perovskite-type oxides was used as a probe of physical properties of a host crystal, but not as a phosphor because observed luminescence efficiency was low. Recent investigations have shown that the luminescence efficiency of SrTiO₃:Pr³⁺ is intensified up to 200 times by addition of Al ions. This paper reviews experimental results on this phenomenon and discusses mechanism of the Al-addition effect. A survey was made to find other materials, the efficiency of which can be improved by the impurity addition. Host-to-activator energy transfer by a coupling of the band-edge recombination energy and an allowed transition of a rare-earth ion is essential to provide a high efficiency. A red phosphor, Al-added SrTiO₃:Pr³⁺, is promising for display applications.     

Self-discharge characteristics of an electric double-layer capacitor with polymer hydrogel electrolyte

An electric double-layer capacitor (EDLC) was assembled with the polymer hydrogel electrolyte prepared from cross-linked potassium poly(acrylate) (PAAK) and KOH aqueous solution, and the self-discharge characteristics were investigated. The EDLC cell with the polymer hydrogel electrolyte showed lower voltage decay on open circuit than that with a KOH aqueous solution. Moreover, it was found that the leakage current of the EDLC cell was markedly suppressed by using the polymer hydrogel electrolyte. The suppression was enhanced with increasing PAAK content in the electrolyte. These results strongly suggest that the PAAK plays an important role in the suppression of self-discharge.     

Design optimization of axial flow hydraulic turbine runner: Part I—an improved Q3D inverse method

With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi‐three‐dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre‐computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright © 2002 John Wiley & Sons, Ltd.     

Total synthesis of dehydroaltenusin

The first total synthesis of dehydroaltenusin, a natural enzyme inhibitor, is described. The key step involves Suzuki-coupling reaction of an aryl triflate prepared from 2,4,6-trihydroxybenzoic acid with a catechol-derived boronic acid or boronic ester. The synthetic product was evaluated as a potent inhibitor against eukaryotic DNA polymerase α and other DNA polymerases.