Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

UV–visible emission in Tb–Yb codoped tellurite glass on 980-nm excitation

UV–visible upconversion emission from terbium in a Tb–Yb codoped tellurite glass has been observed on 980-nm excitation. The ultraviolet and violet upconversion emissions involve three photons and the blue, green, yellow, and red emissions arise due to two incident photons. The mechanism involved in these emissions is discussed. The effects of doping concentration and of the sample temperature on the upconversion emissions have also been studied. PACS 74.25.Gz; 42.70.Hj; 73.61.Jc; 76.30.Kg; 42.70.Ce     

Hydrogen ion source with a cold magnetron cathode and magnetic plasma compression

A hydrogen ion source designed for the injector of a 16-MeV linear proton accelerator with an average beam current of ∼100 μA is presented. New design approaches allowing an improvement in the operating parameters of the ion source are proposed. The results of experimental tests of a source prototype operating in a pulsed mode with a repetition rate of 1–10 Hz and pulse duration of 100–600 μs are described.     

Kaon production from 1 to 40 AGeV

Kaon production is studied within the Giessen Boltzmann–Uehling–Uhlenbeck (GiBUU) model. Results are compared with experiment and with other models. The influence of the kaon potential on the kaon azimuthal distributions at SIS energies is considered. We also discuss the role of the many-body collisions at high-density phase of reaction.     

Catalysis by Ir(III), Rh(III) and Pd(II) metal ions in the oxidation of organic compounds with H2O2

Catalytic activities of three transition metals, as iridium (III) chloride, rhodium (III) chloride and palladium (II) chloride, were compared in the oxidation of six aromatic aldehydes (benzaldehyde, p‐chloro benzaldehyde, p‐nitro benzaldehyde, m‐nitro benzaldehyde, p‐methoxy benzaldehyde and cinnamaldehyde), two hydrocarbons (viz. (anthracene and phenanthrene)) and one aromatic and one cyclic alcohol (cyclohexanol and benzyl alcohol) by 50% H₂O₂. The presence of traces (substrate: catalyst ratio equal to 1:62500 to 1:1961) of the chlorides of iridium(III), rhodium(III) and palladium(II) catalyze these oxidations, resulting in good to excellent yields. It was observed that in most of the cases palladium(II) chloride is the most efficient catalyst. Conditions for the highest and most economical yields were obtained. Deviation from the optimum conditions decreases the yields. Oxidation in aromatic aldehydes is selective at the aldehydeic group only and other groups remain unaffected. This new, simple and economical method, which is environmentally safe, also requires less time. Reactive species of catalysts, existing in the reaction mixture are also discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

The global controllability of some mechanical systems with absolutely elastic impacts

Sufficient conditions are presented for the stabilizability and global controllability of certain natural Lagrangian systems with a non-negative potential energy when there are ideal unilateral constraints. In the general case, the number of controls is less than the number of degrees of freedom and the controls are bounded by preassigned quantities. Examples of globally controlled systems with two degrees of freedom are considered in which the action of the unilateral constraints is modelled within the framework of classical collision theory.     

Solid solubility of the oxisulfides of Y, La, and Gd

The solid solubility in the systems Y₂O₂S---La₂O₂S, Y₂O₂S---Gd₂O₂S, and Gd₂O₂S---La₂O₂S has been investigated. Solid solutions of all compounds, throughout the whole composition range, were readily obtained, using coprecipitated oxalates and a polysulfide flux.     

Non-self-adjoint sturm-liouville operators with matrix potentials

We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm-Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.