Dynamics of acoustoelectromagnetic solitons as a manifestation of higher nonlinearity

The acoustoelectromagnetic interaction is examined in a regime where three mechanisms must be taken into account simultaneously: photoelasticity, quadratic photoelasticity, and elastic nonlinearity. It is shown that beyond the critical conditions, acoustic solitary waves are formed at harmonic and subharmonic frequencies in a crystal. Including damping and nonideal reflection at the boundaries does not lead to the establishment of any sort of stationary state: a soliton spatial-temporal dynamic develops. Fiz. Tverd. Tela (St. Petersburg) 39, 1101–1104 (June 1997)     

Evaluation of stability of silica-supported Fe–Pd and Fe–Pt nanoparticles in aerobic conditions using thermal analysis

The applications of zerovalent iron nanoparticles (nZVI) exploit their high reactivity which decreases due to oxidation in aerobic conditions during manufacture, application, and storage. In this study, we present the new procedure for estimation of the nZVI stability to oxidation in air. The procedure is suitable for characterization of the novel materials based on the supported nZVI. Nanoscale particles were synthesized inside porous silica supports by incipient wetness impregnation with the metal precursor solutions followed by thermal treatment. The TG–DTA studies revealed the decomposition temperature of the supported precursors, as well as the interaction of Fe and precious metal precursors, which resulted in the formation of alloy nanoparticles. Characterization of the samples by XRD confirmed the formation of the nanoparticles of the metallic Pd, Pt, and Fe phases supported on SiO₂ carriers, as well as the formation of solid solutions based on the structure of precious metals. The new procedure for estimation of the nZVI stability included (1) TPR with hydrogen up to 400–425 °C followed by isothermal reduction at these temperatures; (2) in situ reoxidation with oxygen at room temperature. The samples were reduced “as obtained” and after in situ reoxidation. The results of the TPR studies exhibited that introduction of both Pd and Pt protected the Fe nanoparticles from oxidation with oxygen and air at ambient conditions.     

On a Characterization of Idempotent Distributions on Discrete Fields and on the Field of <Emphasis Type="Italic">p</Emphasis>-Adic Numbers

We prove the following theorem. Let X be a discrete field, and \(\xi \) and \(\eta \) be independent identically distributed random variables with values in X and distribution \(\mu \). The random variables \(S=\xi +\eta \) and \(D=(\xi -\eta )^2\) are independent if and only if \(\mu \) is an idempotent distribution. A similar result is also proved in the case when \(\xi \) and \(\eta \) are independent identically distributed random variables with values in the field of p-adic numbers \({\mathbf {Q}}_p\), where \(p>2\), assuming that the distribution \(\mu \) has a continuous density.     

Recent advances in catalytic asymmetric epoxidation using the environmentally benign oxidant hydrogen peroxide and its derivatives

There has been a recent drive to develop asymmetric catalytic methods to produce epoxides using environmentally benign oxidants, especially hydrogen peroxide. This critical review discusses the advances that have been made using both metal-based and organocatalytic homogeneous catalysts (142 references).     

Plasma Parameters around a Chain-Like Structure of Dust Particles in an External Electric Field

The formation of a 1D chain-like structure of dust particles in a low-temperature argon plasma was studied. A new numerical model for calculation of the self-consistent spatial distribution of plasma parameters around a chain of dust particles was presented. The model described the motion of positively charged ions in the electric potential of several negatively charged dust particles, taking into account the action of an external electric field. The main advantage of the model was that the charges of the dust particles and the interparticle distances were determined self-consistently. As a result of numerical simulations, the dependencies of the spatial distributions of the plasma parameters (the densities of electrons and ions and the self-consistent electric potential) near the dust particles chain on the strength of the external electric field, an external force acted on the last particle, and the mean free path of the ions was determined. The obtained results made it possible to describe the process of the formation of chain-like structures of dust particles in discharge plasma.     

Narrow transmittance peaks in a multilayered microsphere with a quasiperiodic left-handed stack

We studied the photon spectrum in coated microspheres with alternating quasiperiodic layers having left-handed (LH) materials included. It is found that the band gap (spectral zone of nearly zero transmittancy) in such a system is strongly enhanced. At an increase of the quasiperiodicity parameter γ, the boundaries of the spectral band gaps acquire the intended shape. When γ exceeds the inverse golden mean value, a structure with extremely narrow separated resonant peaks with nearly complete transmittance arises. At increased γ, such resonances migrate to the center of the band gap. This effect allows creating optical filters with extremely narrow passbands.     

On the Skitovich–Darmois theorem for some locally compact Abelian groups

Let X be a locally compact Abelian group, \(\alpha _{j}, \beta _j\) be topological automorphisms of X. Let \(\xi _1, \xi _2\) be independent random variables with values in X and distributions \(\mu _j\) with non-vanishing characteristic functions. It is known that if X contains no subgroup topologically isomorphic to the circle group \(\mathbb {T}\), then the independence of the linear forms \(L_1=\alpha _1\xi _1+\alpha _2\xi _2\) and \(L_2=\beta _1\xi _1+\beta _2\xi _2\) implies that \(\mu _j\) are Gaussian distributions. We prove that if X contains no subgroup topologically isomorphic to \(\mathbb {T}^2\), then the independence of \(L_1\) and \(L_2\) implies that \(\mu _j\) are either Gaussian distributions or convolutions of Gaussian distributions and signed measures supported in a subgroup of X generated by an element of order 2. The proof is based on solving the Skitovich–Darmois functional equation on some locally compact Abelian groups.