Fractal character of effective Hall properties of a three-dimensional disordered composite

The dependencies of the effective Hall properties on a scale, obtained by means of an iterative averaging method, manifest their fractal character. The influence of an intensity of the Hall effect on the fractal character of the Hall properties was considered. Scale ranges and dimensional characteristics of the effective Hall properties behavior were calculated and discussed.     

Preparation of colloidal solutions of noble metals stabilized by polyoxometalates and supported catalysts based on these solutions

Conditions for the preparation of stable aqueous monometallic and bimetallic colloidal solutions (sols) of noble metals (Ru, Rh, Pd, Pt, Ir, Ag, and Au) in the presence of polyoxometalates containing W, Mo, V, and Nb were found. The stability of sols against coagulation at room temperature was studied. The metal/C samples prepared by metal adsorption from sols were studied by powder X-ray diffraction analysis and transmission electron microscopy. The following factors of importance for the preparation of a stable sol are discussed: (1) the formation of a sol of a metal polyhydroxo complex stabilized by a polyoxometalate (preliminary stage) and (2) the formation of polyoxometalate-metal clusters in the course of reduction of polyhydroxo complexes.Translated from Kinetika i Kataliz, Vol. 45, No. 6, 2004, pp. 921–929.Original Russian Text Copyright © 2004 by Maksimova, Chuvilin, Moroz, Likholobov, Matveev.     

On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Light Modulates Electric Phenomena in Hornet Cuticle¶

In the cuticle of live social hornets, such as Vespa orientalis (Hymenoptera, Vespinae), endogenous electric effects are encountered, i.e. voltages of 100–200 mV under illumination and currents amounting to several microamperes on its subjection to darkness—clearly a process of charging and discharging. Of the various wavelengths of sunlight, UV was found to be the most contributory to the active cuticular voltage generation. Throughout the warm season of the yearthe–the active period in colonies of social hornets and wasps—colony members exit from the dark nest during the daytime and fly to the field under the hot sun for various foraging purposes, ultimately returning to the nest. Thus, each hornet, be it queen, worker or drone, probably undergoes daily cyclical process of electric charge and discharge in the exterior part of their integument, cuticle, which lasts up to 30–40 min. Such photoelectric phenomenon was detected in both live, ether‐anaesthetized hornets and dead hornets, albeit in the latter the electric values recorded were lower. The present study addresses the possible impact of the phenomenon on vespan daily life and also compares it with a parallel occurrence in electric fish.     

On the Existence of Periodic Solutions of a System of Two Differential Equations with Pulse Influence

We investigate the problem of the existence of periodic solutions of a system of two linear differential equations with pulse influence on a plane in the case where a stable knot or a stable focus is a singular point of this system.     

Iodinated 1,4-naphthoquinones

Iodination of 5-amino- and 6-amino-1,4-naphthoquinones with I₂ and HIO₃ in aqueous dioxane occurs only at the benzoid ring. Depending on the reaction conditions, either aminoiodo- or aminodiiodonaphthoquinones are produced. Diazotization of these compounds followed by reduction or replacement of the diazo group with iodine affords mono- or polyiodo derivatives of 1,4-naphthoquinone. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1465–1469, June, 2005.