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.     

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.     

Synthesis and molecular structure of new acyclic analogues of nucleotides with a 1,2-alkadienic skeleton

Reaction of 1-chloro-4-(diethoxyphosphonyl)alka-2,3-dienes 14,15 with purine and pyrimidine heterocyclic bases in the presence of cesium carbonate afforded new acyclic analogues of nucleotides containing a 1,2-alkadienic skeleton 18-23. Dealkylation of 18-23 furnished phosphonic acids 2a-f. In contrast, alkylation reaction with 1-chloro-4-(diethoxyphosphonyl)octa-2,3-diene 16 led to Z- and E-1,3-alkadienic phosphonates 25a,b and 26a,b. A similar reaction with 1-chloro-4-(diethoxyphosphonyl)-2-methylbuta-2,3-diene 17 led to the elimination of hydrochloride and formation of 4-(diethylphosphonyl)-2-methylbut-1-en-3-yne 24. Molecular structures of new acyclic nucleotides 18 and 2f are determined by X-ray crystallographic analysis.     

Critical phenomena in the topochemical reaction of water vapor with solid N,N′-ethylenebis (acetylacetoniminato)copper (II)

The effects of water vapor and temperature on the phase transition between anhydrous N,N-ethylenebis(acetylacetoniminato) copper (II) and the monohydrate have been studied by a piezoelectric microbalance method. The presence of a branch point and critical deceleration of the phase transition dynamics near that point have been observed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 29, No. 2, pp. 149–153, March–April, 1993.This work was supported by a fundamental research grant from the State Committee on Science and Technology, Ukraine Council of Ministers.     

Electron-cluster interactions

Beam depletion spectroscopy has been used to measure absolute total inelastic electron-sodium cluster collision cross sections in the energy range fromE0.1 toE6 eV. The investigation focused on the closed shell clusters Na₈, Na₂₀, and Na₄₀. The measured cross sections show an increase for the lowest collision energies where electron attachment is the primary scattering channel. The electron attachment cross section can be understood in terms of Langevin scattering, connecting this measurement with the polarizability of the cluster. For energies above the dissociation energy the measured electron-cluster cross section is energy independent, thus defining an electron-cluster interaction range. This interaction range increases with the cluster size.     

Dispersity and kinetic characteristics of dissociation of mono- and hemiaquo adducts of copper N,N′-ethylenebis(acetylacetoniminate) under nonisothermal conditions

Using optical microscopy and thermogravimetry, we have established that determination of the kinetic characteristics of dissociation for the monoaquo adduct of copper N,N-ethylene-bis(acetylacetoniminate) with particle size 0.5–2 mm is hindered by self-dispersal processes. Using a piezoquartz microbalance, we have obtained the kinetic parameters for thermolysis for a phase whose crystal sizes are substantially smaller than the minimal size after self-dispersal of a block of a large crystal (0.5–2 m). For thermolysis of the hemiaquo adduct not accompanied by self-dispersal, the kinetic characteristics of the process for phases of dispersity 0.5–2 mm and 0.5–2 m are comparable.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 3, pp. 226–231, May–June, 1992.