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.     

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.     

Supramolecular structural variations with changes in anion and solvent in silver(I) complexes of a semirigid, bitopic tris(pyrazolyl)methane ligand

The bitopic ligand p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (pz = pyrazolyl ring) that contains two tris(pyrazolyl)methane units connected by a semirigid organic spacer reacts with silver(I) salts to yield [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgX)(2)]( infinity ), where X = CF(3)SO(3)(-) (1), SbF(6)(-) (2), PF(6)(-) (3), BF(4)(-) (4), and NO(3)(-) (5). Crystallization of the first three compounds from acetone yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgCF(3)SO(3))(2)]( infinity ) (1a), [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))(2)[(CH(3))(2)CO](2)]( infinity ) (2b), and [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)AgPF(6)]( infinity ) (3a), where the stoichiometry for the latter compound has changed from a metal:ligand ratio of 2:1 to 1:1. The structure of 1a is based on helical argentachains constructed by a kappa(2)-kappa(1) coordination to silver of the tris(pyrazolyl)methane units. These chains are organized into a tubular 3D structure by cylindrical [(CF(3)SO(3))(6)](6)(-) clusters that form weak C-H...O hydrogen bonds with the bitopic ligand. The same kappa(2)-kappa(1) coordination is present in the structure of 2a, but the structure is organized by six different tris(pyrazolyl)methane units from six ligands bonding with six silvers to form a 36-member argentamacrocycle core. The cores are organized in a tubular array by the organic spacers where each pair of macrocycles sandwich six acetone molecules and one SbF(6)(-) counterion. The structure of 3a is based on a kappa(2)-kappa(0) coordination mode of each tris(pyrazolyl)methane unit forming a helical coordination polymer, with two strands organized in a double stranded helical structure by a series of C-H...pi interactions between the central arene rings. Crystallization of 2-4 from acetonitrile yields complexes of the formula [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)[(AgX)(2)(CH(3)CN)(n)]]( infinity ) where n = 2 for X = SbF(6)(-) (2b), X = PF(6)(-) (3b) and n = 1 for X = BF(4)(-) (4b). All three structures contain argentachains formed by a kappa(2)-kappa(1) coordination mode of the tris(pyrazolyl)methane units linked by the organic spacer and arranged in a 2D sheet structure with the anions sandwiched between the sheets. Crystallization of 5 from acetonitrile yields crystals of the formula [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgNO(3))(2)(CH(3)CN)(4)]( infinity ), where the nitrate is bonded to the silver. The argentachains, again formed by kappa(2)-kappa(1) coordination, are arranged in W-shaped sheets that have an overall configuration very different from 2b-4b. Treating [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))(2)]( infinity ) with a saturated aqueous solution of KPF(6) or KO(3)SCF(3) slowly leads to complete exchange of the anion. Crystallization of a sample that contains an approximately equal mixture of SbF(6)(-)/PF(6)(-) from acetonitrile yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)[Ag(2)(PF(6))(0.78(1))(SbF(6))(1.22(1))(CH(3)CN)(2)][(CH(3)CN)(0.25) (C(4)H(10)O)(0.25)]]( infinity ), a compound with a sheet structure analogous to 2b-4b. Crystallization of the same mixture from acetone yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))[(CH(3))(2)CO](1.5)]( infinity ), where the metal-to-ligand ratio is 1:1 and the [C(pz)(3)] units are kappa(2)-kappa(0) bonded forming a coordination polymer. The supramolecular structures of all species are organized by a combination of C-H...pi, pi-pi, or weak C-H-F(O) hydrogen bonding interactions.