Notes on symmetric g-functions

A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable. The project is supported by the NNSF (10571151) and NSF (2006J0397) of Fujian Province of China.     

The categoricity of the group of all computable automorphisms of the rational numbers

We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the rational numbers is its only model among the groups that are embeddable in the group of all computable permutations. Supported by a Scheme 2 grant from the London Mathematical Society. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 649–662, September–October, 2007.     

Modeling of single- and multimode photonic-crystal planar waveguides with the plane-wave admittance method

One-foil targets emit most transition radiation (TR) power in storage ring synchrotrons. Such one-foil TR emitting targets (OFTRTs) are optimized, with respect to the foil material and the foil thickness, for use as X-ray lithography (XRL) sources. The best possible elemental material and the foil thickness of OFTRTs for XRL are determined for our storage ring synchrotrons MIRROIRCLE-20SX and MIRRORCLE-6X, which operate with electrons accelerated to 20 MeV and 6 MeV, respectively. It is shown that the XRL efficiency of a OFTRT, with an optimum thickness, increases when the elemental foil material has a lower atomic number Z. The best elemental OFTRT, for performing XRL by MIRRORCLE-20SX, should contain one Be foil with a thickness of d≅240 nm, while the second best OFTRT should be made of one C foil with d≅220 nm. The best elemental OFTRT, for performing XRL by MIRRORCLE-6X, should contain one C foil with d≅35 nm, while the second best OFTRT should be made of one Be foil with d≅100 nm, because there are no thinner Be foils. The XRL efficiency of a C-foil OFTRT increases when a higher-density foil is used. A OFTRT containing one foil of a given material with optimum thickness, in MIRRORCLE-20SX, has approximately 100 times larger XRL efficiency in comparison with such a target in MIRRORCLE-6X. PACS 41.50.+h; 29.25.-t; 81.16.Nd; 41.60.Ap; 29.20.Dh     

Simultaneous approximation for the Bézier variant of Baskakov-Beta operators

In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation.     

Collective radiation of a system of two three-level V-type atoms in a two-mode resonator with losses

Collective spontaneous radiation of a system of two three-level V-type atoms interacting with two modes of a quantum electromagnetic field in a resonator with finite Q-factor is investigated based on the control kinetic equation for the density matrix. Time dependences of the average number of photons and radiation intensity of each mode are derived for the case in which atoms at the initial moment of time are in different excited states. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 78–83, February, 2006.     

The role of intrachain dipole interactions in the formation of the supramolecular structure of crystallizing ferroelectric polymers

The role of intrachain dipole interactions in the formation of a lamellar morphology is investigated using a number of statistical vinylidene fluoride copolymers with nonpolar components as an example. It is shown that the large and interlamellar spacings regularly increase as the intrachain dipole interaction weakens.     

Electrocatalytic activity of sol-gel-prepared RuO2/Ti anode in chlorine and oxygen evolution reactions

Electrocatalytic properties of RuO₂/Ti anode with different coating masses, which are prepared by the alkoxide sol-gel procedure, are investigated in chlorine and oxygen evolution reactions by polarization measurements and electrochemical impedance spectroscopy in H₂SO₄ and NaCl electrolytes. According to polarization measurements, the activity of anodes at overpotentials below 100 mV is independent of coating mass. However, impedance measurements above 100 mV reveal changes in the activity of anodes in chlorine evolution reaction for different coating masses. The diffusion limitations related to the evolved chlorine are registered in low-frequency domain at 1.10 V (SCE), diminishing with the increase in potential to the 1.15 V (SCE). The observed impedance behavior is discussed with respect to the activity model for activated titanium anodes in chlorine evolution reaction involving formation of gas channels within porous coating structure. Gas channels enhance the mass transfer rate similarly to the forced convection, which also increases the activity of anode. This is more pronounced for the anode of greater coating mass due to its more compact surface structure. The more compact structure appears to be beneficial for gas channels formation. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1173–1179. The text was submitted by the authors in English.     

Nanophotonics and nanometrology with planar X-ray waveguide-resonator

The mechanism of X-ray waveguide-resonance propagation or the radiation superstream model, which can become the ground of X-ray nanophotonics, is discussed briefly. Some attention is devoted to features consideration of the simplest devices characterized by the waveguide-resonance transportation of X-ray beams. The experimental data showing the user possibilities of a simplest waveguide-resonators application for diffractometry are presented. We discuss the main reasons to improve the metrological characteristics for total reflection X-ray fluorescence (TXRF) analytical method in case when the target exciting beam is formed by a waveguide-resonator. Some problems appearing during the waveguide-resonator application are formulated.     

SILEX-1装置上等离子体尾场加速电子初步实验

激光等离子体加速电子机制可以产生准单能的高能电子束, 近年来成为国际上的研究热点. 中国工程物理研究院激光装置已经能够达到286TW的输出功率, 为国内在该领域的研究提供了实验条件. 文章介绍了在SILEX-1装置上开展的激光等离子体加速电子的初步实验, 并对测得结果进行讨论, 为下一步实验的进行提供了准备条件.