Selective survey on Subset Combinatorics of Groups

We survey recent results concerning the combinatorial size of subsets of groups. For a cardinal ??, according to its arrangement in a group G, a subset of G is distinguished as ??-large, ??-small, ??-thin, ??-thick, and P _?? -small. By analogy with topology, there arise the following combinatorial cardinal invariants of a group: density, cellularity, resolvability, spread, etc. The paper consists of 7 sections: Ballean context, Amenability, Ideals, Partitions, Packings, Around thin subsets, and Colorings.     

Determination of nanoparticle sizes by X-ray diffraction

Different procedures for analysis of particle sizes by the X-ray diffraction method are compared by the example of nanoparticles of nickel and iron(3+) oxide (Fe₂O₃). A modified Warren-Averbach method is proposed for the analysis of the X-ray diffraction line profile based on the approximation by the Voigt function, which yields stable solutions, and the efficiency of the method is shown. The analysis within the frame-work of the Warren-Averbach method makes it possible to restore the distribution function of nanoparticles (crystallites) over true diameters, which satisfactorily correlates with electron microscopy data. The applicability of the Warren-Averbach method to the estimation of crystallite sizes by the analysis of a single diffraction line is substantiated. The range of the applicability of the Scherrer, Williamson-Hall, Warren-Averbach, and modified Warren-Averbach methods to the substructure analysis by the X-ray diffraction is determined as depending on the method of nanostructure formation.     

Energy efficiency of femtosecond laser ablation of polymer materials

We present the results of an experimental study of the ablation spectral energy thresholds for a number of polymer materials ((C₂F₄) _n , (CH₂O) _n ) exposed to femtosecond (τ_0.5 ~ 45–70 fs) laser pulses (λ ~ 266, 400, 800 nm) under atmospheric conditions and under vacuum (p ~ 10–2 Pa). We have analyzed the energy thresholds and the efficiency of optical, thermophysical, and gasdynamic processes in laser ablation vs. the laser pulse duration and photon energy.     

Optimization of the velocity of motion for a flow according to Föppl-Lavrent’ev scheme

Problems concerning the optimal control over the advance of an object in a still water are considered in the framework of the nonstationary Euler hydrodynamical equation. It is assumed that the trail of the flow contains two point vortices of given intensity. The control parameter is the velocity of the advance, as a function of time. These optimization problems for a system of nonlinear partial differential equations having a free boundary (in the form of vortex centers that are no given a priory) are reduced to classical optimal control problems for a system of ordinary differential equations.     

Experimental study of optical gas-dynamic processes of polymeric material ablation by ultrashort laser pulses

Optical gas-dynamic processes occurring in polymeric targets ((CH₂O) _n , (C₂F₄) _n ) exposed to ultrashort laser pulses (τ _0.5 ∼ 45 − 70 fs; λ _I,II,III = 266, 400, 800 nm; and E/S ∼ 0.1 − 40 J/cm² at r ₀ ∼ 20 μm) were studied under normal conditions and in vacuum (p ∼ 10⁻² Pa). The dynamics of the mass flow from the target surface (m′ ∼ 10⁻⁵ − 10⁻⁴ g/J) was studied and the spectral-energy thresholds of laser ablation, the electron density distribution (n _e ∼ 10¹⁴ − 10¹⁸ cm⁻³), the mass-averaged velocity of the material flow from the target surface (∼ 10³ m/s), and the chemical composition and average temperature in the near-surface plasma formation (T ∼ 5000 K) were determined using interference microscopy, emission spectroscopy, and shadowgraphy.     

Probe Mössbauer spectroscopy of the grain boundaries of a Mo-O nanocrystalline system obtained by mechanical alloying

The localization of Fe atoms in the process of mechanical alloying of a Mo powder composite with 8 at % O at boundaries of the bcc Mo grains has been investigated by Mössbauer spectroscopy on impurity ⁵⁷Fe isotope atoms (1 at %), X-ray diffraction, and Auger spectrometry. The process begins with the formation of a nanostructure (～10 nm) in bcc Mo and ends with the formation of a bcc supersaturated solid solution with O atoms at interstitial positions and Fe atoms at substitutional positions. The presence of oxygen in the boundaries of bcc Mo grains leads to an extraordinarily large isomer shift (2 mm/s with respect to α-Fe) for the grainboundary component in the Mössbauer spectrum. This circumstance makes it possible to consider ⁵⁷Fe-O complexes as new probes for studying grain boundaries of powder nanocrystalline materials. As a result, the following three structural components have been identified in the mechanically activated system: a grain boundary and distorted near-boundary regions with the common name interface and a grain with the perfect (defect-free) structure. For powder nanocrystalline (～10 nm) materials subjected to intense mechanical treatment in a planetary ball mill, the widths of the unrelaxed grain boundary and interface average over the entire volume of particles have been experimentally estimated as 0.2 and 1 nm, respectively.     

Morphisms of Ball's Structures of Groups and Graphs

We introduce and study two kinds of morphisms between ball's structures related to groups and graphs.     

Detector of thermal radiation based on high-temperature superconductor matrix with magnetooptical image-visualization system

We propose a concept for constructing a thermal imaging system of a new type that is based on unique magnetic properties of high-temperature superconductors and on a noncontact magnetooptic information reading from a matrix sensing element.