The Ingham Divisor Problem on the Set of Numbers without kth Powers

Suppose that k and l are integers such that and , M _k is a set of numbers without kth powers, and . In this paper, we obtain asymptotic estimates of the sums over      

Explicit constructions and the arithmetic of local number fields

This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.     

Advances in Modern Information Technologies for Data Analysis in CRYO-EM and XFEL Experiments

Crystallography Reports - A new approach to the organization of data pipelining in cryo-electron microscopy (Cryo-EM) and X-ray free-electron laser (XFEL) experiments is presented. This approach,...     

Modification of a Coating (Tin) – Substrate (Vt1-0) System with High-Intensity Pulsed Electron Beams

Russian Physics Journal - The data on numerical simulation of the temperature fields and phase transformations in a surface layer of a coating (TiN) – substrate (VT1-0) system irradiated with...     

Dislocation structure of kcl crystals grown with vibration of the melt

Summary The amplitude at all frequencies was 0.04 mm. Three crystals were grown at each frequency, with seeds of dislocation density D = 6 × 10⁴ cm^–2. Figure 1 shows the frequency dependence of the final D. Each point in Figs. 1 and 2 is the mean from 50 measurements (50 fields of view). At all frequencies except 180 Hz, D was 2–4 times less than that without vibration, while at 100 and 160 Hz it was less by nearly an order of magnitude.The effects of amplitude (0.02 to 0.2 mm) were examined at 100 Hz, the minimum D occurring at 0.1 mm (Fig. 2). At 0.04–0.08 mm, D was less by a factor 3–4 than for crystals grown without vibration, while at 0.1 mm it was less by an order of magnitude, being 2 × 10^–4 cm^–2. The size of the etch pits on crystals grown at amplitudes up to 0.1 mm did not differ from that for crystals grown at rest, but above 0.1 mm the size increased, by more than a factor 3 at 0.2 mm. Figure 3 illustrates these effects.Optimal vibration reduces D by improving the growth conditions (reduction of temperature gradients by mixing, more uniform impurity distribution).     

Effect of electrical field on growth of gallium arsenide layers from vapour phase

The effect of electrical fields on the growth rate and morphology of gallium arsenide layers in the GaAs AsCl₃ H₂ system is investigated. The fields both parallel and perpendicular to the substrate surface are used. It is found that application of the parallel field results n increase of growth rate of (111)A face but does not change that of 2° (001). The morphology of layers grown in such a field is better than that grown without any. The application of perpendicular field results in decrease of growth rate for both crystallographic orientations, the layer morphology worthening. In both cases the effect is greater when the substrate has a negative potential. Possible mechanisms of the field influence on the growth rates of gallium arsenide layers are discussed such as: supersaturation decrease because of nucleation in vapour phase and the change in the rates of surface processes.     

Structure and Properties of a Coating (TiCuN) – Substrate (А7) System Modified with a High-Intenisty Electron Beam

Russian Physics Journal - The data obtained via an analysis of the structure and properties of a surface layer of technical grade aluminum (A7) modified by forming a thin TiCuN coating, followed by...