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We introduce a parameter space containing all algebraic integers β ∈ (1, 2] that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution ν β . This allows us to show that dimH(ν β ) = 1 for all β with representations in certain open regions of the parameter space.

Various methods for limiting the plasma volume made it possible to produce a continuous point-like high-temperature terahertz discharge at the Novosibirsk free-electron laser (NovoFEL). When a krypton-nitrogen jet was injected into the focus of the NovoFEL radiation, as compressed as possible and having an average power of about 200 W, a spherical plasma with a diameter of 1 mm, temperature of 4–4.5 eV (46 000–52 000 K), and density of 3.5 × 1017 cm−3 was obtained. The ion composition of the plasma is represented mainly by triply and doubly ionized krypton atoms (Kr IV and Kr III). The absolute stability of the plasma, which tends to self-oscillate, is achieved through the use of a special negative optical feedback.

Density of Al-Ni-Co-R (R = Nd, Sm, Gd, Tb, Yb) glass-forming alloys is studied experimentally by gamma-absorption method in a wide temperature range including crystalline and liquid states. Molar volumes and thermal expansion coefficients are calculated from the experimental data. It is shown that these melts remain strongly microheterogeneous systems at small overheatings above liquidus. Some regimes of melt heat treatment before quenching are discussed.

We report the results of studying a compact laser system designed for manipulating a quantum state of the optical qubit based on the 2S1/2 → 2D3/2 quadrupole transition in the 171Yb+ ion at a wavelength of 435.5 nm. An emission power of the laser system reaches 500 μW at λ = 435.5 nm and the relative frequency instability of at most 3 × 10−15 is achieved at averaging intervals from 0.5 to 50 s with a subtracted linear frequency drift. The compactness of the developed system makes it possible to employ it in transportable systems including optical clocks.

Hyperfine parameters and the pressure dependence of the magnetic transition temperatures of FeRhGe2 have been investigated. Sample has been prepared using high pressure—high temperature synthesis technique. FeRhGe2 consists of two B20 structure phases with close lattice constants. The phase separation stays constant in the temperature range 4–300 K. The magnetic transition temperatures T c 1 = 213 K and T c 2 = 135 K of FeRhGe2 slightly increases with pressure in the range 0–4.5 GPa. We have compared this pressure dependence with some others compounds in the family Fe 1 − x Rh x Ge. The two phases in FeRhGe2 have slightly different values of the hyperfine magnetic fields.

Excited states in low-energy spectra of Ni are considered. Accordingly, pairing forces in the form of surface delta interaction are employed to account for the formation of the ground state multiplet with seniority states. The multiplet splitting is described with mass relationships of masses of neighboring nuclei. Subsequently, the seniority model is adopted to reproduce or predict the states in odd-even isotopes and in even-even isotopes. The correct account of the state should allow for the description of the reversed order of states with and observed in experiments. The results obtained are compared with the structure of similar multiplets in isotones.

The article discusses the design of an algorithm for the formation of personalized user recommendations. The basis of the algorithm is a recurrent neural network with reinforcement. The use of neural networks in the recommendation algorithm will help to increase persistence as it becomes possible to identify weak relationships of implicit factors.

The work investigated the durability of the labelling of sports equipment made of composite materials. Professional hockey sticks were taken for research. Research has been done on hockey stick wear for different players: centre and winger and defender. In addition, a study was made of hockey sticks for left-handers and right-handers. In the study of the wear of printed elements, sports equipment of various lengths was used. Contact research was carried out during training and competition. The study of the number of contacts was carried out on the basis of video recordings of trainings and games of the teams “Energija” - Elektrėnai (Lithuania) and the national team of the Belarusian Republic. The study carried out showed that the hockey stick wear of the centre striker and the winger during the competition and training is similar. During the competition, the hockey sticks of the centre strikers are most often in contact. It was found that the difference between contacts during training and playing depends on the intensity of the game, penalty time and strategy. When conducting a study of the wear of the printed elements applied to the hockey stick, depending on the position of the player, it was found that the wear of the sticks of the winger and the defender is the same, but that of the centre striker is different. When conducting a study of hockey stick wear depending on its length, the following conclusion was made: the taller the player, the longer his hockey stick and the maximum contact area. Research has shown that hockey stick wear is not affected by how the player holds the hockey stick, i.e. whether he is left-handed or right-handed. To study the abrasion of elements using the UGRA method, an original stand was created. With the help of this stand, studies of the abrasion of printed elements were carried out. Based on the study, it was concluded that the abrasion of printed elements most often occurs at the moment of contact of the objects of research, both with each other and with objects on the playing field. As a result, the printed elements split, peel off and become less noticeable, in addition, the name of the manufacturer's company is worn out and the hockey stick loses the player's personal identification data printed on the hockey stick. Recommendations are given on the peculiarities of printing and the location of printed elements on sports equipment.

A multiple-mirror confinement is an alternative concept in fusion energy development that improves the particle and energy confinement times in open traps (linear magnetic systems). The paper discusses the development progress of the GOL-NB multiple-mirror experiment that was recently commissioned at BINP. The reference description of the GOL-NB hardware is presented. Properties of a low-temperature start plasma are discussed. The first results from test experiments with injection of one 25 keV neutral beam are shown. Methods of plasma stabilization in the non-min-B configuration are discussed. In general, the ongoing commissioning progress and results of the preliminary experiments are modestly optimistic for the expected device performance.

The results of the polymer film investigation are considered in that paper. These films are obtained in atmospheric pressure barrier discharge from aniline with simultaneous generation of carbon particles in the films. It is demonstrated that the structure of these films corresponds to one of the amorphous polymers. Carbon particles produce agglomerates with a concentration that slightly depends on the discharge energy density. The authors show that the conductivity of aniline films with carbon particles mainly depends on water saturation.

A detailed study of the general transport properties of the FT-2 tokamak shows significant isotopic difference in ohmically heated quasi-stationary plasma in high density regimes 〈n e〉 ≈ (6–9) × 1019 m−3. For deuterium, the signatures of a transition to the H-mode are found at a plasma density exceeding a certain value, while hydrogen plasma remains in L-mode in all comparable discharge scenarios. The origin of this isotopic discrepancy is studied both with energy transport analysis and direct turbulence and plasma velocity measurements performed with Langmuir probes and microwave diagnostics. A special, more complicated dynamic experimental series with current ramp up, performed in these high density regimes, demonstrated the stability and robustness of an improved energy confinement in deuterium, whereas a comparable confinement improvement in hydrogen plasma was observed.

Plasma created in focused beams of electromagnetic waves in the terahertz frequency range is a fairly new object in gas discharge physics. The specified range, located between the microwave and infrared regions of the spectrum of electromagnetic waves, is currently being actively developed. However, until recently, the study of discharge phenomena in it was practically inaccessible. Recent advances in its development are associated primarily with the creation of powerful sources of terahertz radiation—gyrotrons and free electron lasers. This article presents an overview of the latest results of studies of a gaseous terahertz discharge: gas breakdown, discharge propagation, features of the discharge glow, and prospects for a gaseous terahertz discharge as a point source of UV radiation.