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Abstract: On the real line, we study the generalized Dunkl harmonic analysis depending on a parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\in\mathbb{N}$$\end{document}. The case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=0$$\end{document}corresponds to the usual Dunkl harmonic analysis. All constructions depend on the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\ge 1$$\end{document}. The differences and moduli of smoothness are defined using a generalized translation operator. The Sobolev space and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K$$\end{document}-functional are defined using a differential-difference operator. An approximate Jackson-type inequality is proved. The equivalence of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K$$\end{document}-functional and the modulus of smoothness is established.

Abstract: In this paper, we discuss new data obtained by petrographical, geochemical, geochronological, and isotopic–geochemical study of magmatic rocks within the Malmyzh and Gion gold–copper-porphyry ore fields. Geochronological data show a Late Cretaceous age of their magmatic crystallization: Cenomanian (97–99 Ma) and Campanian (76–82 Ma) ages, respectively. Based on a comparative analysis of the studied samples igneous rocks with each other and with magmatic rocks of worldwide porphyry deposits, the results of a study using a secondary ion mass spectrometer of the patterns of distribution of trace elements (REE + Y, Hf, Ti, U, Th, and Pb) in accessory zircons from igneous rocks of the Malmyzh and Gion ore fields are discussed in order to estimate their potential ore content in the gold–copper-porphyry mineralization. Despite the fact that economic gold–copper ore mineralization within the potential Gion ore field was previously unknown, an analysis of the results shows, that according to the obtained values of indicative geochemical parameters of accessory zircons, the granitoids involved in its geological structure practically do not differ from the granitoids of both the neighboring Malmyzh deposit and most of the worldwide porphyry gold–copper deposits.

Abstract: Technological analysis of the preserved structural elements of a gugu headdress (also known as boqta or bocca) from burial 2, kurgan 8, at the Peschany I burial ground in Rostov region makes it possible to reconstruct a female headdress made up of a low column-shaped cylindrical frame with a bootlike capital. Additional studies suggest that the outer surface of the headdress elements made of birch bark was painted with red pigment and that the headdress was covered with a twill-weave cloth. The comparative analysis with Mongolian headdresses from Orenburg, Astrakhan, and Volgograd regions provide an opportunity to discuss general stylistic and technological methods of making gugu hats as well as distinctive stylistic solutions. The radiocarbon date obtained for this assemblage from the Peschany I burial ground places the discovered headdress between the end of the 13th century and the early 14th century, it can be considered to be the first radiocarbon date that provides an estimate of the period when such items were in use in the Lower Don and Volga regions.

Abstract: A generalization of the Dunkl transform can be the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k,a)$$\end{document}-generalized Fourier transform, but it deforms good classes of functions, for example, the Schwartz space. In this paper, we study the nondeformed generalized Dunkl transform on the line. Two generalized translation operators are defined. Integral representations are obtained for them and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}-boundedness is proved. Two convolutions are defined for which the Young theorem is established. As an application, we study conditions for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}-convergence of generalized means.

Abstract: For the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k,1)$$\end{document}-generalized Fourier transform on the real line \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}$$\end{document}, the Riesz transform is defined. For this transform, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-inequalities with power and piecewise power weights are proved for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<p<\infty$$\end{document}.

Abstract: A comparative morphological study of the structure and distribution of sensilla on the maxillary and labial palps in caddisflies of the family Hydropsychidae was performed. Morphology of palpal sensilla was studied by scanning electron microscopy in 17 species from 12 genera. The palps of the studied species have four types of sensilla: long trichoid, chaetoid, campaniform, and petaloid; at the same time, no basiconic and pseudoplacoid sensilla were found on the palps. All the studied species lack apical sensory complexes at the tips of both pairs of palps, where only long chaetoid sensilla are present. Petaloid sensilla form sensory fields on the 4th (in Arctopsychinae) or on the 3rd and 4th segments (in Diplectroninae, Hydropsychinae, Macronematinae) of the maxillary palps, but sensilla of this type are never present on the labial palps. The sensory fields include from 5–10 sensilla in Hydropsychinae to 40 sensilla in Arctopsychinae.

In this study, three different ilmenite-limonite (ILC) concretes were modeled in terms of determining the effect of filler type and filler size on the enhancement of radiation shielding properties in the 0.142–1.33 MeV gamma-ray energy range. Accordingly, ILC concrete, micro (50 µm) and nano (50 nm) WO3, and micro (50 µm) and nano (50 nm) PbO filler added ILC samples were modeled. MCNPX simulations of micro- and nano-sized particles inside of the ILC sample were performed using lattice (LAT) and universe (U) features of MCNPX (version 2.7.0) code. The greatest increase in mass attenuation coefficient was reported from micro-PbO to nano-PbO filler as 7.88% at 0.142 MeV energy value. The study’s findings indicated that decreasing the particle size of the additive material decreases the mean free path and so increases the quantity of gamma radiation interacting per unit distance. Although we validated the consistency of our input against the standard NIST database, several points, such as experimental investigations of nanoparticles in ILC concrete, nanoparticle distributions, and the effect of this distribution on overall shielding enhancement, should be investigated further.

Abstract: A comparative morphological study of the structure and localization of antennal sensilla in scorpionflies (Mecoptera) was carried out. Scanning electron microscopy was used to study the morphology of antennal sensilla in four species from the families Panorpidae, Bittacidae, Nannochoristidae, and Boreidae. According to our new findings and the literature data, seven types of sensilla are present on the antennae of Mecoptera: long trichoid, short trichoid, chaetoid, campaniform, basiconic, coeloconic sensilla, and Böhm’s bristles. The antennal sensory apparatus in the studied species is represented mostly by long trichoid and basiconic sensilla. Specialization is manifested only by a few coeloconic sensilla, which show specific distribution on the segment surface. The basiconic sensilla are more common at the anterior segment margins, and they form clusters in one species of Boreidae. Comparison with the related orders shows reduced diversity of sensilla in scorpionflies.

Abstract: A comparative morphological study of structure and localization of antennal sensilla in the caddisfly superfamily Psychomyioidea was carried out for the first time. The morphology of antennal sensilla was studied using scanning electron microscopy in 21 species from the families Psychomyiidae (6), Xiphocentronidae (1), Dipseudopsidae (3), Polycentropodidae (9), and Pseudoneureclipsidae (2). Seven types of antennal sensilla were revealed in the studied species: long trichoid, curved trichoid, chaetoid, basiconic, coronary, styloconic, and pseudoplacoid. The distribution of different types of sensilla in the studied families mainly corresponds to the ground plan of the antennal sensory surface in Trichoptera. Long trichoid and pseudoplacoid sensilla usually have nonspecific distribution; chaetoid ones have fixed distribution; basiconic, coronary, and styloconic sensilla have specific distribution. Sensory fields of curved trichoid sensilla are located on the basal antennal segments, always on their ventrolateral surfaces. Three types of shape of sensory fields were revealed in the studied species. The antennal sensory surface is generally conservative in species of the superfamily Psychomyioidea, but particular evolutionary lineages show modifications in the structure and localization of sensilla.

A novel device for fast visualisation of gas-liquid two-phase flows was developed and tested during loss-off-coolant accident simulations at the thermal hydraulic test facility PSBVVER, a 1 : 300 integral model of the VVER-1000. The device is an ultrasonic mesh sensor. It consists of a metallic frame where transmitter and receiver wave-guides are fixed, that form two grids inside the measurement cross section. Ultrasonic pulses are transmitted into the fluid by the 8 wave-guides of the first plane. A second plane of another 8 wave-guides, that cross the ones of the first plane under an angle of 90 deg, serves as receives. The measurement is based on the acoustic conductivity of the two-phase mixture at the locations where the wave-guides cross. The sampling frequency is 250 frames per second. This allows both void fraction measurements and a fast flow visualisation. The sensor is applicable to high pressures and temperatures. All parts and surfaces that are in contact with the fluid are manufactured from stainless steel. During the tests at PSB-VVER the flow pattern in the hot leg of the primary circuit model was visualised for the first time.

Abstract—: The second part of the article (see the beginning in No. 6-2021) analyzes the negative consequences of the so-called health care optimization. It is shown that as a result of its implementation, the availability of medical care has decreased. A possible way to improve the territorial organization of medical services is considered. The effectiveness of the Russian health care system in the fight against the coronavirus pandemic was assessed.

Cyber-physical systems are widely used in energy systems, industry, and the economy. This type of systems allows intelligent resource management of systems of this class, in order to optimize pre-selected processes. This study presents a cyber-physical system for smart infrared heating control. The system is based on the following technologies: Lora, IoT, and fuzzy control. The structure of the cyber system is presented in details. Then the functionality of the developed system is presented and its advantages and application in production, industry, and economy are shown. The results of the study show that the developed cyber-physical system reduces electricity consumption and provides optimal working conditions. The system also allows expansion and application for multiple rooms, thanks to its architecture and applied technologies.

Abstract: We study the problem of P. L. Chebyshev (proposed in 1883) concerning the extreme values of moments of nonnegative polynomials with weight on the interval \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1,1]$$\end{document}at a fixed zero moment, as well as this problem in a more general form. In the case of the first moment , the problem was solved by P. L. Chebyshev (1883) in the case of unit weight and by G. Szegö (1927) for an arbitrary weight. We have previously obtained a solution to Chebyshev’s problem for moments of odd order, which is largely based on the monotonicity of the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^{2k+1}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\in\mathbb{N}$$\end{document}. The function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^{2k}$$\end{document}is not monotone on the interval \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1,1]$$\end{document}, and the problem for moments of even order becomes more difficult. The paper provides a solution to Chebyshev’s problem on the largest values of moments of even order for polynomials of even degree. The problem of the smallest value of the second moment for polynomials of even degree is solved under an additional condition for the weight.

Abstract—: The paper (part 1) analyzes the dynamics of indicators characterizing the state of health of the Russian population. A comparative analysis of the development of healthcare in Russia and other countries is carried out. The conclusion is confirmed that the main problem in the development of Russian healthcare is the insufficient volume of public funding. The drawbacks and limited potential of the adopted funding model are assessed. A possible way to increase public funding is proposed. It is shown that the availability of medical care is reduced as a result of the so-called optimization of healthcare. A possible way to improve the territorial organization of medical services is considered. The effectiveness of the Russian healthcare system in the fight against the coronavirus pandemic is assessed.

Abstract: Primary CKα, NKα, and OKαspectra are recorded in single crystals of carbonates, nitrites, and nitrates by the electron probe microanalysis (EPMA). The shift and width of the Kαlines are used for determining the patterns of variations in charge and spin densities around the emitting atom in the low-dimensional magnetics. The method has made it possible to obtain experimental knowledge about the indirect exchange interaction in the study samples of single crystals, including micron-sized ones at room temperature. The structure of resonance levels (plasmons) is identified in the nitrogen spectra in nitrates and nitrites in the conduction bands.

This paper details the development and testing of the first working prototype of the S-band high-power klystron, accomplished at the Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences (BINP SB RAS). Upon testing, the klystron demonstrated the following parameters: an operating frequency of 2856 MHz and a peak power output of 50 MW. The paper presents the klystron's design, its constituent units, and pertinent processing procedures, along with discussions on the measurement of its parameters.

Abstract: The relaxation processes in polycrystalline PZT films formed on silicon substrates have been studied during a quasi-static change in an external electric field. The dielectric relaxation is shown to be characterized at least by three relaxation times depending on the direction of the self-polarization in the film, the value of the polarizing field, and also the PZT film annealing temperature.

Communicated by Ramaswamy H. Sarma

Abstract—: The second part of the article (see the beginning in No. 5, 2019) presents the scenarios of forecast calculations for formulating guidelines for social policies to ensure the recovery of the growth of the Russian economy. A comparative analysis is given of measures to stimulate the economy and the underlying theoretical structures used in Europe, the United States, and China.

We define a fractional power of the Dunkl Laplacian, a fractional modulus of smoothness, and a fractional K-functional on Lp-spaces with Dunkl weight. As an application, we extend our previous results and prove direct and inverse theorems of approximation theory and some inequalities for entire functions of spherical exponential type in the fractional setting.

The list of the caddisfly species found in the Langkawi Island has 68 species from 31 genus and 15 families, 24 of which are new to the fauna of Malaysia. A new species from the family Ecnomidae, Ecnomus jubilaearissp. n.is described.

The structure of pseudoplacoid sensilla characteristic of Amphiesmenoptera was studied by SEM and TEM methods by the example of the mushroom-like sensilla in Philopotamus montanusDon., a member of the primitive family Philopotamidae. These sensilla were found to be different from the externally similar placoid sensilla in the presence of a socket-like depression and a sensillar stem arising from it. The expanded terminal part filled with the dendrites of the sensory neurons has numerous pores on its upper and lower surfaces. The sensillar dendrites have subterminal expansions filled with electron-transparent fluid, while their thin terminal parts have electron-dense central elements. The pseudoplacoid sensillum of Ph. montanuscomprises three sensory neurons. The mushroom-like pseudoplacoid sensilla of Ph. montanusare compared with chemoreceptive sensilla of other insects.

Investigation of the antennal surfaces in four species of the family Ecnomidae (Ecnomus insularis, E. maheensis, E. jethet, and E. tenellus) has revealed the presence of antennal structures including long trichoid, curved trichoid, mushroom-like pseudoplacoid, basiconic, styloconic, and chaetoid sensilla, as well as Böhm’s bristles. The mean number and diversity of the sensilla decrease toward the antenna apex. Interpopulation differences in the size and numbers of sensilla, mostly the curved trichoid ones, were observed in the widespread species Ecnomus tenellus, for the first time in insects. Quantitative differences in the composition of sensilla were found between all the studied species; these differences are probably adaptive. The evolutionary significance of the revealed divergence is discussed.

This paper presents the results of comparative field tests of rangefinders with an eye-safe radiation wavelength of λ=1.54  μm and a radiation wavelength of λ=1.06  μm under the same weather conditions. It was shown that the rangefinder with the radiation wavelength of λ=1.54  μm provides similar parameters for measuring the distance as the rangefinder with the radiation wavelength of λ=1.06  μm at significantly lower output radiation energies (by a factor of 3 to 4).

The spectroscopic characteristics and luminescence decay kinetics of Sr9Sc(PO4)7:Pr3+(1%) were investigated using synchrotron radiation of ultraviolet (UV), vacuum ultraviolet (VUV) and X-ray ranges, as well as pulsed cathodoluminescence (PCL) methods at temperatures of 10, 90, and 295 K. The luminescence spectra contain three groups of bands and lines. In the UV range, the observed bands correspond to interconfigurational 5d→ 4ftransitions in Pr3+ions. In the visible spectrum, the wide luminescence band of defects dominates, as well as narrow lines associated with intraconfigurational 4f→ 4ftransitions in Pr3+ions. When excited by an electron beam (5 Hz), the main component with a decay time τ ∼ 17 ns dominates in the decay kinetics of the 5d→ 4fluminescence. The decay kinetics of 5d→ 4fluminescence upon excitation with high-frequency (τ ∼ 8 MHz) synchrotron radiation of the X-ray range contains a fast component (τ ∼ 15 ns) against the background of the slow component of the μs-range. An effective nonradiative energy transfer is observed from impurity centers to defects, as well as from the host to Pr3+ions and defects.

A sharp Jackson inequality in the space Lp(ℝd), 1 ≤ p< 2, with Dunkl weight is proved. The best approximation is realized by entire functions of exponential spherical type. The modulus of continuity is defined by means of a generalized shift operator bounded on Lp, which was constructed earlier by the authors. In the case of the unit weight, this operator coincides with the mean-value operator on the sphere.

We report on the development of plasma-based sources of extreme ultraviolet radiation for the next-generation lithography and mask inspection and the development of equipment for spectral diagnostics of such sources.

Porous ceramic materials based on oxide fibers, which have lower specific density and thermal conductivity, are able to function at temperatures exceeding 1000°C, including in an oxidizing atmosphere, which allows this class of materials to have a wide range of applications in various industries. The disadvantage of such materials is the hydrophilicity caused by the chemical composition of the fibers and the highly developed porous structure, which severely limits their use, particularly in arctic and subarctic climates characterized by high humidity. The authors have investigated and proposed a method of hydrophobization using the technology of low-temperature postradiation graft polymerization of tetrafluoroethylene molecules. The technology makes it possible to apply polymer coatings to oxide fibers, providing high hydrophobic properties, which is manifested in the increased value of the contact angle of wetting the surface of the material, which in turn substantially improves their operational characteristics and expands the possibilities of practical application as heat-shielding and heat-insulating materials.

Methods and relevant software were developed to study frequency dispersion parameters of wideband high‐frequency (HF) radio channels over propagation paths of different lengths: near vertical incidence skywave paths (up to 500 km) and long‐distance radio paths (from 1,000 up to 3,500 km). We developed a universal ionosonde (in terms of methods and signals) to do experimental research into HF radio wave propagation and dispersion using software‐defined radio technology and platform Universal Software Radio Peripheral N210. The multipurposeness of the ionosonde is manifested in the sounding methods used (oblique incidence and vertical incidence) as well as in the spread spectrum signals used (binary phase shift keying, frequency modulated continuous wave, and frequency modulated interrupted continuous wave). The characteristics of the megahertz‐bandwidth HF channels were studied. The dependences of the variation of the third‐order dispersion parameter on the time of day, the radio path length, and the channel carrier frequency were experimentally found. A method for obtaining dispersion characteristic and calculating impulse response of wideband channels depending on the dispersion parameters was developedData on the third‐order dispersion parameters was obtained depending on a midband frequency of a megahertz‐bandwidth HF channel as well as on the path lengthThe developed SDR‐based universal sounding system is an effective tool for studying HF radio wave propagation and dispersion in the ionosphere