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The history of the construction of Russian fortresses (ostrog) in Siberia offers many examples, of when due to various circumstances their rapid and full-fledged building, as well as effective use failed. This is also relevant for the time of construction of new fortification facilities in the basin of the Middle and Upper Yenisei during the exploration of these territories. As a result of the conflict (“rebellion”, “shatost”) between the local administration of the Krasnoyarsk district and the garrison the latter delayed or even refused to build fortresses. The article is aimed to identify and chara terize the facts related to these phenomena. It considers the case, when, because of the actions and decisions of the all-Siberian and local administrations in a conflict with the garrison and the population of the Krasnoyarsk ostrog and the district in 1718–1720, the construction of the fort beyond the Sayan (modern Tuva), on the territory that was in the actual possessions of the Mongol khans, who were subjects of the Qing empire, was terminated. These events, rarely being in the focus of research, were called the second Krasnoyarsk “rebellion”. The article identifies and characterizes the circumstances related to it, assess their influence on decisions toward the construction of new forts, analyzes the activities of the central and local administrations to overcome such crisis situations, highlights the consequences of these actions, etc. It concludes by discussing some of the quality and features of the defense policy, regarding defense infrastructure in particular, in Siberia at the beginning of the 18th century.

In the culture and folklore of the Turkic-Mongolian ethnic groups, as well as the population of Tungus origin, despite the strong rooting of Christianity, Islam and Buddhism, elements of beliefs of their own origin are still clearly noted, including the tripartite structure of the supreme deities – Tengri (divine sky, the highest power in the universe ), Yer-sug (native earth and water) and Umai (providing fertility on earth). There is also a lot of archaeological evidence of the existence of the Umai cult. But at the same time, only in four cases on the planet there are direct indications of the exact place and natural objects where this goddess lives and from where she acts. One of them is Mount Umai and a nearby rock formation, called the “tower” of Umai, on the right bank of the Yenisei at its exit from the West Sayan Canyon. Despite the numerous mentions of the mountain in the folklore of the Khakasses, including in already published materials, it has not yet received a detailed description. The presence of a rock formation of an original form next to it was not mentioned at all in the scientific literature. Thus, an unusually shaped mountain (in the form of a female breast) and a rock formation (looking like a tower) on the Yenisei, in combination, have the characteristics of a sacred center for such a chthonic character as Umai. Both of these natural objects can confidently be included in the number of sacred places associated with it. Based on this evidence, a number of aspects of the history of migrations in Eurasia can be traced, in particular, the boundaries of settlement, the degree of mobility and interethnic contacts, mainly of Turkic-speaking, as well as the population of Tungus-Mongolian origin.

Previously, burials at Ryabchikov Klyuch-1 on the Kan River near Kansk were dated to the Late Middle Ages (pre-Russian period) and attributed to an autochthonous group. In 2015, two burials were discovered at the cemetery, with the remains of an adolescent girl and a child. A comprehensive analysis of the burial rite and grave goods suggests that the burials date to the 12th century. Numerous archaeological and ethnographic parallels were found. Morphologically, the girl’s cranium reveals generally eastern traits, specifically those common in Western Siberian (Uralic and Ob-Irtysh) populations. The cranium was restored, and a graphical reconstruction of the face was made. Burial practices of the 17th–19th century Middle Kan populations are described. They were Ket-speaking Kotts, Turkic-speaking Karagas, and Samoyed-speaking Kamasins. The analysis of sources suggests that the buried people were likely ancestors of the Kotts.

Purpose. The results of archaeological survey in 2021 along the western shore of the Krasnoyarsk reservoir in the Koksa Bay area are presented in the process of field research. Previously unknown cultural and historical objects were revealed – a quarry on Mount Bol’shoi Togurtag, presumably of medieval times, and mounds in the form of rounded stone objects at the foot of the mountain 1 250 m from the Koksa bay.Results. The material extracted from the quarry was used in the construction of these mounds, located at the foot of the mountain. This assumption is evidenced by a similar type of rock in the quarry and on the mounds (they are of magmatic origin). Previously, similar objects for this territory were not mentioned in the scientific literature. Is the technological originality in stone processing techniques evidence of the migration to this territory of any mobile group of the population from the outside, where such technology was traditional? For example, medieval Kyrgyz kurgans in the Usinsk valley of the Western Sayan, where there are many rocks of igneous origin, are similar to them in their appearance and composition of the building material. Therefore, it is logical to assume that here, on the Middle Yenisei, some group of “Usintsy” migrated, which was quite likely as part of the process of returning to their homeland of the Yenisei Kyrgyz after the Great Power era. An exhaustive answer to this question can be given in the future only after an archaeological study of the rounded stone structures located here, similar to medieval “сhaatas” and “suukter” mounds, but composed, as indicated, of material of magmatic origin, unusual for this territory, in the form of large and medium-sized blocks of “torn” forms.Conclusion. The quarry on Bol’shoi Togurtag Mount demonstrates more labor-intensive process of obtaining stone material in comparison even with the extraction of “slabs” from layers of Devonian sandstone for the construction of mounds of the Tagar culture. All of the above and determines the originality of this object among those known in Khakassia. In this regard, their further study seems to be very relevant and expedient for the formation of a complete picture of the origin of medieval archaeological sites on the left bank of the Yenisei.

Purpose. An important direction in the historical and archaeological research of the Siberian ostrogs at this stage is the solution of specific problems associated with the main events of their history. This study is devoted to solving a set of problems related to the history and archaeology of the Urtamsky ostrog in Kozhevnikovsky District of the Tomsk Region: it’s localization, the determination of the foundation date and reconstruction of its architectural appearance, taking into account its transformation over time. Results. Based on the analysis of the written sources, it is proved that the ostrog was founded in 1685, contrary to the point of view in the historiography that the ostrog was established in 1684. Based on the analysis of the written sources, cartographic material and archaeological survey data, a reasoned hypothesis is made about the location of the Urtamsky ostrog on the north-eastern outskirts of the modern village Urtam. Here, material was gathered and artifacts from plundering excavations were collected, indicating the long-term presence of the Russian population in this area. In the course of analyzing the complex of written sources, it was established that the ostrog from the moment of its foundation until the mid-1730s at least once was substantially rebuilt, which resulted in the construction of a new log wall and the replacement of the two corner barn towers with the two gate towers. An analysis of the architectural parameters of the first Urtamsky ostrog showed that the log walls were equal in height to the height of the tower log cabins (about 4 m). Only the roofs of the towers towered above the log wall. At the same time, the towers themselves had a squat appearance and served as barns. Probably, it was this circumstance that prompted S. U. Remezov to depict the Urtamsky ostrog as having no towers, since the towers, neither architecturally nor functionally, did not fully correspond to their classical appearance and purpose. It is possible that the other ostrogs, depicted by S. U. Remezov with no towers, had towers similar to those of the Urtamsky ostrog. Conclusion. The study made it possible to significantly clarify the history of the origin and the reconstruction of the Urtamsky ostrog. The prospects for further research of this object are associated with the archaeological excavations.

The problem of radiation of a radial electric dipole located on the axis of rotation of an axisymmetric body consisting of a homogeneous dielectric sphere and an external inhomogeneous dielectric layer is considered. The new numerical algorithm developed to solve the problem is based on a projection method that includes the projection of fields to transverse spherical harmonics in combination with a one-dimensional finite element method in a projection form along the radial coordinate. The algorithm is also generalized to the case in which the inner sphere is perfectly conducting. Numerical results, which characterize both the efficiency of the method and the effect of various parameters of the body on the directional pattern of the dipole, are presented.

We propose a method for two-stage compression of laser pulses, which makes it possible to shorten laser pulses of tens of picoseconds to an optical period with an energy efficiency of tens of percent. The method involves sequential use of the Raman compression (compression to a duration of tens of femtoseconds and the self-compression of the pulse to the field period when exciting the wake plasma wave. In this case, the seed pulse is focused to the input of the second gas jet to achieve the relativistic intensity required for the self-compression realization when exciting the plasma wave.

This study introduces a new southern Siberian rock art site, situated on the Unyuk Mountain, in the Minusinsk Basin, and studied in 20I6-20I7. Stylistically, the main petroglyphs date to the Late Bronze Age, i.e. late 2nd to early 1st millennia BC. Of special interest are images of oxen with ropesfixed in their noses. Such petroglyphs are rare in that region. In one case, the ox is tied to a pillar; in the other case, a man leads it. The composition consisting of a man and an ox walking in one direction is repeated thrice. All the known petroglyphic images of a man holding a rope attached to an ox’s nose were found on the right bank of the Yenisei. This may be due to the cultural and economic specificity of the southeastern, forest-steppe part of the Minusinsk Basin. At the same time, these images may be a local variant of the composition “man walking with an ox”, which occurs mainly in more southerly areas of the Altai-Sayan. Another rare petroglyph found on the Unyuk Mountain shows a pillar with a triple top. Its parallels, found at other petroglyphic sites in the Minusinsk Basin, are described. They may refer either to everyday practice or to beliefs about the dead person’s travel to the nether world.

Introduction.Construction of engineering structures is impossible without building and road machines. The large volume of financing is allocated for such machines’ purchase. The main ways of reducing costs of the equipment consist in more rational operation of the equipment and also in decrease of equipment’s cost by constructive changes. The paper demonstrates the new design of the single-bucket hydraulic excavator with smaller cost.Materials and methods.The main ways of cost reduction for construction machines are more rational operation and depreciation of a design with the required characteristics’ maintaining. The paper describes constructive changes of the working equipment of the single-bucket hydraulic excavator, which allow decreasing the production costs.Results.The authors describe the new bucket design of the single-bucket hydraulic excavator. Moreover, the authors carry out the analysis of the existing buckets’ design. The paper also illustrates the functioning on bucket forces while digging process. The authors describe the solutions of the problem for productivity increase of the single-bucket in hydraulic excavators. In addition, the authors make the scheme of the bucket loading while digging process. Such scheme helps to reduce resistance forces of digging.Discussion and conclusions.As a result, the paper presents the design of the working equipment of the hydraulic excavator’s single-bucket, which allows reducing resistance forces of digging. Such results would help to establish buckets of bigger capacity and would lead to the productivity increase.

A method for generating subrelativistic laser pulses with a sharp leading edge is proposed, which is based on Raman backscattering of an intense short pump pulse by a counter-propagating long low-frequency pulse propagating in a thin plasma layer. A thin plasma layer serves both to attenuate parasitic effects and to effectively reflect the central part of the pump pulse when the field amplitude exceeds the threshold value. A prepulse with a lower field amplitude passes through the plasma almost without scattering. This method works for subrelativistic laser pulses with durations up to 100 fs. The contrast of the leading edge of the laser pulse is determined by the seed pulse amplitude.

The generation of Raman solitons in the mid-IR range in a multicore fiber with two zero-dispersion wavelengths is studied analytically and numerically. The estimate for the maximum shift of the Raman soliton wavelength depending on the parameters of the media dispersion, the frequency-dependent losses, and the nonlinearity decreasing is obtained, which is in good agreement with the results of numerical simulation. A realistic design of a 10-core fiber made of a pair of compatible glasses is proposed for the Raman shift of the wavelength of soliton pulses propagating in an out-of-phase mode. The nonlinear dynamics of a laser pulse, specified at the wavelength of $2.3\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$, energy of 1.5 nJ, and duration of 100 fs, during propagation in a fiber with this design, is studied numerically. The generation of Raman solitons in the mid-IR range at wavelengths exceeding $4\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$, as well as dispersion waves in the $5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ range, emitted by a soliton when approaching the second zero-dispersion wavelength, is demonstrated.

An equation is derived for analyzing the self-action of a wave packets with few optical cycles in multicore fibers (MCF). A new class of stable out-of-phase spatio-temporal solitons with few cycle durations in the MCF with cores located in a ring is found and analyzed. The stability boundary of the obtained solutions is determined. As an example of using such solitons, we considered the problem of their self-compression in the process of multisoliton dynamics in the MCF. The formation of laser pulses with a duration of few optical cycles at the output of a ten-core MCF is shown.

The coherent propagation and amplification of high-power laser radiation in a multicore fiber consisting of a square array of weakly bound cores are studied. Exact stable analytical solutions are found for the out-of-phase mode, which describes the coherent propagation of wave beams in such fibers. The analytical results are confirmed by direct numerical simulation of the wave equation. The stability conditions of the out-of-phase mode in the active medium are found.

The method of the laser pulse self-compression in the process of noise-seeded Raman scattering in a plasma created by a counterpropagating ionized pulse is considered. The sharpness of the ionization front ensures the formation of an output pulse close to the $\ensuremath{\pi}$-pulse solution with a sharp leading edge. The dependence of the gain increment on the transverse wave number leads to the formation of a smooth phase front of the output pulse. The energy efficiency in the output pulse reaches 28% of the total pump energy. A study of the influence of quasistatic inhomogeneities showed only a slight slowdown in the process, even in a plasma with 8% density modulation.

Compact fiber-based sources generating optical pulses with a broadband spectrum in the mid-IR range are in demand for basic science and many applications. Laser systems producing tunable Raman solitons in special soft-glass fibers are of great interest. Here, we report experimental microstructured tellurite fibers and demonstrate by numerical simulation their applicability for nonlinear soliton conversion in the mid-infrared (-IR) range via soliton self-frequency shift. The fiber dispersion and nonlinearity are calculated for experimental geometry. It is shown numerically that there are two zero dispersion wavelengths for the core size of 2 &mu, m and less. In such fibers, efficient Raman soliton tuning is attained up to a central wavelength of 4.8 &mu, m using pump pulses at 2.8 &mu, m.

On the basis of the materials of the Sayansky Ostrog (fort), built in the Northern Sayan in 1718, we reconstruct the type of building that was common during the initial stage of the Russian colonization (1600s and 1700s). This is one of the few well preserved Russian forts. While its buildings, their function, and location are known from written sources and from the findings of a complete archaeological excavation, their construction has been hitherto unknown. To reconstruct their size and appearance, we collated archaeological and ethnographic findings, museum materials, and written evidence about the layout of buildings and construction techniques. Judging from the totality of data, we suggest the reconstructions of buildings, such as powder magazine, supply depot, barn with cellar, forge, and commandant’s house. We describe traditions and innovations in construction techniques, choice of building materials, details and blocks, layout of floors, ceilings, and roofs. The commandant’s house reproduces the architectural standards of that time, set by Domenico Trezzini, who designed buildings in the capital and in provincial Russian towns.

We study the influence of a nonstationary nonlinear response of a medium on self-compression of soliton-like laser pulses in active fibres with a finite gain bandwidth. Based on the variational approach, we qualitatively analyse the self-action of the wave packet in the system under consideration in order to classify the main evolution regimes and to determine the minimum achievable laser pulse duration during self-compression. The existence of stable soliton-type structures is shown in the framework of the parabolic approximation of the gain profile (in the approximation of the Gnizburg – Landau equation). An analysis of the self-action of laser pulses in the framework of the nonlinear Schrodinger equation with a sign-constant gain profile demonstrate a qualitative change in the dynamics of the wave field in the case of a nonsta­tionary nonlinear response that shifts the laser pulse spectrum from the amplification region and stops the pulse compression. Expressions for a minimum duration of a soliton-like laser pulse are obtained as a function of the problem parameters, which are in good agreement with the results of numerical simulation.

We consider Raman compression of laser pulses in a plasma under the conditions of an experiment planned at the Institute of Applied Physics of the Russian Academy of Sciences on the PEARL laser facility. The analysis is based on the equations describing, among other things, the effect of plasma dispersion and relativistic nonlinearity, as well as the dynamics of the field near the plasma wave breaking threshold. It is shown that the main limiting factors are excessive frequency modulation of the pump pulse and a too low plasma density in which the plasma wave breaking can occur. To reduce the negative influence of these effects, we suggest using an intense and short (on the order of the plasma period) seed laser pulse. Numerical simulation shows the possibility of a hundredfold increase in the intensity of the compressed pulse in comparison with the intensity of the pump pulse at a length of uniform plasma of 2 cm.

Two processes of shortening an intense laser pulse are discussed in a transparent plasma: self-compression at wake wave excitation (Balakin et. al, 2013) and at stimulated Raman backscattering (Malkin et. al, 1999). Studying the possibility of amplification and compression of ultrashort (up to several field periods) laser pulses in a plasma based on the process of stimulated Raman backscattering is an important task aimed at creating next-generation superpower laser systems that generate ultrashort petawatt and exawatt laser pulses. However, there is a number of negative physical processes that may limit the effectiveness of Raman amplification. Most of these negative processes have been studied and ways are suggested to neutralize them. Among the most dangerous is the nonlinear frequency shift near the threshold for the overturning of the plasma wave (Balakin et. al, 2018). The use of a highly inhomogeneous jet plasma gives a significant density gradient along the jet. Accordingly, it is possible to compensate an excessively large frequency modulation of the pump due to the use of density inhomogeneity along the gas jet. In this case, Raman compression occurs without a significant loss of energy efficiency. Using a nozzle for a gas jet in the form of a long slit allows one create a long and uniform plasma in one of the directions having a wedge shape. The possibility of obtaining a high-energy output signal using wide-aperture laser pulses in a wedge-shaped plasma is predicted. Optimal parameters of the gas jet and laser pulses are proposed to ensure high efficiency and focusability, close to the ideal case. This research was supported by the Russian Science Foundation (Project 17-72-20111).

The successful development of fiber-optic technologies in recent decades has stimulated research on the replacement of components of solid-state laser systems with fiber components, which can drastically change the attractiveness of the corresponding applied developments. Yielding on the energy characteristics of solid-state systems, fiber lasers and nonlinear optical devices have high efficiency of conversion of pump energy to radiation energy associated with waveguide geometry, high quality of the spatial profile of the laser beam, as well as low cost, compactness, lack of alignment in work process. Note that the maximum achievable radiation power in a single fiber is limited primarily by the process of self-focusing, which leads to fiber damage. The use of a multi-core fiber (MCF), consisting of identical equidistant weakly coupled optical fibers, makes it possible to realize initially coherent propagation of laser radiation with a total power noticeably higher than it can be transmitted in a single optical fiber. However, as theoretical and experimental studies have shown, such systems have its own critical power (Balakin et al., 2016) whereby the self-focusing of the quasihomogeneous distribution of the wave field and its separation into a set of incoherent structures occurs. Therefore, we have considered a small-sized optical system of 2N identical weakly coupled optical fibers arranged in a ring (Balakin et. al., 2018). In such systems, it is possible to find stable distributions of intense wave beams, which allow coherent radiation transport over long distances. The total radiation power in the found distributions can significantly (up to 2N times) exceed the critical self-focusing power in continuous media. This manifests itself most clearly for the distribution of un ~ (-1)n with antiphase fields in neighboring waveguides, which is stable at an arbitrary wave beam power. Direct numerical simulation of a nonlinear wave equation confirms the stability of the field distributions found. The research was supported by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

Based on a discrete nonlinear Schrodinger equation (DNSE), we studied analytically and numerically the peculiarities of the self-action of one-dimensional quasi-optic wave beams injected into a spatially inhomogeneous medium consisting of a set of equidistant mutually coupled optical fibers. A variational approach allowing the prediction of the global evolution of localized fields with the initially plane phase front was developed. The self-consistent equations are obtained for the main parameters of such beams (the position of the center of mass, the effective width, and linear and quadratic phase-front corrections) in the aberrationless approximation. The case of radiation incident on a periodic system of nonlinear optical fibers at an angle to the axis oriented along them is analyzed in detail. It is shown that for the radiation power exceeding a critical value, the self-focusing of the wave field is observed, which is accompanied by the shift of the intensity maximum followed by the concentration of the main part of radiation only in one of the structural elements of the array under study. In this case, the beams propagate along paths considerably different from linear and the direction of their propagation changes compared to the initial direction. Asymptotic expressions are found that allow us to estimate the self-focusing length and to determine quite accurately the final position of a point with the maximum field amplitude after radiation trapping a channel. The results of the qualitative study of the possible self-channeling regimes for wave beams in a system of weakly coupled optical fibers in the aberrationless approximation are compared with the results of direct numerical simulations within the DNSE framework.

The propagation of laser pulses in multicore fibers (MCFs) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasisoliton homogeneous solutions of the wave field in the MCF considered are found. The stability of the in-phase soliton distribution is shown analytically and numerically. At low energies, its wave field is distributed over all MCF cores and has a duration that exceeds the duration of the nonlinear Schr\"odinger equation (NSE) soliton with the same energy by many (i.e., five to six) times. In contrast, almost all of the radiation at high energies is concentrated in the central core with a duration similar to the NSE soliton. The transition between the two types of distributions is very sharp and occurs at a critical energy, which is weakly dependent on the number of cores and on the coupling coefficient with the central core. The self-compression mechanism of laser pulses was proposed. It consists in injecting such MCFs with a wave packet being similar to the found soliton and having an energy larger than the critical value. It is shown that the compression ratio depends weakly on the energy and the number of cores and is approximately equal to six times with an energy efficiency of almost 100%. The use of longer laser pulses allows one to increase the compression ratio up to 30--40 times with an energy efficiency of more than 50%. The obtained analytical estimates of the compression ratio and its efficiency are in good agreement with the results of a numerical simulation.

A mechanism for self-compression of laser pulses in a multicore fiber on the basis of nonlinear combining of radiation from many cores, surrounding the central core in a ring and its trapping into the central core in a chirp-free and pedestal-free soliton-like pulse, is proposed. It is shown that the compression ratio is weakly dependent on the energy and the number of cores in the fiber and approximately equal to 6 with an almost 100% energy efficiency. The compression ratio can be increased to 40 with an efficiency of more than 50% by using additional compression of longer pulses with approximately the same energy. The possibility of a 38-fold compression of a laser pulse to a duration of 15 fs with a pulse energy of 4 nJ in the fiber with realistic parameters was demonstrated numerically.

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrodinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

The coherent propagation and amplification of high-power laser beams in a multicore fiber (MCF) of and lattices of weakly coupled cores is studied. Exact stable analytical nonlinear solutions are found in the form of the out-of-phase distribution that describe the coherent propagation of wave beams in such MCFs. The use of these distributions makes it possible to operate with laser radiation with a power of up to 2N times of the critical self-focusing power in homogeneous media. The analytical results are confirmed by the direct numerical simulation of the wave equation. The limitations on active fiber parameters for stable amplification of the found out-of-phase solution are determined.

Propagation and amplification of intense coherent laser pulses in a multicore fiber of 24 weakly coupled cores arranged in the form of seven close-packed hexagons were studied. Exact stable analytical solutions are found for the out-of-phase mode, which describes the coherent propagation of wave beams and temporal soliton solutions in such fibers. Their stability is demonstrated. The analytical results are confirmed by the direct numerical simulation of the wave equation.

The paper studies the effect of parameters of a thin-layer copper-based coating applied by magnetron sputtering on the wear resistance of samples made of steel 18Cr2Ni4WA when working in a friction pair “18Cr2Ni4WA – cast iron GG 15”. The rational values for the thickness of the applied copper coating are determined, at which the lowest friction torque during the burn-in period and the minimum burn-in time are achieved. Jeol JCM-5700 Scanning Electron Microscope is used to study the friction track of samples and counter bodies. It is found that in the process of friction, the coating is selectively transferred from copper to the surface of the counter body, which significantly reduces the wear of the counter body.

The out-of-phase soliton distribution of the wave field was found for a multicore fiber (MCF) from an even number of cores located in a ring. Its stability is proved both with respect to small wave field perturbations, including azimuthal ones and to small deformations of the MCF structure. As an example of using this soliton distribution, the problem of laser pulse compression in an active MCF is studied. The optimal fiber parameters, the minimum duration of the output pulse, and the compression length have been found, which are in good agreement with the results of numerical simulation. In order to achieve high energies in the output laser pulse, the requirements for MCF deformations are determined.

The features of the self-action of a wave field in a small-sized optical system consisting of $2N$ identical light guides, which are disposed equidistantly along a ring, and an isolated fiber in the center are studied analytically and numerically. Stable exact solutions are found for intense wave beams in such a system, allowing long-distance coherent transport of radiation in a set of optical fibers. The total beam power in this case can exceed several times the critical power of self-focusing in the continuous medium. This is clearly manifested for the out-of-phase spatial distribution of ${u}_{n}={(\ensuremath{-}1)}^{n}f$, which is stable at arbitrary powers. Direct numerical simulation of the nonlinear unidirectional wave propagation equation confirms the stability of found wave field distributions.

Analytical and numerical studies of the coherent propagation of laser radiation in a small-sized system of weakly coupled fibers are carried out. Configurations of the wave field in a multi-core fiber are found to ensure coherent propagation of radiation with a power exceeding the critical for self-focusing in a homogeneous medium. Analogous solutions in form of temporal solitons are found in such a small-sized discrete system for pulsed laser radiation.

The self-action features of wave packets propagating in a two-dimensional system of equidistantly arranged fibers are studied analytically and numerically on the basis of the discrete nonlinear Schr��dinger equation. Self-consistent equations for the characteristic scales of a Gaussian wave packet are derived on the basis of the variational approach, which are proved numerically for powers $\mathcal{P} < 10 \mathcal{P}_\text{cr}$ exceeding slightly the critical one for self-focusing. At higher powers, the wave beams become filamented, and their amplitude is limited due to nonlinear breaking of the interaction between neighbor light-guides. This make impossible to collect a powerful wave beam into the single light-guide. The variational analysis show the possibility of adiabatic self-compression of soliton-like laser pulses in the process of their three-dimensional self-focusing to the central light-guide. However, the further increase of the field amplitude during self-compression leads to the longitudinal modulation instability development and formation of a set of light bullets in the central fiber. In the regime of hollow wave beams, filamentation instability becomes predominant. As a result, it becomes possible to form a set of light bullets in optical fibers located on the ring.

The paper presents the results of experimental studies to determine the rational technological parameters of shock-acoustic treatment (SAT) in order to provide the best antifriction properties for the outer surfaces of parts made of Steel 45. On the basis of experimentally selected processing modes, the specified values of overlap coefficients for the ultrasonic instrument and workpiece contact areas are determined. The use of shock-acoustic treatment with simultaneous application of a solid lubricant coating allows the surface microhardness to be increased almost by the factor of two and the roughness to be reduced to Ra 0.2.

A detailed theoretical analysis is carried out of the hose instability of relativistically strong laser pulses propagating in a plasma, whose duration is less than the period of a plasma wake wave. An analytic expression is obtained for the displacement of the mass center of a wave pulse, and the effect of this instability on the modification of the spectrum of laser radiation is analyzed for a wide range of initial parameters. It is shown that the development of instability is characterized by a power-law (rather than exponential) time dependence along the propagation path and does not deteriorate the self-compression of laser pulses.

Indefinite integrals arising in the projection methods applied for analysis of wave scattering by penetrable bodies of revolution in spherical coordinates are considered. Explicit expressions for the integrals of products of associated Legendre functions of different degrees and the same orders are derived. Recurrent relations for the integrals of Legendre functions of the same degrees and the same orders, as well as expressions for the indicated integrals via integrals of products of functions of the same degree but of the order smaller by unity, are obtained. All the integrals are expressed via the associated Legendre functions themselves providing a convenient algorithm for using in the MATLAB software.

The paper reviews the methods of cleaning plastic parts from flash. The principle of plant operation to obtain L. A. Yutkin electro-hydraulic effect is considered. The design of a pilot plant, as well as replaceable devices used to remove the flash from the edges of plastic parts is presented. The results of experimental studies of the electro-hydraulic effect for deflashing are presented.

The features of Raman backscattering of laser pulses in a wedge-shaped jet plasma with a significant density gradient are analyzed. The possibility of compensating for an excessively large pumping chirp due to the use of density inhomogeneity along the gas jet is shown. In this case, Raman compression occurs without a significant loss of energy efficiency. The possibility of obtaining a high-energy output signal using wide-aperture laser pulses in a wedge-shaped plasma is demonstrated. The optimal parameters of the gas jet and laser pulses are determined to ensure high efficiency and focusability, which is close to the ideal case.The features of Raman backscattering of laser pulses in a wedge-shaped jet plasma with a significant density gradient are analyzed. The possibility of compensating for an excessively large pumping chirp due to the use of density inhomogeneity along the gas jet is shown. In this case, Raman compression occurs without a significant loss of energy efficiency. The possibility of obtaining a high-energy output signal using wide-aperture laser pulses in a wedge-shaped plasma is demonstrated. The optimal parameters of the gas jet and laser pulses are determined to ensure high efficiency and focusability, which is close to the ideal case.

Excavations at the Bai-Dag I cemetery, the Eerbek River valley, Tuva, have revealed a burial rite typical of the Aldy-Bel culture, Early Scythian period. Above-ground and underground structures, principal features of the burial rite, and burial goods are described with regard to sex and age. Basic trends in the evolution of early nomadic funerary ritualism in Tuva are reconstructed.

The analytical and numerical study of the radiation self-action in a system of coupled light guides is fulfilled on the basis of the discrete nonlinear Schr\"odinger equation (DNSE). We develop a variational method for qualitative study of DNSE and classify self-action modes. We show that the diffraction of narrow (in grating scale) wave beams weakens in discrete media and, consequently, the ``collapse'' of the one-dimensional wave field with power exceeding the critical value occurs. This results in the ability to self-channel radiation in the central fiber. Qualitative analytical results were confirmed by numerical simulation of DNSE, which also shows the stability of the collapse mode.

We show that a self-focusing mode for intense laser pulses comprising less than about ten optical cycles is resistant to the transverse modulational instability. For such pulses, a method of pulse self-compression based on adiabatic decrease of the duration of a solitonlike wave packet and transverse cumulating of energy during the self-focusing in Kerr-like media with anomalous dispersion is proposed. This method can be used for generation of high-quality, high-energy, few-cycle pulses down to a single-cycle duration.

The elementary problem of scattering of an E-polarized plane wave by a circular perfectly conducting cylinder is used for verifying the efficiency of the boundary deformation method (BDM) that has recently been proposed as a generalization of the extended boundary condition method (EBCM). It is shown that the BDM can ensure the highly accurate fulfillment of the null-field condition on an interior contour spaced from the boundary in accordance with this method. However, when the accuracy of the fulfillment of the aforementioned condition on the contour near the boundary or on the boundary itself corresponds to the solution found for the current, this accuracy is substantially worse than the accuracy achieved in the case when the standard EBCM with a contour located near the boundary is applied. In addition, it is shown that, when the singularities of the wave field are enclosed by the contour chosen according to the BDM, a correct solution to the problem is not guaranteed.