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Background. In conditions of keen competition in the markets for goods and services, a huge emphasis is put on the stages of subject-wise planning, issuing design specification, and front-end engineering design when manufacturing new products. These stages are primarily responsible for the key technical and economic products’ characteristics that directly identify the product conceptual design and marketability. Current information and analytical systems (IAS) that dictate a choice of perspective directions to develop newly created products and their most preferred specimens basically use knowledge of experts about the value of estimation indicators. The latter usually serve as a basis for opting the best specimens of the newly designed technical systems. Evaluation of quality and technical level (TL) of complex technical systems using the created IAS often involves value functions (for instance, Fishburn function), which imply that a dialogue with a decision-maker (DM) produces information about his views of “value systems” or “preference systems”, used to construct value functions. Developers of new products experience considerable difficulties in choosing a value function of estimation indicators when working with IAS. Materials and methods. The paper proposes to determine a value function for numerical indicators using the newly designed information model, based on expert estimations consistent with estimation of truck TL. A technical device and algorithm to determine value functions of unit estimation CTS indicators were developed according to the method. An invention was registered, and a patent was issued. The method also implies taking random factors into account when evaluating CTS TL for, as an example, “reliability” as the key estimation indicator. Results and conclusions. Two patents of the Russian Federation were obtained for invention of a time digitizer and a device for estimating effectiveness of various systems through sampling random values. The suggested method of generating a value function enables a scientist to choose the type and nature of a value function that will allow to increase the degree of CTS TL evaluation reliability, and optimize the cost of obtaining initial information when predicting CTS reliability due to evaluation of adaptive digitalization of random processes initiated in IAS. The paper materials may be of service to designers of complex systems at the initial stages of developing thereof in evaluating possible alternatives of CTS implementation, and determining TL at all stages of CTS life cycle.

Background. The problem of evaluation of the special (singular) solutions of Clairaut-type partial differential equations attracts a lot of interest studying various transformations of nonlinear equations of mathematical physics, for example, Legendre transformations. Also this type of equations are significant in applied problems of theoretical physics, for example, in quantum field theory there is a connection between a special solution of the Clairaut-type equation and an effective action for composite fields. In a theory with composite fields, a one-loop effective action is determined by an equation containing an unknown nonlinear functional and its variational derivatives, which has the Clairaut-type form. The aim of this article is to find the conditions for the existence of singular solutions for the Clairaut-type partial differential equations, as well as, to obtain singular solutions for inverse trigonometric functions. The search of the special solutions of Clairaut-type partial differential equations for certain functions of derivatives in the equations remains poorly studied and is an interesting scientific field. Materials and methods. A method is proposed for finding singular solutions of the Clairaut-type equation with a certain function on partial derivatives, using the inverse trigonometric functions as an example. The the method is to reduce the problem of finding partial derivatives of the decision function to the problem of finding convolutions of partial derivatives of the decision function with fixed parameters. The described method is applicable for finding singular solutions of the Clairaut-type equations when the function of the derivatives of the decision function has a special form. Results. We formulate a criterion for the existence of a singular solution of the Clairaut-type partial differential equation for the case when the functions of the derivatives are the inverse trigonometric functions of linear combinations of partial derivatives. The singular solutions obtained in this paper were calculated for the case of an arbitrary number of variables, and present the main results of the paper. It is noted that in all considered cases, for a given choice of function in the equation, it is possible to solve a system that defines a singular solution of the differential equation. Conclusions. Differential equation of the Clairaut-type is a nonlinear partial differential equations of the first order. This equation is a generalization of the wellknown ordinary differential Clairaut equation. The paper describes the problem of finding a singular solution to a Clairaut-type partial differential equation for the case when the functions of the derivatives are inverse trigonometric functions. We discuss the conditions for the existence of the singular solutions and the structure of a function of derivatives for which the described method is applicable. From the course of differential equations, it is known that singular solutions of Clairaut-type partial differential equations do not always exist. Therefore, the question of finding specific functions of partial derivatives in an equation for which special solutions exist remains open and represents a promising area for further study.

This article gives information additional to the existing editions about drying and keeping herbarium between the spunbond sheets, the approach not mentioned in Kew’s «The herbarium handbook». The invention was patented: Patent no. 71212, Russian Federation, priority number 2007137443 of 09.10.2007. Spunbond, nonwoven polymeric fabric, allows to introduce technologies which might exclude paper and other moisture absorptive materials from the process of herbarium making. The idea of the new way of drying plants for the herbarium consists in creating thin air linen around the plant in the herbarium press with the use of spunbond. Thanks to the free air access, plants dry very quickly and stay flat at the same time. The plants are dried in the herbarium press with the use of black spunbond, with the density from 60 grams per square meter to 150 grams per square meter, instead of usual newspapers. In 2009-2011 Multi-purpose Herbarium Press was tried out in Central Russia, In the Northern Ural, Northern Africa and France. In all these parts of the world scientists were absolutely satisfied with the results. Spunbond can also be used for keeping the herbarium. It lasts longer and is cheaper than paper. It doesn’t break into small pieces, doesn’t absorb moister from the outside, doesn’t deteriorate because of the sun, and cannot be damaged by insects. The use of spunbond when making herbarium allows to avoid using wood (shelves and cupboards) and paper in the rooms where herbariums are kept, because they are kept on metal shelves. This will help to avoid a big number of pests, which is especially a big problem for tropical herbariums.

The paper suggests a new approach to solving the problems of conservation biology. The design of the approach was stimulated, on the one hand, by the absence of a system of theoretical concepts and adequate methods for nature conservation and restoration and, on the other hand, by the need for adequate estimation of nature preservation in the reserves. The paper analyzes classical ideas about potential vegetation and short comings of this approach for evaluating the state of plant cover and predicting its development. On the basis of a synthesis of modern concepts of synecology: hierarchical continuum, gap mosaic, mosaic cycle concept of ecosystem, natural disturbance, keystone species, ecosystem engineer and population-demographic concept – new notions of “potential ecosystem cover” and “potential ecosystem” are suggested. The paper demonstrates perspectives of using the system of synecological concepts for development of ideas about successions and climax and for model reconstruction of the potential ecosystem cover. General approaches and specifics of reconstructing the potential ecosystem cover of forests and steppes are described.

Background. The paper proposes a new method for studying differential operators with discontinuous coefficients. We study a sequence of differential operators of high even order whose potentials converge to the Dirac delta function. It is assumed that the operator’s potential is a piecewise-summable function on the segment of the operator task. At the points of discontinuity of the potential, the fulfillment of the “gluing” conditions is required to correctly determine the solutions of the corresponding differential equations. The spectral properties of differential operators defined on a finite segment with one of the types of separated boundary conditions are investigated. For large values of the spectral parameter, the Naimark method is used to obtain the asymptotics of the fundamental system of solutions of the corresponding differential equations. With the help of this asymptotics, the conditions for “gluing” the considered differential operator are studied. Then the boundary conditions of the operator under study are studied. As a result, we derive an eigenvalue equation for the operator under study, which is an entire function. The indicator diagram of the eigenvalue equation, which is a regular hexadecimal, is investigated. In various sectors of the indicator diagram, the method of successive Picard approximations has been used to find the eigenvalue asymptotics of the studied differential operators. In the limiting case, the found asymptotics of the eigenvalues tends to the asymptotics of the eigenvalues of an operator whose potential is the Dirac delta function. Materials and methods. The asymptotics of the solutions’ fundamental system of differential equations with summable potentials for large values of the spectral parameter is obtained by the generalized Naimark method. To find the roots of the equation for the eigenvalues of the operator under study, the Bellman-cook method is used to study the indicator diagram, which is a regular hexadecagon. The asymptotics of the eigenvalues of the studied differential operators in various sectors of the indicator diagram are found by the method of successive Picard approximations. Results. The spectrum of a previously unexplored family of differential operators of high even order whose potentials converge to the Dirac Delta function is studied. Taking into account the “gluing” condition at the points of discontinuity of the potentials, it is proved that the eigenvalue equation is a quasi-polynomial, the roots of which can be found by the Bellman-Cook method. Similar results can be obtained for other types of separated boundary conditions. Conclusions. The new results obtained on the asymptotics of the spectrum of a family of differential operators can be applied to the study of the basis property of the eigenfunctions of similar operators, the study of the Green’s function, and the calculation of formulas for regularized traces of operators whose sequence of potentials converges to the Dirac delta function. The delta potential method is used in physics to study short-range impurities and defects in various systems. In atomic and nuclear physics, the model of point potentials is very popular; this confirms the need to study operators with delta potentials.

Background. Printed circuit boards of modern analog, digital and digital-analog electronic devices of medium complexity and higher have a base in the form of a stack-a set of layers for various purposes, which are subsequently pressed into a single printed circuit board. The materials used for the formation of these layers play a significant role in the further performance of the electronic device, since they have different electrical, thermal and mechanical parameters that determine the advantages of a particular stack and, accordingly, the possible limitations of the device made on its basis. Materials and methods. The quality of the materials used for printed circuit boards is characterized by a variety of technical parameters that can significantly affect the characteristics of the final electronic devices. The negative impact of the materials of the printed circuit board stack can manifest itself both immediately after the manufacture of the product, and during operation, leading to instantaneous or delayed failures of various types of criticality. Results. It is established that in the conditions of production of modern electronic devices and printed circuit boards for them, including those operating in high-frequency bands, the quality of their work can be influenced by a variety of factors. The paper shows that in order to minimize the possible risks associated with various physical phenomena and the resulting parasitic parameters of printed circuit board materials, it is necessary to conduct a simulation of its operation, taking into account the possible parameters of the materials used and their impact on at least the most critical areas – the printed circuit board, the installation sites of microcircuits and other radio elements. The values of the amount of heat released per unit of its area are determined, since many characteristics of electronic components and printed circuit board materials, their performance depends on the temperature regime within which they operate. Conclusions. The performed studies allow us to exclude possible consequences of an increase in temperature in the device, for example, a change in the shape of the transmitted signals, degradation of materials, thermal expansion of the board elements and, as a result, rupture or damage to the copper tracks at the junction-the outer layer-the transition hole.

Background. This work is devoted to a connection of a variant of a supernumerary additional bronchus of the left lung’s lower lobe with a certain amount of subsegmental bronchi of the left segment six. Materials and methods. During the two-year period, we analyzed the results of 86 primary bronchoscopies (100.00%) in patients with additional bronchi in the left lung’s lower lobe of the basal pyramid. We study the connection of a variant of a supernumerary additional bronchus of the left lung’s lower lobe with a certain amount of subsegmental bronchi of the left segment six. Results. One of the variants of a supernumerary additional bronchus of the left lung’s lower lobe was suspected to be a dystopia of the subsegmental bronchus B6a to the basal pyramid area. We introduce the notions “displaced additional bronchus of the basal pyramid” and “supernumerary additional bronchus of the basal pyramid”. Conclusions. This paper states several unresolved questions of endoscopic anatomy of the left lung’s lower lobe. However, these questions cannot be resolved with a usual bronchoscopy.

Background. In the Republic of Bashkortostan, macromycete fungi are insufficiently studied. The paper presents the results of a study of the mycobiota of the Gafuriysky district of the Republic of Bashkortostan. The territory of the Gafuri district was studied during one growing season (May – November 2020), and therefore it is impossible to say that the list of fungi presented in this work is the final version. Materials and methods. Material – macromycetes fungi. Methods – practical (collection and definition), descriptive, computer-statistical. Results. The species composition of macromycetes fungi is presented in an annotated list of 44 species. A taxonomic analysis of mycobiota consisting of two divisions (Ascomycota and Basidiomycota), two classes (Pezizomycetes and Agaricomycetes), 8 orders, 25 families, and 33 genera is given. The trophic structure was analyzed. Conclusions. The predominant groups are saprotrophs on destroyed wood – Crepidotus mollis, Pleurotus ostreatus, Coprinus micaceus, etc. (27.3 %) and mycorrhizal agents – Cortinarius triumfans, Russula cyanoxantha, Russula vesca, etc. (15.9 %).

Background. One of the central tasks in microwave electronics is the construction of miniature antennas with high performance. The main equations used in modeling wire antennas of various configurations are the Pocklington, Gallen equations, singular and hypersingular integral equations. In the numerical solution of the Pocklington and Gallen equations, the methods of moments and Galerkin are mainly used. Since the Pocklington and Gallen equations belong to the class of ill-posed problems, when implementing the methods of moments and Galerkin, additional difficulties arise due to the instability of computational schemes. In this paper, to solve the Pocklington and Gallen equations, it is proposed to apply a continuous method for solving operator equations, which has the effect of regularization. This effect is due to the fact that the continuous method for solving operator equations is based on the Lyapunov theory of stability of solutions of differential equations. Materials and methods. The article investigates approximate methods for solving the Pocklington and Gallen equations. The method for constructing computational schemes is as follows. The initial equations are approximated by a system of linear algebraic equations constructed using the spline collocation method. The system of linear algebraic equations is solved by a continuous operator method. The advantages of the proposed method should be noted: 1) its stability under perturbation of the kernels of equations and right-hand sides; 2) the construction of a computational scheme allows taking into account the boundary conditions at the ends of the vibrator. Results. New stable numerical methods for solving the Pocklington and Gallen equations are constructed. The effectiveness of the proposed methods is demonstrated by solving model examples. Conclusions. The proposed method for constructing and justifying the convergence of computational schemes can be extended to equations that model various antenna modifications and are analogous to equations of the Pocklington and Gallen type.

Background. The study of Backlund 's transformations is one of the current topics in the theory of differential equations in partial derivatives. Such transformations are used to find solutions to nonlinear differential equations, including solitonic equations. At the same time, they represent an example of the differential-geometric structure generated by differential equations. Backlund transformations made it possible to obtain not only pairs of equations, but also the solution of one if the solution of the other was known. Transformation data played an important role in integrable systems, as it revealed internal relationships between different integrable properties, such as the definition of symmetry, the presence of a Hamiltonian structure. In recent years, many studies have been carried out in this area. The aim of the work is to obtain new Backlund transformations and auto-transformations for generalized Liouville’s equations with indicative-degree nonlinearity having a multiplier dependent on the first derivatives. Materials and methods. This paper examines the construction of Backlund transformations for nonlinear equations in second-order partial derivatives of salt-ton type with logarithmic nonlinearity and hyperbolic lie-neon part. The construction of transformations is based on the method suggested by Clairen for second-order equations of the Monge-Ampere type. Results. For the equations examined in the article, new equations have been found by means of the Backlund transformations, which make it possible to find solutions to the original nonlinear equations, as well as to identify internal connections between different integrable equations. Conclusions. The results are of interest in the study of nonlinear differential equations in partial derivatives, particularly soliton equations. The new equations obtained by differential linkages can be used for further research of equations of this type, as well as in solving many applications in physics and engineering.

Background. The article is devoted to technologies and virtual reality systems as comprehensive solutions for immersion of the user into virtual reality using specialized devices and interfaces. Technologies for wire/wireless transfer of audio-visual and parametric information in virtual reality systems are discussed. The purpose of the article is to analyze and summarize advantages and disadvantages of modern facilities for multimedia and parametric information transmission used in virtual reality systems. Materials and methods. The research materials used the search method of scientific publications in Russian and international journals of scientific citation databases. Results. The paper analyzes the features (advantages and disadvantages) of using virtual reality in conditions of optical information transfer, wireless protocols (WiFi, Bluetooth, Wireless USB, LIDAR, ZigBee), and wire interfaces (Display Port, HDMI, USB) that provide user communication with virtual reality system. Virtual reality forms a new artificial real world transferred to the user via various wire/wireless (WiGig (802.11ad), WiFi 6 (802.11ax), WiHD (802.15.3c), and Display Port 2.0) interfaces, taking into account physiological, physical and psychometric indicators. Conclusions. Modern technical solutions should give impetus to the creation of adaptive virtual reality with a total immersion effect, when the user cannot distinguish a virtual world from real events.

Background. The paper is devoted to certain issues of the tracheobronchial tree endoscopic anatomy and in particular to anatomical features of left lung lower lobe, which bronchoscopists often encounter. Materials and methods. The results of 5474 primary bronchoscopies (100.00 %) were studied. When evaluating the endobronchial picture, we used the tracheobronchial tree systematics according to the generally accepted classification of the lungs segmental structure by Oho K.-Amemiya R. (1984). Non-parametric McNemar test was used for the statistical assessment of the revealed anomalies of the left lung lower lobe bronchial branching frequency compared to the respective frequency in the right lower lobe, as well as for the assessment of anatomical shape features of the left lung lower lobe segmental bronchi. Results. In the left basal pyramid, the spindle-shaped form of bronchus B9 is noted in 0.86 % cases. On the right, this anatomical version has never occured. We also propose a method for differential diagnosis of the left bronchus B9 spindle-shaped form as a variant of the anatomical norm or as bronchus deformation reflecting pathological changes. We establish a statistically significant increase in the number of the basal pyramid additional bronchial tubes and “separate” B6a bronchus on the left (5.10 % and 0.68 %, respectively), compared to similar changes in the right lung lower lobe (0.42 % and 0.05 %). Differences in the frequency of additional cardiac bronchi detection did not reach the level of statistical significance. Conclusions. Additional left lung lower lobe endoscopic anatomy features (except for previously known absence of segmental bronchus B7) include: the frequent spindle-shaped form of segmental bronchus B9, a statistically significant increase in the incidence of the left lung lower lobe additional bronchi in the basal pyramid region and the “separate” bronchus B6a.

Background. The theory of solving inverse problems of mathematical physics is one of the most actively developing branches of modern mathematics. The interest of researchers in such problems is primarily due to the large number of their applications that have appeared in recent years in connection with the rapid development of physics and technology. Despite the large number of methods for solving inverse problems, at present, there is still a great need for the further development of new methods of solving that take into account the incorrectness of a number of inverse problems. In this paper, we propose numerical methods for solving one class of inverse problems, namely, problems of recovering the initial conditions for equations of parabolic and hyperbolic types. Materials and methods. The technique for constructing numerical methods for solving problems of recovering initial conditions for linear parabolic and hyperbolic equations is as follows. According to the well-known formulas for the generalized solution of linear parabolic and hyperbolic equations, a transition is made to the equivalent initial problems of linear integral equations of the first kind, which are then solved approximately using the continuous operator method. For this, an auxiliary system of linear differential equations is compiled and solved, which is then solved by the numerical Euler method. At the same time, numerical examples show that due to a suitable number of steps of the Euler method, a regularization of the solution of the problem can be achieved (if necessary). The convergence of the method is substantiated in terms of the stability theory of the solution of differential equations. Results. Numerical methods are developed for the approximate solution of the problem of recovering the initial condition for linear parabolic and hyperbolic equations. The authors have successfully applied the continuous operator method to the solution of the above problem. The solution of a number of model examples showed the effectiveness of the proposed results. Conclusions. Effective numerical methods are proposed for solving one class of inverse problems of mathematical physics, namely, the problem of recovering the initial condition in Cauchy problems for linear equations of hyperbolic and parabolic types. Numerical examples show that the continuous operator method can be successfully applied to the solution of the indicated types of inverse problems of mathematical physics.

Rationale and Goals. Recent decades have witnessed an increasing anthropogenic impact on Kalmykia’s steppe landscapes. Active oil fields, numerous filling stations and vehicles adversely affect the environment. Oil and oil products impair the growth and development of plants, not to mention that oil products are toxic to plants even at minor concentrations. The study aims at investigating phytotoxic properties of Kalmykia soils when polluted with oil and oil products. Materials and Methods. The laboratory studies were performed with the help of methods customary for biology and soil science. The work pays special attention to simulation experiments. The objects of research are key zonal soil types of the Republic of Kalmykia. The experiments have been performed in vegetation vessels and Petri dishes with oil and oil products serving as polluting agents. The target test plant is radish. Numberous research works prove that radish is a good indicator of oil pollution, and its relatively short vegetation period allows using it for laboratory experiments. The phytotoxicity was estimated by numbers of germinated seeds, lengths of sprouts and roots. Results. The work provides an insight into phytotoxicity of Kalmykia’s oil-polluted soils and reveals the influence of oils with mineralized stratal waters on the growth and development of the target test plant. The paper draws up a data series by degree of influence of oil and oil products on changing phytotoxic properties, supplemented with a data series to characterize Kalmykia soils by degree of oil pollution resistance. Conclusions. All the examined oil-polluted soils show severe phytotoxic impact on target test plant organisms, the exception being brown semi-desert soils where low-concentration of oil-fuel and kerosene pollution resulted in some extension of plant sprouts and roots length.

The paper analyzes the seasonal and long-term dynamics of marine interstitial ciliates communities as a result of the processes of system self-organization (of increasing complexity) in constantly fluctuating environment. The traits of simple structure of ciliate community include substantial variability in the composition (even in case of stable environment) and the lack of sustainable combinations of species. The mechanism of the current state maintenance is the lack of energy supply in certain periods or in specific loci of space, as well as large amplitude and unpredictable fluctuations of environmental factors. An indication of the community’s complexity is availability of stable combinations of species in time and space. The mechanisms of formation of stable species combinations are a constant flow of external energy, optimal values and stability of environmental factors (including repeatability of seasonal cycles) and the use of space resources by species according the principle of complementarity of ecological niches.