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We discuss the measurements of aerosol optical depth (AOD) of the atmosphere and aerosol (NA) and black carbon (MBC) concentrations in 2018-2019 at two Arctic stations: Barentsburg (Archipelago Spitsbergen) and “Cape Baranov” (Archipelago Severnaya Zemlya). The average aerosol characteristics at “Cape Baranov” had been: AOD (0.5 μm) = 0.11, NA = 5.24 cm-3, MBC = 47 ng/m3 in 2019; and AOD (0.5 μm) = 0.07, MBC = 68 ng/m3 in 2018. The aerosol characteristics in Barentsburg, on the average, have larger values: AOD (0.5 μm) = 0.12, NA = 6.09 cm-3, MBC = 91 ng/m3 in 2019; and AOD (0.5 μm) = 0.087, NA = 6.54 cm-3, MBC = 109 ng/m3 in 2018.

In the paper we take the first steps in studying the dynamics of systems with one-sided differential constraints defined by inequalities in the phase space. We give a general definition of motion for systems with such constraints. Within the framework of the classical non-holonomic model, and also for systems with servoconstraints (according to B/eghin), we present the conditions under which the system leaves two-sided differential constraints. As an example, we consider the Chaplygin sleigh with a one-sided constraint, which is realized by means of an anisotropic force of viscous friction. Variational principles for the determination of motion of systems with one-sided differential constraints are presented.

We have developed a modified method of headspace analysis of water samples with the control of temperature and total pressure in the gaseous phase of a closed heterogeneous system followed by a gas chromatographic measurement of methane concentration with the methane content in the lake water of < 500 nl СН4/L. Here, we describe the background concentrations and vertical distribution of dissolved methane in the water column of Lake Baikal, which were obtained for several years.

Airborne backscatter lidar measurements at 532 nm were carried out over Siberia in July 2013 and June 2017. The Russian Tu-134 flew over major Siberian cities (Novosibirsk, Tomsk, Krasnoyarsk, Yakutsk), the gas flaring fields of the Ob valley and Siberian Taiga in order to sample several kinds of Siberian aerosol sources. Aerosol types are derived using the Lagrangian FLEXible PARTicle dispersion model (FLEXPART) simulations, Moderate Resolution Imaging Spectrometer (MODIS) Aerosol Optical Depth (AOD), Infrared Atmospheric Sounding Interferometer (IASI) CO total column and AOD at 10 μm. Forest fire detection is based on NASA Fire Information for Resource Management System (FIRMS) from MODIS and the Visible Infrared Imaging Radiometer Suite (VIIRS) observations and airborne in-situ measurements when available. Six aerosol type could be identified in this work: (i) Dusty aerosol mixture (ii) Ob valley industrial emission (iii) fresh boreal forest fire plumes (iv) aged forest fire plumes (v) pollution over the Tomsk/Novosibirsk region (vi) long range transport of Chinese pollution over Yakutsk. The backscatter to extinction ratio and then the corresponding lidar ratio (LR) were derived for each of these 6 identified aerosol type, using an iterative method based on the Fernald forward inversion constrained by the 10 km MODIS collection 6 AOD distribution closed to the airborne lidar observation. The LR analysis showed that the lowest LR range was obtained for the Dusty Mix case (26–40 sr) and the highest for the urban and industrial pollution from the Tomsk/Novosibirsk area (71–90 sr). The comparison is good with previous estimate of LR according to the aerosol classification. The range of lidar ratio obtained for gas flaring emission (43–60 sr) was lower than the high values encountered in the Tomsk/Novosibirk urban area and has never been characterized using lidar observations. Airborne lidar backscatter ratio vertical structure, aerosol types and integrated LR derived from the airborne data analysis were compared to nearby CALIOP overpasses. These comparisons showed three main differences with the CALIOP LR and aerosol type classification over Siberia: (i) CALIOP aerosol layer can be classified as Elevated smoke instead of Polluted continental and vice versa, but with little influence on the LR value (ii) aging and transport of aerosol layers effect on the CALIOP LR value is not always properly accounted for even when the CALIOP classification is correct (iii) the lack of discrimination between fresh and old fire plume leads to an overestimation of the optical depth for the fresh fires in the CALIOP AOD over the fire source region.

The paper presents the transfer function of the information-measuring system based on phase displacement sensors, which determines the relationship between the linear displacement value and the output voltage, or current value. An analysis of the transfer function of the measuring device is carried out by changing the phase shift of output voltage relative to the reference voltage. The obtained results can be used to control information-measuring systems. Factors affecting the initial phase of the output signal, such as sensor electrical parameters and the position of the magnetic shunt on the information line, are determined. The paper also considers the transfer function of an unbalanced sensor, in which circuit resistance of the cosine winding is not equal to circuit resistance of the sine winding. This difference complicates the equation expressing the dependence of the output voltage phase on the shunt displacement. We used mathematical modeling, in which real physical processes were described by the corresponding analytical dependencies. Amplitude-frequency and phase-frequency characteristics of the information-measuring system were obtained. They allow us to analyze errors and dynamic properties of the system, to select the optimal generator frequency for obtaining the maximum voltage at the system output, and to increase the system resistance to external factors. Recommended values for the information-measuring system are given.

Hydrophysical studies and mathematical modeling of ring structures during ice cover on Lake Baikal have shown that their existence at the stage of ice cover degradation is due to anticyclonic currents. Such currents can be generated as a result of local upwelling, which we associate with the rise of methane hydrates from the top layer of bottom sediments and their dissociation. Analysis of satellite images shows that the radii of ice rings range from 1300 to 2400 m, which is close to the baroclinic Rossby radius. The measured ice thicknesses in the area of the rings are in agreement with model calculations. Deep water renewal in Lake Baikal can also be associated with the rise of hydrates.

We discuss the problem of existence of a smooth endomorphism of a closed n-dimensional manifold carrying a differential n-form into a prescribed volume form. Of course, we assume that the integrals of these forms over the whole manifold are equal. The solution of this problem for the n-dimensional torus reduces to the problem of small denominators well known in analysis.

Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system ℋ, we mean the Schrodinger quantization of another Hamiltonian system ℋ1 for which the Hamiltonian equation is the Schrodinger one obtained by the quantization of the original Hamiltonian system ℋ. The phase space of ℋ1 is the realification ℍR of the complex Hilbert space ℍ of the quantum analogue of ℋ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of ℍ.

The results of experimental investigations of the micronozzle-chocking phenomenon under diffusion combustion of a hydrogen microjet at a high outflow velocity in the case of ignition of hydrogen near the nozzle cut are presented. It is found that the cause of micronozzle chocking is the heating of the nozzle walls from the flame-neck region retained up to transonic velocities and preventing nozzle cooling and the passage of the hydrogen jet to the supersonic-flow velocity. It is shown that hydrogen ignition far from the nozzle cut with a developed hydrogen supersonic flow into the flooded space leads to the disappearance of the flameneck region, flame detachment from the nozzle cut, and, correspondingly, termination of the nozzle heating and the possibility of the microjet coming out at the supersonic-flow velocity for the hydrogen jet. It is established that the flame-neck region is a stabilizing factor for the subsonic combustion of a hydrogen microjet up to transonic velocities. In the second case, the presence of supersonic cells stabilizes the supersonic diffusion combustion of the hydrogen microjet.

A chain of quadratic first integrals of general linear Hamiltonian systems that have not been represented in canonical form is found. Their involutiveness is established and the problem of their functional independence is studied. The key role in the study of a Hamiltonian system is played by an integral cone which is obtained by setting known quadratic first integrals equal to zero. A singular invariant isotropic subspace is shown to pass through each point of the integral cone, and its dimension is found. The maximal dimension of such subspaces estimates from above the degree of instability of the Hamiltonian system. The stability of typical Hamiltonian systems is shown to be equivalent to the degeneracy of the cone to an equilibrium point. General results are applied to the investigation of linear mechanical systems with gyroscopic forces and finite-dimensional quantum systems.

Systems of equations f 1 = ··· = f n−1 = 0 in ℝ n = {x} having the solution x = 0 are considered under the assumption that the quasi-homogeneous truncations of the smooth functions f 1,..., f n−1 are independent at x ≠ 0. It is shown that, for n ≠ 2 and n ≠ 4, such a system has a smooth solution which passes through x = 0 and has nonzero Maclaurin series.

We consider the problem of the existence of first integrals that are polynomial in momenta for Hamiltonian systems with two degrees of freedom on a fixed energy level (conditional Birkhoff integrals). It is assumed that the potential has several singular points. We show that in the presence of conditional polynomial integrals, the sum of degrees of the singularities does not exceed twice the Euler characteristic of the configuration space. The proof is based on introducing a complex structure on the configuration space and estimating the degree of the divisor corresponding to the leading term of the integral with respect to the momentum. We also prove that the topological entropy is positive under certain conditions.

The paper adduces the relators for algebraic operations on graphs using the numeric codes of the graphs. The special algebra of codes has been devised with consideration of the principles of graph transformation. This paper demonstrates the relevance of numeric coding of graphs for solving the problems of enumeration, systematization, and compact representation of the information about the structural and functional characteristics of the systems of flow distribution and conversion of rocket and space technology and for conducting the modeling transformations of given systems in the course of the structural and functional studies as well.

The objective of this work is an experimental study of the influence of initial and boundary conditions at the nozzle exit upon diffusion combustion of a hydrogen microjet. It is found that the initial mean velocity profile and the presence (or absence) of a material with large heat capacity surrounding the nozzle exit may have a pronounced effect on the flame structure and combustion of the round hydrogen microjet. The rates of fuel consumption (i.e., the efflux velocities of hydrogen) providing diffusion combustion of the round hydrogen microjet, the flame detachment, and the origination of the «bottleneck flame» in the cases of a top-hat and a parabolic mean velocity profiles at the nozzle exit are determined. The variations of the extent of «bottleneck flame» with the hydrogen flow rate are made clear. Also we examine the diminution of the extent of «bottleneck flame» with the growth of hydrogen flow rate in three cases of initial conditions at the nozzle exit.

New data on under-ice currents in Lake Baikal have been obtained with the use of high-accuracy instruments. The obtained data were used to analyze the time and space variations of under-ice currents, to calculate the coefficients of horizontal turbulent exchange and turbulent energy dissipation rates, and to derive spectral estimates of the obtained results. The estimated structures of the under-ice boundary layer near the Angara opening and far from it (up to 5 km) were compared.

Experimental data and a new model of ice buildup are used to assess and to study variations of heat flux at the water–ice interface. The latter plays an important part in ice cover formation but still is poorly known because of the lack of field temperature measurements with sufficient spatial and temporal resolution along the phase transition boundary, which knowledge gap is filled by this study.

In the paper, we study the dynamics of planar n-gons, which can be considered as discrete models of threads. The main result of the paper is that, under some weak assumptions, these systems are not integrable in the sense of Liouville. This holds for both completely free threads and for threads with fixed points that are placed in external force fields. We present sufficient conditions for the positivity of topological entropy in such systems. We briefly consider other dynamical properties of discrete threads and we also consider discrete models of inextensible yet compressible threads.

Results of measurements of optical and microphysical characteristics of atmospheric aerosol at the Mys Baranova ice base in 2018 are analyzed. Peculiarities of monthly average variability of aerosol characteristics are considered. The data are compared with the analogous (in particular, many-year) data obtained at the Barentsburg polar station and the midlatitudinal Fonovaya Observatory. The impact of transported smokes on the measured parameters is demonstrated.

This paper presents the results of a theoretical study of a fiber-optic delay line with an electro-optical modulator. On the basis of this line, radio-photon generators and frequency converters of microwave signals are performed. The results of experimental studies of such radio-photon devices are also given in this paper.

Airborne backscatter lidar at 532 nm and in-situ measurements of black carbon (BC), carbon monoxide excess above background (ΔCO), and aerosol size distribution were carried out over Siberia in July 2013 and June 2017 in order to sample several kinds of aerosol sources. Aerosol types are derived using the Lagrangian FLEXible PARTicle dispersion model (FLEXPART) simulations and satellite observations. Six aerosol types could be identified in this work: (i) dusty aerosol mixture, (ii) Ob valley gas flaring emission, (iii) fresh forest fire, (iv) aged forest fire, (v) urban emissions over the Tomsk/Novosibirsk region (vi) long range transport of Northern China urban emission. The altitude range of aerosol layers is discussed for each aerosol type, showing transport above the boundary layer for long range transport of Northern China emissions or fresh forest fire. Comparisons of aerosol optical properties, BC and ΔCO are made between aged and fresh plumes for both the urban and forest fire emissions. An increase of aerosol optical depth at 532 nm (AOD532), aerosol particle size and ΔCO is found for aged forest fire plumes. Similar results are obtained when comparing the aged urban plume from Northern China with fresh urban emissions from Siberian cities. A flight above gas flaring emissions corresponds to the largest AOD532 and provides a possible range of 50–60 sr for the lidar ratio of these aerosol plumes often encountered in Siberia. Black carbon concentrations are relatively higher for the flaring plume (0.4–0.5 μμg.m−3) than for the urban plume (0.2 μμg.m−3). The largest BC concentrations are found for the fresh forest fire plume. The aerosol type identification and AOD532 provided by CALIOP Version 4.2 data products in air masses with similar origin generally agree with the results obtained from our detailed analysis of the aerosol plume origins.

Consider a Lagrangian system with the Lagrangian containing terms linear in velocity. By analogy with the systems in celestial mechanics, we call a bounded connected component of the possible motion area of such a system a Hill’s region. Suppose that the energy level is fixed and the corresponding Hill’s region is compact. We present sufficient conditions under which any point in the Hill’s region can be connected with its boundary by a solution with the given energy. The result is illustrated by examples from mechanics.

The problem of the reversibility of the trajectories of a reversible mechanical system with a non-compact configuration space is discussed. To identify the conditions of reversibility in systems with a non-negative potential energy, an invariant Gibbs measure is used. Despite the non-compactness, the Gibbs measure of the entire phase space can be finite, which guarantees reversibility of almost all phase trajectories. Sufficient conditions for reversibility of trajectories of systems with a homogeneous, non-negative potential energy are indicated. As a consequence, reversibility of almost all phase trajectories of the Yang–Mills Hamiltonian with three degrees of freedom is established.

Data on the quality of timber used for building chapels – small buildings for public worship, enabled determination of visual criteria used for the selection of timber in the Republic of Karelia, located in the north-western part of the Russian Federation. It was revealed that as for the majority of timber structures in the region, Scots pine ( Pinus sylvestris L.) logs were selected for the chapels. Trees perceived as 'Holy' such as spruce ( Picea abies Kr.), were not used in these worship structures, in contrast to practices in the neighboring Leningrad Region. The age of the logged trees was 100–150 years, with a high proportion of young trees. Data obtained proved convincingly that compared with huge parish churches, selection of timber for these small chapels was not so strict. Multivariate analysis of variance showed that an ethnological factor played a significant role in the selection of wood for the buildings. Mature trees with narrow tree rings were preferred for worship structures preserved in villages populated by Karelians – the Baltic-Finnic tribe living in the region since ancient times. In villages with a dominantly Russian population, young pines with wide annual rings were dominantly used. A correlation between the height of the structures and the average diameter of the logs used was found with the coefficient of determination high in Karelian villages and lower in Russian villages.

This paper is concerned with the problem of the integrable behavior of geodesics on homogeneous factors of the Lobachevsky plane with respect to Fuchsian groups (orbifolds). Locally the geodesic equations admit three independent Noether integrals linear in velocities (energy is a quadratic form of these integrals). However, when passing along closed cycles the Noether integrals undergo a linear substitution. Thus, the problem of integrability reduces to the search for functions that are invariant under these substitutions. If a Fuchsian group is Abelian, then there is a first integral linear in the velocity (and independent of the energy integral). Conversely, if a Fuchsian group contains noncommuting hyperbolic or parabolic elements, then the geodesic flow does not admit additional integrals in the form of a rational function of Noether integrals. We stress that this result holds also for noncompact orbifolds, when there is no ergodicity of the geodesic flow (since nonrecurrent geodesics can form a set of positive measure).

In the second part of the present study, experimental results on the round and plane hydrogen microjets diffusion combustion at various nozzle diameter depending on microjet velocity are shown. Of special interest is the contribution to the combustion process of the so-called «bottleneck flame» region which is observed at diffusion combustion of hydrogen both in the round and plane microjets. The «bottleneck flame» appears as a spherical closed volume of laminar combustion at mixing of the hydrogen microjet with ambient air. This spherical volume is surrounded by a narrow layer of density gradient overcoming which the laminar microjet and its flame become turbulent. A diminution of the «bottleneck flame» with growth of the microjet velocity is revealed.

In the first part of this study, experimental (hot–wire and visualization) results on the effect of transverse acoustic oscillations on characteristics of round and plane air microjets at low Reynolds numbers and on their propane and hydrogen combustion are presented. In both cases, the transverse acoustic excitation results in the flame bifurcation. A phenomenon observed at the nozzle exit is the so-called «bottleneck flame». This is found both at acoustic excitation and without it at combustion of hydrogen. More details on this phenomenon are given in the second part of the study titled as: “Features of diffusion combustion of hydrogen in round and plane high-speed microjets (Part II)”.

For integrable systems with two degrees of freedom there are well-known inequalities connecting the Euler characteristic of the configuration space (as a closed two-dimensional surface) with the number of singular points of Newtonian type of the potential energy. On the other hand, there are results on conditions for ergodicity of systems on a two-dimensional torus with short-range potential depending only on the distance from an attracting or repelling centre. In the present paper we consider the problem of conditions for the existence of nontrivial first integrals that are polynomial in the momenta of the problem of motion of a particle on a multi-dimensional Euclidean torus in a force field whose potential has singularity points. These conditions depend only on the order of the singularity, and in the two-dimensional case they are satisfied by potentials with singularities of Newtonian type. Bibliography: 13 titles.

We consider two classical celestial-mechanical systems: the planar restricted circular three-body problem and its simplification, the Hill’s problem. Numerical and analytical analyses of the covering of a Hill’s region by solutions starting with zero velocity at its boundary are presented. We show that, in all considered cases, there always exists an area inside a Hill’s region that is uncovered by the solutions.

This study is devoted to experimental investigation of hydrogen-combustion modes and the structure of a diffusion flame formed at a high-velocity efflux of hydrogen in air through round apertures of various diameters. The efflux-velocity range of the hydrogen jet and the diameters of nozzle apertures at which the flame is divided in two zones with laminar and turbulent flow are found. The zone with the laminar flow is a stabilizer of combustion of the flame as a whole, and in the zone with the turbulent flow the intense mixing of fuel with an oxidizer takes place. Combustion in these two zones can occur independently from each other, but the steadiest mode is observed only at the existence of the flame in the laminar-flow zone. The knowledge obtained makes it possible to understand more deeply the features of modes of microjet combustion of hydrogen promising for various combustion devices.

We discuss conditions for the existence of invariant measures of smooth dynamical systems on compact manifolds. If there is an invariant measure with continuously differentiable density, then the divergence of the vector field along every solution tends to zero in the Ces𝑎ro sense as time increases unboundedly. Here the Ces𝑎ro convergence may be replaced, for example, by any Riesz summation method, which can be arbitrarily close to ordinary convergence (but does not coincide with it). We give an example of a system whose divergence tends to zero in the ordinary sense but none of its invariant measures is absolutely continuous with respect to the `standard' Lebesgue measure (generated by some Riemannian metric) on the phase space. We give examples of analytic systems of differential equations on analytic phase spaces admitting invariant measures of any prescribed smoothness (including a measure with integrable density), but having no invariant measures with positive continuous densities. We give a new proof of the classical Bogolyubov-Krylov theorem using generalized functions and the Hahn-Banach theorem. The properties of signed invariant measures are also discussed.

A linear transformation with an invariant being a nondegenerate quadratic form is symplectic. The geometric properties of such transformations are discussed. A complete set of quadratic invariants which are pairwise in involution is explicitly specified. The structure of the isotropic cone on which all these integrals simultaneously vanish is investigated. Applications of the general results to the problem on the stability of a fixed point of a linear transformation with a quadratic invariant are discussed.

Paradoxical formulas which have been proposed by a number of authors for evaluating divergent continued fractions are discussed. The point of the paradoxes is that limit passages (which are to be rigorously defined) result in the convergence real sequences to complex values. These formulas are refined and substantiated on the basis of the theory of uniform distribution supplemented with certain statements of complex analysis.