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Despite the fact that the representation of epithelium as a tessellation of a plane into polygons has existed for several centuries, it is still not clear exactly how cellular geometry affects the transformation from plane epithelial monolayers into structures with complex geometry. In this work we study the topological characteristics of cell packing depending on the shape of the epithelium. More than 50 micrographs of plane and spherical epithelium were analyzed. The average topological defectiveness of flat and spherical monolayers is compared. The obtained distributions of cells according to the number of their neighbors demonstrate a previously unknown difference between spherical and planar cases. Topological defects in the packing of these cells are also analyzed in the work. In contrast to more ordered abiotic packings, it is impossible to distinguish linear topological defects in the form of scars or pleats in the spherical monolayers of investigates cells.

The attenuation of the acoustic-gravitational nondivergent f-mode and inelastic γ-mode in the Earth’s upper atmosphere due to viscosity and thermal conductivity is studied. To analyze the attenuation, a system of hydrodynamic equations is used, including the modified Navier–Stokes and heat transfer equations. These modified equations take into account the contribution of the background density gradient to the transfer of energy and momentum by waves. Dispersion equations are obtained for f- and γ-modes in an isothermal dissipative atmosphere. It is shown that viscosity and thermal conductivity have little effect on the frequency of these modes under typical conditions in the thermosphere. Expressions are obtained for the damping decrements of the f- and γ-modes. It was established that the decrement of the γ-mode attenuation is almost an order of magnitude higher in the Earth’s thermosphere than the corresponding decrement of the f-mode. It is also found that the attenuation of the f-mode does not depend on the thermal conductivity but is due only to the dynamic viscosity and increases with an increase in the relative contribution of the bulk viscosity. The dissipation of the γ-mode is caused by dynamic viscosity and thermal conductivity and does not depend on the bulk viscosity. The time variation of the perturbation amplitudes for the f- and γ-modes at different heights of the thermosphere is considered. The characteristic attenuation times of the f- and γ-modes at different heights depending on the wavelength, as well as at different levels of solar activity, are calculated. The boundary heights in the thermosphere above which the f-and γ-modes cannot exist due to dissipation are determined.

The propagation of evanescent acoustic-gravity waves in the atmosphere with an arbitrary altitude temperature profile is investigated. The possibility of the existence of two types of evanescent wave modes in a vertically nonisothermal atmosphere is shown. The first type is the f-mode in which the dispersion does not depend on the altitude inhomogeneity of temperature and, therefore, is carried out at any altitude level of the nonisothermal atmosphere. The second type is a recently discovered $$\gamma $$ ‑mode in which the dispersion depends on the altitude temperature gradient and can be fulfilled only at certain altitude intervals. The possibility of realizing the f- and $$\gamma $$ - modes in the Earth’s atmosphere is considered, taking into account the model altitude temperature profile. It is shown that these modes can exist at the heights of local temperature extremes in the atmosphere. Moreover, they are realized only in a narrow range of spectral parameters for which the conditions for a decrease in the wave energy above and below the level of their propagation are satisfied. For the f-mode, this energy condition is fulfilled at the altitudes of the local temperature minima, while that for the $$\gamma $$ -mode is at the altitudes of the local maxima. Recommendations are given regarding the possibility of observing these modes in the atmosphere of the Earth and the Sun. In the Earth’s atmosphere, the f-mode can presumably be observed near the mesopause with the characteristic wavelength $${{\lambda }_{x}} \approx 75\,{\text{km}}$$ and in the solar atmosphere at the heights of the chromospheres with $${{\lambda }_{x}} \approx 1600\,{\text{km}}$$ . The period of the f‑mode propagating in the region of the temperature minimum slightly exceeds the Brent-Vaisala period at this altitude. In the Earth’s atmosphere, the $$\gamma $$ -mode can be realized in the regions of maximum temperature, for example, at the height of the stratopause with $${{\lambda }_{x}} \approx 100\,{\text{km}}$$ and a period slightly larger than the Brent-Vaisala period at the altitude of its propagation.

A new approach to the study of acoustic-gravity waves in the Earth’s atmosphere in the presence of vertical temperature inhomogeneity is proposed. Using this approach, the local AGW dispersion equation was obtained for the atmosphere with a small vertical temperature gradient. The modification of the acoustic and gravitational regions of freely propagating AGWs on the spectral plane $$\left( {\omega ,{{k}_{x}}} \right)$$ depending on the temperature gradient was investigated. It is shown that the acoustic and gravitational regions approach each other with a positive temperature gradient, while the distance between them increases with a negative gradient. On the spectral plane, the indicators of the location of the acoustic and gravitational regions of freely propagating AGWs are the dispersion curves of the non-divergent and inelastic horizontal wave modes. The possibility of overlapping the acoustic and gravitational regions of AGWs in a nonisothermal atmosphere was investigated.

Within the model of a dissipative isothermal atmosphere, the attenuation of acoustic−gravity waves (AGWs) is studied on the basis of the modified Navier−Stokes and heat-transfer equations. Besides the usually considered velocity gradient, the modification of these equations takes into account the additional transfer of the momentum and energy induced by AGWs due to the density gradient. This results in that additional terms appear in the hydrodynamic equations of motion and heat transfer. Under these assumptions, the local dispersion equation for AGWs in an isothermal dissipative atmosphere, as well as an expression for the damping decrement, is obtained. In the limiting cases of high frequencies (sound waves) and low frequencies (gravitational waves), the nature of the attenuation allows a clear physical interpretation. Special aspects of the time-dependent attenuation for the evanescent acoustic−gravity modes of various types, including the Lamb waves and Brent−Vaisala oscillations, are also considered.

As is known from multiyear theoretical and experimental studies, acoustic−gravity waves (AGW) determine the dynamics and energy balance of the atmospheres of planets and the Sun to a considerable extent. Linear wave perturbations in the atmosphere can be described with a system of second-order equations for the vertical and horizontal components of the perturbed velocity. It follows from this system that small perturbations in the atmosphere may be considered as oscillations of coupled oscillators with two degrees of freedom. This suggests that it is worth studying more thoroughly the linear acoustic−gravitational wave modes in the atmosphere with well-developed methods of the theory of oscillations. To study small perturbations in the Earth’s atmosphere, the methods of the theory of coupled oscillatory systems were used. It has been shown that acoustic−gravity waves in an isothermal atmosphere can be considered as a superposition of oscillations that occur simultaneously at two natural frequencies—acoustic and gravitational. The equations for the natural frequencies of oscillations, as well as for the components of the perturbed velocity under specified initial conditions, were derived. From the analysis of temporal changes in the components of the perturbed velocity, new features in their behavior were found. All solutions are presented with the use of real quantities only. This representation is more convenient for comparison with observational data than the complex one commonly used in the theory of acoustic−gravity waves. The conditions under which the usual single-frequency oscillation mode can be realized in the atmosphere are analyzed. The results of the study can be used to explain some features in space-borne observations of wave perturbations in the Earth’s atmosphere that do not fit the framework of the known theoretical concepts.

Available 2-chloro-3-nitropyridines were used to synthesize new representatives of 6-substituted 3-benzoylisoxazolo[4,3-b]pyridines, which were found to react with neutral C-nucleophiles to give 1,4-addition products.

We present in detail the algorithm of the electrostatic–quasi-stationary–electromagnetic/MHD approximations and equivalent external sources (EQUEMES method) to develop the quasi-stationary–electromagnetic models of seismo-ionospheric coupling. The penetration of the electromagnetic field created by near-Earth alternative currents of ULF range was simulated by solving equations for the horizontal electric field components Ex, Ey of the second order with respect to the vertical coordinate z. This system of two second-order equations is derived from the system of Maxwell equations. The penetration of rather strong horizontal electric field [of order of (1–10) mV/m] to the ionospheric E and F layers has been modeled. The corresponding variations in the electron concentration in the E and lower F layers of the ionosphere reach a value of order of (1–10)%. Farther increase in these variations can be connected with the related synergetic processes. A possibility of the effective initiation of electron concentration perturbations in the unstable near-equatorial plasma in the F layer of the ionosphere by the packet of atmospheric gravity waves radiated by the near-ground source is illustrated. A good correspondence of the results obtained on the basis of this model to the data of satellite observations is shown.

The problem with the penetration of electric fields from atmospheric near-Earth electric current sources to the ionosphere is investigated both within the dynamic simulations of the Maxwell equations in the frequency domain and within the simplified quasi-electrostatic approach. Two cases of the geomagnetic field lines are considered. The first case is the penetration of the geomagnetic field lines deeply into the magnetosphere (open field lines), whereas the second one is the return of these lines into the Earth’s surface (closed field lines). The proper boundary conditions are formulated. It is demonstrated that in the case of the open field lines the results of the dynamic simulations differ essentially from the quasi-electrostatic approach, which is not valid there. In the case of the closed field lines, the results of simulations are practically the same both within the dynamic approach and within the quasi-electrostatic one. From realistic values of the densities of atmospheric electric currents ~0.1 µA/m2, the values of the electric fields within the ionosphere F-layer may reach about 1–10 mV/m.

The objects of research in this work are evanescent wave modes in a gravitationally stratified atmosphere and their associated pseudo-modes. Whereas the former, according to the dispersion relation, rapidly decrease with distance from a certain surface, the latter, having the same dispersion law, differ from the first by the form of polarization and the nature of decrease from the surface. Within a linear hydrodynamic model, the propagation features of evanescent wave modes in an isothermal atmosphere are studied. Research is carried out for different assumptions about the properties of the disturbances. In this way, a new wave mode – anelastic evanescent wave mode – was discovered that satisfies the dispersion relation ω2=kxgγ-1. Also, the possibility of the existence of a pseudo-mode related to it is indicated. The case of two isothermal media differing in temperature at the interface is studied in detail. It is shown that a non-divergent pseudo-mode with a horizontal scale kx∼1/2H1 can be realized on the interface with dispersion ω2=kxg. Dispersion relation ω2=kxgγ-1 at the interface of two media is satisfied by the wave mode, which has different types of amplitude versus height dependencies at different horizontal scales kx. The applicability of the obtained results to clarify the properties of the f-mode observed on the Sun is analyzed.

1,3-Dipolar cycloaddition of various 2-substituted 3,5-dinitropyridines and unstabilized N-methyl azomethine ylide has been studied. It was found that, depending on the nature of the substituent, the reaction results in addition of one or two equivalents of 1,3-dipole to the pyridine ring. Eventually, a convenient method for the synthesis of differently substituted heterocyclic systems containing one or two pyrrolidine fragments fused with a pyridine ring has been demonstrated.

A new analytical model has been developed to determine the characteristics of the VLF complex eigenmodes in the waveguide Earth-Ionosphere (WGEI). The developed analytical model, in combination with appropriate numerical methods, provides all important characteristics of (i) complex eigenmodes and their excitation by external electric current source in WGEI, (ii) radiation from WGEI of ELF waves into the upper ionosphere/magnetosphere. After propagation of electromagnetic waves over a certain distance (~ 100 km) from input antenna, either set of complex modes or input boundary conditios for an effective beams may be determined and then the theory [1] for coupled VLF beams in WGEI may be applied. This approach is considered in the context of Nonlinear evolution equations for wave processes in layered structures (NEELS) method for modeling wave processes in layered artificial/natural media [2] (i) taking into account importance of boundary conditions at the input of waveguide region, where the external current source is located, as well as complex impedance boundary conditions at WGEI boundaries [1] and (ii) using appropriate system of evolution equations for coupled wave beams. The measurements of VLF in Japan (from Hayakawa Institute of Seismo Electromagnetics) were used in this study. Fluctuations in VLF amplitudes are revealed with the periods of (i) 2-3 hours; (ii) 5-10 minutes corresponding to the fundamental mode of acoustic-gravity waves (AGW) near the Brunt–Väisälä period (to the best of our knowledge for the first time it has been done based on VLF signals). There is also a weekly antropogenic trend in VLF data. Since 2019, a number of VLFs and LFs signals (radiated mostly by European transmitters) have been monitored at NCCSSAU and demonstrate the quasi-wave disturbances with periods of ~10 minutes. The analysis of the relevant data indicates the need to eliminate the impact of hardware effects. Significant influence on the distribution of TEC geomagnetic perturbations was found, in particular, during analysis of St. Patrick's Day geomagnetic storm (March 17, 2015). To use global TEC maps for studying ionospheric processes, including possible precursors of the most powerful earthquakes, it is recommended to use data with less then one minute time resolution. Different spectral methods for data processing and entropy approach for detecting pre-catastrophic state of LAIM system are discussed. The developed methods can be useful for ionospheric monitoring of catastrophic events in the LAIM system, based on the complex studies (i) of ionospheric disturbances in VLF and TEC, in particular caused by the same source located in the lithosphere/lower atmosphere, magnetosphere or ionosphere; and (ii) the impact of AGW on VLF characteristics in WGEI. [1] Rapoport Y., Grimalsky V., … Grytsai A., Fedun V. et al. Model of propagation of VLF beams in the waveguide Earth-Ionosphere. Principles of tensor impedance method in multilayered gyrotropic waveguides , Ann. Geo., 2020, 38, 207–230.[2] Boardman A.D., Alberucci A., … Rapoport Yu. G., … Ivchenko V.M. [et al.]. Spatial Solitonic and Nonlinear Plasmonic Aspects of Metamaterials // World Scientific Handbook of Metamaterials and Plasmonics, 2017, 4, 419-469.

A simple method has been proposed to determine acoustic-gravity wave (AGW) characteristics at lower ionosphere (mesosphere) heights by measuring VLF radio signal amplitudes. For relatively short radio paths (less than ∼ 1500 km long) we obtained the simple relations for estimation of AGW neutral density fluctuation and for vertical displacement of an elementary volume of atmospheric gas. The proposed method has been verified by using VLF radio wave amplitude measurements on several radio paths. AGW properties based on these measurements are approximately calculated at heights of radio signal reflection. The relative fluctuation of 3%–6% of neutral particle concentration and elementary volume displacement of 0.6–1.2 km have been obtained. These results are in good agreement with AGW theory in the Earth atmosphere.

A number of novel 6-R-isoxazolo[4,3-b]pyridines were synthesized and their reactions with neutral C-nucleophiles (1,3-dicarbonyl compounds, π-excessive (het)arenes, dienes) were studied. The reaction rate was found to be dependent on the nature of the substituent 6-R. The most reactive 6-nitroisoxazolo[4,3-b]pyridines are able to add C-nucleophiles in the absence of a base under mild conditions. In addition, these compounds readily undergo [4+2]-cycloaddition reactions on aromatic bonds C=C(NO2) of the pyridine ring, thus indicating the superelectrophilic nature of 6-NO2-isoxazolo[4,3-b]pyridines.

The peculiarities of acoustic-gravity waves propagating in inhomogeneous polar thermosphere flows have been investigated. It is shown that a spectrum filtration and a change in amplitudes of acoustic-gravity waves occur in the region of polar thermosphere circulation. As a result, the waves with horizontal lengths of 500–700 km and periods of ∼ 10 min are predominated in satellite observations. We have shown that such spectral properties correspond to the waves which are blocked in the counter flow. The amplitudes of the blocked waves are greatly enhanced due to their interaction with the non-uniform flow. A ground-based observer registers these waves with periods from 30 min to more than 1 h, depending on the flow velocity. Taking in to account the interaction of the waves with the flows we can explain the discrepancy between the results of satellite and ground-based observations of acoustic-gravity wave in the polar regions.

Based on satellite measurements, we investigated the properties of acoustic-gravity waves in different geographical areas of the Earth’s upper atmosphere. To study wave activity at high latitudes, we used the concentration of neutral particles measured by the low-altitude polar satellite Dynamic Explorer 2 and measurements from the equatorial satellite Atmosphere Explorer-E for analysis of waves at low latitudes. In the range of heights 250–400 km, there are observed latitudinal variations of amplitudes, together with variations in the morphological and spectral properties of acoustic-gravity waves. In the polar regions of thermosphere, the wave amplitudes amount to 3–10% in terms of relative variations of density and do not exceed 3% at low and middle latitudes. At low latitudes, regular fluctuations induced by the solar terminator are clearly seen with a predominant wave mode moving synchronously with terminator. Moreover, at low and middle latitudes, there are observed sporadic local wave packets of small amplitudes (1–2%) that can have origins of various natures. We also investigated the relation between some of the observed wave trains and the earthquakes.

The properties of acoustic-gravity waves in the polar regions of the Earth’s thermosphere have been studied. It has been shown that the change in AGW amplitudes occurs against the background of large-scale rotational movements of the medium in the polar thermosphere. The amplitudes of waves increase with AGW propagation against the motion of the medium and decrease when AGW propagate along rotation. An analytical expression for the gain coefficient of AGW perturbations is obtained; the wave’s amplification effect in the opposite wind given the characteristic parameters of the thermosphere is estimated. The results are consistent with the measurements of AGW parameters in the polar regions from the “Dynamic Explorer 2” satellite.)

The objects of research in this work are evanescent wave modes in a gravitationally stratified atmosphere and their associated pseudo-modes. Whereas the former, according to the dispersion relation, rapidly decrease with distance from a certain surface, the latter, having the same dispersion law, differ from the first by the form of polarization and the character of its decreasing away from the surface. Within a linear hydrodynamic model, the propagation features of evanescent wave modes in an isothermal atmosphere are studied. Research carried out for different assumptions about the properties of the medium. On this way, a new wave mode – anelastic evanescent wave mode – was discovered. Also, the possibility of the existence of a pseudo-mode related to it is indicated. The case of two isothermal media differing in temperature at the interface is studied in detail. It is shown that a non-divergent pseudo-mode with the dispersion of solar f-mode type can be realized on the interface for the specified horizontal scale. The newly discovered dispersion relation, at the interface of two media, is satisfied by the wave mode, which has different types of amplitude versus height dependencies at different horizontal scales. The applicability of the obtained results to clarify the properties of f-mode observed on the Sun is analyzed.

We present a study correlating the spatial locations of young star clusters with those of molecular clouds in NGC~5194, in order to investigate the timescale over which clusters separate from their birth clouds. The star cluster catalogues are from the Legacy ExtraGalactic UV Survey (LEGUS) and the molecular clouds from the Plateau de Bure Interefrometer Arcsecond Whirpool Survey (PAWS). We find that younger star clusters are spatially closer to molecular clouds than older star clusters. The median ages for clusters associated with clouds is 4~Myr whereas it is 50~Myr for clusters that are sufficiently separated from a molecular cloud to be considered unassociated. After $\sim$6~Myr, the majority of the star clusters lose association with their molecular gas. Younger star clusters are also preferentially located in stellar spiral arms where they are hierarchically distributed in kpc-size regions for 50-100~Myr before dispersing. The youngest star clusters are more strongly clustered, yielding a two-point correlation function with $\alpha=-0.28\pm0.04$, than the GMCs ($\alpha=-0.09\pm0.03$) within the same PAWS field. However, the clustering strength of the most massive GMCs, supposedly the progenitors of the young clusters for a star formation efficiency of a few percent, is comparable ($\alpha=-0.35\pm0.05$) to that of the clusters. We find a galactocentric-dependence for the coherence of star formation, in which clusters located in the inner region of the galaxy reside in smaller star-forming complexes and display more homogeneous distributions than clusters further from the centre. This result suggests a correlation between the survival of a cluster complex and its environment., Comment: 17 pages, 12 figures. Accepted for publication in MNRAS

The dissipation of acoustic–gravity waves in the thermosphere due to molecular viscosity and thermal conductivity based on a modified system of hydrodynamic equations is studied. A modification of the system of equations consists in additional taking into account in the linearized Navier–Stokes equations and heat transfer additional terms describing the transfer of momentum and energy due to the background density gradient, except for the usually taken into account velocity gradient. Using these modified equations, the local dispersion equation of acoustic–gravity waves in an isothermal dissipative atmosphere is obtained. On this basis, new general expressions for the attenuation rates in time and in space for both acoustic and gravity waves in the entire spectral range are derived in the paper. The relationship between the rates of AGW temporal and spatial attenuation is analyzed. The results obtained are consistent with satellite-based observations of AGW at the heights of the thermosphere, indicating filtering of the wave spectrum due to viscosity and thermal conductivity.

Wave disturbances caused by moving solar terminator were studied using in situ satellite measurements. Neutral species densities measured by low-latitude satellite Atmosphere Explorer-E in the altitude range of 250–400 km were used for analysis. Wave disturbances of neutral species density with amplitudes of 2–4% were observed during few hours after passing the terminator, predominantly in time intervals of 6–9 LST and 20–23 LST. These disturbances were interpreted as the acoustic-gravity waves. Spatial scales of such waves range from few hundred to few thousand kilometers, major part of wave spectral power being concentrated in the horizontal wavelength range from 1000 km to 1200 km. It was shown that vertical and horizontal components of phase velocity of these waves coincide with vertical and horizontal components of terminator velocity, i.e. observed wave are synchronized with the terminator.

A number of novel 6-R-isoxazolo[4,3-b]pyridines were synthesized and their reactions with neutral C-nucleophiles (1,3-dicarbonyl compounds, &pi, excessive (het)arenes, dienes) were studied. The reaction rate was found to be dependent on the nature of the substituent 6-R. The most reactive 6-nitroisoxazolo[4,3-b]pyridines are able to add C-nucleophiles in the absence of a base under mild conditions. In addition, these compounds readily undergo [4+2]-cycloaddition reactions on aromatic bonds C=C(NO2) of the pyridine ring, thus indicating the superelectrophilic nature of 6-NO2-isoxazolo[4,3-b]pyridines.

The article presents a summary of the main findings of the systematic study of acoustic-gravity waves (AGWs) in the polar thermosphere. This study was based on the in situ measurements made by the Dynamics Explorer 2 (DE2) spacecraft late in its mission when it descended low enough (250–400 km). It was found out that AGWs in the polar thermosphere are observed within a narrow frequency band close to the Brunt–Väisälä frequency and with horizontal wavelengths about 500–600 km. The broadband spectrum of travelling ionospheric disturbance (TID) frequencies observed by radars is caused by the Doppler effect. The AGW amplitudes do not depend on the altitude, but grow almost linearly with the wind velocity. They propagate towards the wind.

Recently acquired WFC3 UV (F275W and F336W) imaging mosaics under the Legacy Extragalactic UV Survey (LEGUS) combined with archival ACS data of M51 are used to study the young star cluster (YSC) population of this interacting system. Our newly extracted source catalogue contains 2834 cluster candidates, morphologically classified to be compact and uniform in colour, for which ages, masses and extinction are derived. In this first work we study the main properties of the YSC population of the whole galaxy, considering a mass-limited sample. Both luminosity and mass functions follow a power law shape with slope -2, but at high luminosities and masses a dearth of sources is observed. The analysis of the mass function suggests that it is best fitted by a Schechter function with slope -2 and a truncation mass at $1.00\pm0.12\times10^5\ M_\odot$. Through Monte Carlo simulations we confirm this result and link the shape of the luminosity function to the presence of a truncation in the mass function. A mass limited age function analysis, between 10 and 200 Myr, suggests that the cluster population is undergoing only moderate disruption. We observe little variation in the shape of the mass function at masses above $1\times10^4\ M_\odot$, over this age range. The fraction of star formation happening in the form of bound clusters in M51 is $\sim20\%$ in the age range 10 to 100 Myr and little variation is observed over the whole range from 1 to 200 Myr., Comment: 25 pages, 19 figures, 10 tables. Accepted for publication in MNRAS (14 Sep. 2017)

According to measurements on the Dynamic Explorer 2 satellite, features of the propagation of acoustic gravity waves (AGWs) in the multicomponent upper atmosphere have been investigated. In the altitude range 250–400 km in wave concentration variations of some atmospheric gases, amplitude and phase differences have been observed. Using the approach proposed in this paper, in different gases, AGW variations have been divided into components associated with elastic compression, adiabatic expansion, and the vertical background distribution. The amplitude and phase differences observed in different gases are explained on the basis of analyzing these components. It is shown how to use this effect in order to determine the wave propagation, the vertical displacement of the volume element, the wave frequency, and the spatial distribution of the wave energy density.

The paper deals with the theory and methods of statistical simulation of random processes and fields based on their spectral decomposition and Kotelnikov-Shennon modified interpolation sums, as well as applying these methods for environmental geophysical monitoring. Statistical simulation of multivariate random fields (those homogeneous in time and homogeneous isotropic in n other variables) are considered to be essential for seismological research into frequency characteristics of geological media. A statistical model and a numerical algorithm of simulating random fields are built on the basis of Kotelnikov-Shennon modified interpolation decomposition to generate adequate realizations of seismic noise. The paper examines real-valued random fields ξ(t,x),tϵÎR,xÎRn, those homogeneous in time and homogeneous isotropic ones relative to spatial variables in the multidimensional space. It also considers approximation of random fields by the random fields with a bounded spectrum. There is made an analogue of the Kotelnikov–Shannon theorem for random fields with a bounded spectrum. Besides, there are obtained estimates of the mean-square approximation of random fields in the space R´Rn by a model constructed with the help of spectral decomposition and Kotelnikov–Shannon interpolation formula. The paper provides a mechanism for statistical simulation of Gaussian random fields with a bounded spectrum; namely, those homogeneous in time and homogeneous isotropic ones relative to spatial variables in the multidimensional space. Proved have been the theorems of the mean-square approximation of random fields (those homogeneous in time and homogeneous isotropic ones relative to n- other variables) by special partial sums. A simulation method was used to formulate an algorithm of numerical simulation by means of these theorems. There are also considered ways to carry out spectral analysis of generated seismic noise realizations. Finally, there have been developed universal methods of statistical simulation (Monte Carlo methods) of multi-parameter seismology data for generating seismic noise on 2D and 3D grids of the required detail and regularity.

The relationship between the directions of polar acoustic gravity waves and a wind at 250–350 km altitudes has been studied based on an analysis of the Dynamics Explorer 2 satellite measurements. A method, which makes it possible to determine the direction of these waves relative to the satellite velocity vector based on one-point measurements of different neutral atmosphere parameters, is presented. It has been established that acoustic gravity waves observed over the polar caps systematically propagate upwind, which argues for their spatial wind filtering. In the polar regions, waves mainly propagate in two directions: toward magnetic noon and 15–16 MLT. Waves tend to move counterclockwise and clockwise over the northern and southern polar caps, respectively.