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The comparative effect of two factors on the translatory motion of the centers of mass of the Pluto–Charon system is investigated. The first important factor is the non-sphericity of the shape and gravitational field of the bodies in the system. The second factor is the gravitation of the Sun. As a measure of the influence of both factors we use the ratio of the corresponding perturbing acceleration to the main one. The main acceleration is caused by the mutual Newtonian attraction of Pluto and Charon. It has been established that for the first factor this measure is on the order of 10–6, while for the second factor it is two orders of magnitude smaller. This explains why the Lidov–Kozai effect (despite a large mutual slope of 96° between the planes of the satellite’s orbit around the planet, and the barycenter of the system around the Sun) does not appear. The situation is similar to the case with the satellites of Uranus. As a result, the Pluto–Charon system remains stable at least on a timescale of millions of years. The tidal effect of the Sun on the surface shape of the bodies under study is also estimated. The ratio of the tidal potential of the Sun at a point on the surface of the body to the gravitational potential of the body itself at this point is taken as a measure of impact. It turned out to be on the order of 3 × 10–12, which is more than six orders less than the influence of rotation and mutual attraction of Pluto and Charon. In fact, the Sun does not affect the figures of the bodies of the system.

Owing to the high resolving power and efficiency of DNA sequencing, researchers have discovered the extremely high diversity of bacterial, fungal, protist, and microinvertebrate communities in the soil, wood, phyllosphere, and other natural media. Studies on the properties of these communities require powerful tools for analyzing multicomponent systems. One of them is the analysis of ecological networks, which makes it possible to solve a broad range of problems. This review briefly describes the possibilities of network analysis, its concepts, and metrics of network topology.It also indicates limitations related to specific features of DNA sequencing (compositionality and data sparsity) and potential sources of errors in the interpretation of results (relic DNA, artifactual DNA sequences and spurious connections in a network). The focus is on the communities of microorganisms, but the discussed issues are relevant for most other groups of the biota.

We consider the dynamical evolution of planetary systems whose structure is nearly circular and coplanar. The analysis is performed by the Hori–Deprit averaging method within the theory of the first order in planetary masses. A convenient set of canonical elements and a rarely employed variety of astrocentric coordinates are used to derive the equations of motion. Owing to the use of the chosen system of canonical elements, the expansions of the right-hand sides of the averaged equations contain a relatively small number of terms. Compared to other widespread coordinate systems, the astrocentric coordinates used by us allow a more convenient representation of the disturbing function to be obtained and do not require its expansion into a series in powers of a small parameter. On time scales $${\sim}10^{5}{-}10^{7}$$ years we have studied the long-term evolution of the planetary systems HD 12661, $$\upsilon$$ Andromedae, and some model systems by numerical integration of the averaged equations. Possible secular resonances have been revealed in the systems considered.

Parameters of pulsed electric discharges arising between insulated metal parts of helicopter rotor blades, which generate electromagnetic interferences for onboard radio stations operating in the very short wave (VSW) and ultrashort wave (USW) bands have been studied. These discharges appear as a result of the in-flight engine-driven differential charging of helicopters. In-flight and laboratory experiments were used to determine the range of discharge voltages and currents and the amplitude and spectral characteristic of electromagnetic interferences produced by these discharges for onboard antennas.

The electric state of the near-surface atmosphere up to a height of 400 m is investigated using a tethered balloon with a measuring platform and a ground-based information-measuring complex of the Borok middle-latitude geophysical observatory. For the first time, measurements were taken simultaneously for vertical profiles of the atmospheric electric field, polar electrical conductivities, size distribution of aerosol particles, and the volume activity of radon, which have allowed estimating the average values and variability of the space charge density and conduction current in the atmosphere. The height dependence of the electric potential with respect to the Earth’s surface and electrical resistance of the near-surface atmospheric column under different conditions of the temperature stratification is studied.

A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarecanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems.

We analyze the results of an experiment using an explosive sound source in the tropical part of the Indian Ocean. We consider the time structure of sound signals in geometric shadow zones to a distance of 270 km and the scheme of how the sound field in the shadow zone is formed by rays reflected from horizontally extended fine-structured sound velocity layers. From the results of calculation using a wave program that realizes the method of psuedodifferential parabolic equations, we analyze the influence of signal scattering by fine-structure sound velocity inhomogeneities on the sound field distribution in a waveguide. We show that the field formed by spots of light in each of the shadow zones is generated by a regular field and propagates in parallel to it, taking energy from the regular zone in the near field and in each subsequent convergence zone. This mechanism causes an additional decrease in the field in illuminated zones, which can be interpreted as additional attenuation of the regular sound field.

An expansion of the Hamiltonian for the N-planet problem into a Poisson series using a system of modified (complex) Poincare´ canonical elements in the heliocentric coordinate system is constructed. The Lagrangian and Hamiltonian formalisms are used. The first terms in the expansions of the principal and complementary parts of the disturbing function are presented. Estimates of the number of terms in the presented expansions have been obtained through numerical experiments. A comparison with the results of other authors is made.

A special system of canonical variables is considered. An algorithm for expanding the principal functions of Keplerian motion in new elements is presented. The advantage of the proposed system is a relatively small number of terms in the classical expansions of the unperturbed two-body problem. A method for expanding the time derivatives of the rectangular coordinates is proposed. Some estimates of the number of terms in the presented expansions have been obtained through numerical experiments.

A comparative analysis has been performed on the informativity of characteristics of the state of lichen cover calculated by two methods for evaluating lichen abundance (frequency and projective cover). A close correlation of the indices obtained by the two different methods was shown, as well as their significant association with the degree of stress, which confirms their equal usefulness in lichenoindication works. However, comparison of the informativity established that the indices based on frequency have higher resolution capability.

The response to copper pollution was studied in the vegetative progeny of tufted hair grass (Deschampsia caespitosa (L.) Beauv.) and ragged robin (Lychnis flos-cuculi L.) plants growing together in chronically polluted areas around the Middle Ural Copper Smelter or in background areas. The root elongation test was used, with copper sulfate (0.006–0.51 mg Cu/L) being added directly to the nutrient medium. Using multimodel inference, dose-response curves were plotted for each of 85 maternal plants, and their parameters (effective Cu concentrations and curve slope in the linear segment) were evaluated. The pattern of transformation in dose dependence of root increment upon transition from background to impact populations proved to be basically different in the two species. The curves for L. flos-cuculi showed a parallel shift, with their shape remaining generally unchanged. In D. caespitosa, this transition was accompanied by a decrease in sensitivity to Cu, but tolerance to this metal was found to increase only at the highest concentration range. These results provide evidence for different strategies of adaptation to heavy metal pollution, which are discussed by comparing the physiological and ecological properties of the two species.

The capacity of species for expansion and colonization of new habitats is a key condition for the maintenance of their populations. In this study, specific features of the reproductive potential have been analyzed in Lobaria pulmonaria populations growing under contrasting climatic conditions. Certain ecological determinants governing the development of this lichen species have been revealed.

We consider the problem of the creation of the desired intensity distributions with the help of the Gerchberg-Saxton algorithm and hill-climbing algorithm with a constant and variable step. The efficiency of the algorithms for different input parameters is analyzed. For a better correction accuracy, two different hybrid methods are used: the first method consists of the successive use of the Gerchberg-Saxton algorithm after running the hill-climbing algorithm. In the second, more universal method, the Gerchberg-Saxton algorithm is built into the hill-climbing algorithm so that for each iteration of the latter there is a specified number of iterations of the former. The abovementioned algorithms treat the beams a few times more accurately when used in the hybrid regime than when used separately.

A considerable energy variability is observed for quartets of doubly bottom-reflected signals when the acoustic path crosses the frontal zone of the Gulf Stream. The experimental curves exhibit a local increase by a factor of more than two in the energy of individual bottom-reflected signals. According to the data of numerical modeling, the position and magnitude of the energy maxima prove to be highly sensitive to the position of the frontal zone, its horizontal and vertical sizes, and the values of the horizontal sound speed gradients. A conclusion is drawn that the observed phenomenon can be used as an indicator of the position of the frontal zone and as a tool for estimating its parameters.

We study the numerical solution of the initial value problem for a system of differential-algebraic equations with retarded argument on the basis of the method of extending solutions with respect to a parameter. We obtain necessary and sufficient conditions for the problem to admit a reduction to the best argument for which the corresponding system of continuation equations is best conditioned. Such an argument is the arc length along an integral curve of the problem. Consider the numerical solution to the initial value problem for the system of differential-algebraic equations with retarded argument

The numerical solution of the initial value problem for a system of delay differential-algebraic equations is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are obtained for transforming this problem to the best argument, which ensures the best condition for the corresponding system of continuation equations. The best argument is the arc length along the integral curve of the problem. Algorithms and programs based on the continuous and discrete continuation methods are developed for the numerical integration of this problem. The efficiency of the suggested transformation is demonstrated using test examples.

The long-range sound propagation from a deep ocean to a receiving system located on the shelf is modeled. The waveguide model is constructed on the basis of the data of an acoustic-oceanographic experiment carried out in the northwestern Pacific. The sensitivity and the frequency dependence of the difference in the sound field levels at the crossing of the frontal zone on the geoacoustic characteristics of the bottom of the shelf and the continental slope are investigated. It is shown that the level difference decreases by 8.2 dB as the velocity of longitudinal waves increases by 100 m/s in the range within 1490–1820 m/s.

Temporal energy fluctuations of impuse signals generated by powerful explosive sources of sound are considered by using the experimental data obtained on a long-distance stationary path in the northwestern Pacific. The signals were received on the Kamchatka shelf (a characteristic ocean depth of about 200 m) at two points spaced by 115 km in the latitudinal direction, one of the reception points being located on the shelf far from its edge, and the other, on the shelf edge. The signal radiation was performed in the deep ocean, at a distance of about 1000 km from the shelf edge. Charges were exploded every hour for more than five days. The frequency-dependent energy fluctuations of the signals and those of the first mode alone were measured in the frequency range 10–80 Hz. It is shown that the amplitudes of energy fluctuations of the first mode in narrow bands can exceed 10 dB and make the main contribution to the energy fluctuations of the total signal. The maximum energy of the first mode is reached on the high tide. It is hypothesized that internal tide-induced variations of the sound velocity field on the shelf affect the degree of energy interaction between the first mode and the bottom.

In analyzing experimental results obtained with explosive sources in the tropical zone of the Indian Ocean, a good agreement was obtained for spectral-energy characteristics of signals observed in the first geometrical shadow zone with computer calculations of the sound field scattered by fine structure inhomogeneities of the fractal type. From the comparison of the results of calculating the frequency characteristics of sound fields in the shadow zone by the wave code and by the method combining ray acoustics with the wave theory of sound scattering, it was found that both methods are appropriate for describing the real processes of scattering and propagation of sound in the ocean with fine-structured stratification and that these methods can be used for solving inverse problems.