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This article presents a generalization of the RSA cryptosystem for rings with commuting ideals. An analogue of the Euler function for ideals and the concept of an RSA-ideal are defined. An analog of a cryptosystem for the ring with commuting ideals is formulated and a description of the RSA-ideals for which this is possible is obtained., Comment: 7 pages

This paper provides theoretical and practical arguments regarding the possibility of predicting strong and major earthquakes worldwide. Many strong and major earthquakes can be predicted at least two to five months in advance, based on identifying stressed areas that begin to behave abnormally before strong events, with the size of these areas corresponding to Dobrovolsky formula. We make predictions by combining knowledge from many different disciplines: physics, geophysics, seismology, geology, and earth science, among others. An integrated approach is used to identify anomalies and make predictions, including satellite remote sensing techniques and data from ground-based instruments. Terabytes of information are currently processed every day with many different multi-parametric prediction systems applied thereto. Alerts are issued if anomalies are confirmed by a few different systems. It has been found that geophysical patterns of earthquake preparation and stress accumulation are similar for all key seismic regions. The same earthquake prediction methodologies and systems have been successfully applied in global practice since 2013, with the technology successfully used to retrospectively test against more than 700 strong and major earthquakes since 1970.

Terra Seismic can predict most major earthquakes (M6.2 or greater) at least 2 - 5 months before they will strike. Global earthquake prediction is based on determinations of the stressed areas that will start to behave abnormally before major earthquakes. The size of the observed stressed areas roughly corresponds to estimates calculated from Dobrovolskys formula. To identify abnormalities and make predictions, Terra Seismic applies various methodologies, including satellite remote sensing methods and data from ground-based instruments. We currently process terabytes of information daily, and use more than 80 different multiparameter prediction systems. Alerts are issued if the abnormalities are confirmed by at least five different systems. We observed that geophysical patterns of earthquake development and stress accumulation are generally the same for all key seismic regions. Thus, the same earthquake prediction methodologies and systems can be applied successfully worldwide. Our technology has been used to retrospectively test data gathered since 1970 and it successfully detected about 90 percent of all significant quakes over the last 50 years.

The analysis of satellite thermal images of the Earth's surface within the spectral range of 10.5-11.3 mkm has shown that over some linear structures of the Middle-Asian seismically active region there is observed a stable in time and space increasing intensity of the outgoing radiation flux as compared to contiguous blocks. A retrospective analysis of a continuous series of observations of the outgoing IR radiation flux has shown that in certain individual zones of some major tectonic dislocations there appear from time to time positive anomalies of IR radiation, for instance at the point of intersection of the Talasso-Ferghana and Tamdy-Tokrauss faults. These anomalies last from 2 to 10 days. The spontaneous anomalies are characterized by a pulsating variation of area. The space confinement and duration of these anomalies permit distinguishing theme noise anomalies caused by meteorological factors. The time of the appearance of these anomalies coincides with the activation of faults over which there has been detected an increase of the outgoing IR radiation flux. In 1984 the majority of crustal earthquakes, of a magnitude over 4, in the Tien Shan were accompanied by the appearance of a positive anomaly of the IR radiation at the point of the intersection of the faults. The area of anomalies was n*10000 km2. The most outstanding example of such activization is the Ghazli earthquake of 19.03.1984 M7.2. At the point of the intersection of the Tamdy-Tokrauss and Talasso- Ferghana faults there was detected on March 11 a positive anomaly of the outgoing IR radiation flux of exceptional intensity and enormous area (about 100 thousand km2). The subsequent earthquakes in the zone of the Tamdy-Tokrauss fault in the summer of 1984 of the magnitudes from 4.3 to 5.3 were also preceded by the appearance of a positive anomaly of the outgoing IR radiation at the point of intersection of the faults.

NOAA/AVHRR thermal images indicated the presence of positive thermal anomalies that are associated with the large linear structures and fault systems of the Earth's crust. The relation between thermal anomalies and seismic activity was established for Middle Asia on the basis of a 7-year series of thermal images. Thermal anomaly has been located near Beijing, on the border between the mountains and plain. The size of this anomaly is about 700 km long and 50 km wide. The anomaly appeared about 6-24 days before and continued about a week after an earthquake. The anomaly was sensitive to crust earthquakes with a magnitude more than 4.7 and for a distance of up to 500 km. The amplitude of this anomaly was about 3 C.

Purpose - The purpose of this work is to determine dependence of the separative power of the Iguassu gas centrifuge (GC) on the velocity of the rotor. Design/methodology/approach - The dependence is determined by means of computer simulation of the gas flow in the GC and numerical solution of the diffusion equation for the light component of the binary mixture of uranium isotopes. 2D axisymmetric model with the sources/sinks of the mass, angular momentum and energy reproducing the scoops was explored for the computer simulation. Parameters of the model correspond to the parameters of the so-called Iguassu centrifuge. The separative power has been optimised in relation to the pressure of the gas, temperature of the gas, the temperature drop along the rotor, power of the source of angularmomentum and energy, feed flow and geometry of the lower baffle. Findings - In the result, the optimised separative power depends only on the velocity, length and diameter of the rotor. The dependence on the velocity is described by the power law function with the power law index 2.6 which demonstrate stronger dependence on the velocity than it follows from experimental data. However, the separative power obtained with limitation on the pressure growth with the velocity depends on the velocity on the power similar to 2 which well agree with the experiments. Originality/value - For the first time, the optimised separative power of the GCs have been calculated via numerical simulation of the gas flow and diffusion of the binary mixture of isotope., Comment: 12 pages, 3 figures

The detection of the pulsed $\sim 1 $~TeV gamma-ray emission from the Crab pulsar reported by MAGIC and VERITAS collaborations demands a substantial revision of existing models of particle acceleration in the pulsar magnetosphere. In this regard model independent restrictions on the possible production site of the VHE photons become an important issue. In this paper, we consider limitations imposed by the process of conversion of VHE gamma rays into $e^{\pm}$ pairs in the magnetic field of the pulsar magnetosphere. Photons with energies exceeding 1~TeV are effectively absorbed even at large distances from the surface of the neutron star. Our calculations of magnetic absorption in the force-free magnetosphere show that the twisting of the magnetic field due to the pulsar rotation makes the magnetosphere more transparent compared to the dipole magnetosphere. The gamma-ray absorption appears stronger for photons emitted in the direction of rotation than in the opposite direction. There is a small angular cone inside which the magnetosphere is relatively transparent and photons with energy $1.5$~TeV can escape from distances beyond $0.1$~light cylinder radius ($R_{\rm{lc}}$). The emission surface from where photons can be emitted in the observer's direction further restricts the sites of VHE gamma-ray production. For the observation angle $57^{\circ}$ relative to the Crab pulsar axis of rotation and the orthogonal rotation, the emission surface in the open field line region is located as close as $0.4\,R_{\rm{lc}}$ from the stellar surface for a dipole magnetic field, and $0.1\,R_{\rm{lc}}$ for a force-free magnetic field., Comment: 22 pages, 9 figures

Linear waves are investigated in a rotating gas under the condition of strong centrifugal acceleration of the order $10^6 g$ realized in gas centrifuges for separation of uranium isotopes. Sound waves splits into three families of the waves under these conditions. Dispersion equations are obtained. The characteristics of the waves strongly differ from the conventional sound waves on polarisation, velocity of propagation and distribution of energy of the waves in space for two families having frequencies above and below the frequency of the conventional sound waves. The energy of these waves is localized in rarefied region of the gas. The waves of the third family were not specified before. They propagate exactly along the rotational axis with the conventional sound velocity. These waves are polarized only along the rotational axis. Radial and azimuthal motions are not excited. Energy of the waves is concentrated near the wall of the rotor where the density of the gas is largest., Comment: 19 pages, 12 figures

Dynamics of waves generated by scopes in gas centrifuges (GC) for isotope separation is considered. The centrifugal acceleration in the GC reaches values of the order of $10^6$g. The centrifugal and Coriolis forces modify essentially the conventional sound waves. Three families of the waves with different polarisation and dispersion exist in these conditions. Dynamics of the flow in the model GC Iguasu is investigated numerically. Comparison of the results of the numerical modelling of the wave dynamics with the analytical predictions is performed. New phenomena of the resonances in the GC is found. The resonances occur for the waves polarized along the rotational axis having the smallest dumping due to the viscosity., Comment: 4 pages, 2 figures, Proceedings of ICNAAM-2014

The percolation threshold and wrapping probability $R_{\infty}$ for the two-dimensional problem of continuum percolation on the surface of a Klein bottle have been calculated by the Monte Carlo method with the Newman--Ziff algorithm for completely permeable disks. It has been shown that the percolation threshold of disks on the Klein bottle coincides with the percolation threshold of disks on the surface of a torus, indicating that this threshold is topologically invariant. The scaling exponents determining corrections to the wrapping probability and critical concentration owing to the finite-size effects are also topologically invariant. At the same time, the quantities $R_{\infty}$ are different for percolation on the torus and Klein bottle and are apparently determined by the topology of the surface. Furthermore, the difference between the $R_{\infty}$ values for the torus and Klein bottle means that at least one of the percolation clusters is degenerate.

It has been shown that changes in the energy of a system of nonwetting-liquid clusters confined in a random nanoporous medium in the process of relaxation can be written in the quasiparticle approximation in the form of the sum of the energies of local (metastable) configurations of liquid clusters interacting with clusters in the connected nearest pores. The energy spectrum and density of states of the local configuration have been calculated. It has been shown that the relaxation of the state of the system occurs through the scenario of self-organized criticality (SOC). The process is characterized by the expectation of a fluctuation necessary for overcoming a local energy barrier of the metastable state with the subsequent rapid hydrodynamic extrusion of the liquid under the action of the surface buoyancy forces of the nonwetting framework. In this case, the dependence of the interaction between local configurations on the number of filled pores belonging to the infinite percolation cluster of filled pores serves as an internal feedback initiating the SOC process. The calculations give a power-law time dependence of the relative volume of the confined liquid. The developed model of the relaxation of the porous medium with the nonwetting liquid demonstrates possible mechanisms and scenarios of SOC for disordered atomic systems.

The time evolution of the system of water in the Libersorb 23 (L23) disordered nanoporous medium after the complete filling at excess pressure and the subsequent removal of excess pressure has been studied. It has been found that three stages can be identified in the relaxation of the L23-water system under study. At the first stage, a portion of water at the removal of excess pressure rapidly flows out in the pressure reduction time, i.e., following a decrease in the pressure. It has been shown that, at temperatures below the dispersion transition temperature $T < T_d = 284 K$, e.g., $T = 277 K$, the degree of filling ${\theta}$ decreases from 1 to 0.8 in 10 s, following the variation of excess pressure. At the second stage of relaxation, the degree of filling ${\theta}$ varies slowly according to a power law ${\theta} \sim t^{-\alpha}$ with the exponent ${\alpha} < 0.1$ in the time $t \sim 10^5$ s. This corresponds to a slow relaxation of the formed metastable state of the nonwetting liquid in the porous medium. At the third stage when $t > 10^5$ s, the formed metastable state decays, which is manifested in the transition to a power-law dependence ${\theta}(t)$ with a larger exponent. The extrusion-time distribution function of pores has been calculated along with the time dependence of the degree of filling, which qualitatively describes the observed anomalously slow relaxation and crossover of the transition to the stage of decay with a power-law dependence ${\theta}(t)$ with a larger exponent. It has been shown that the relaxation and decay of the metastable state of the confined nonwetting liquid at ${\theta}>{\theta_c}$ are attributed to the appearance of local configurations of liquid clusters in confinement and their interaction inside the infinite percolation cluster of filled pores.

The physical model describing the influence of the electronic subsystem on the properties of one-dimensional chains of metal is presented. It is shown that depending on an interaction potential between atoms in one-dimensional system formation of chains of various length is possible. In case the characteristic depth of the potential well of the interatomic interaction does not exceed a certain magnitude, the chains in 1D system are formed with length of several angstroms, while the increase the depth of the well also leads to the possibility of formation of metal chains of greater length., Comment: 12 pages, in Russian

The dependency of the melting point of supported metal nanoclusters as function of clusters height is theoretically investigated in the framework of the uniform approach. The vacancy mechanism describing the melting point shift in nanoclusters with decrease of their size is proposed. It is shown that the essential role in clusters melting point shift is played by van der Waals forces of cluster-substrate interaction. It is shown, that the account of layer--by--layer fusion of a cluster allows to satisfactorily describe the melting of nanoclusters of various metals, deposited onto a different substrates. The proposed model satisfactorily accounts for the experimental data.

The dependencies of the melting point and the lattice parameter of supported metal nanoclusters as functions of clusters height are theoretically investigated in the framework of the uniform approach. The vacancy mechanism describing the melting point and the lattice parameter shifts in nanoclusters with decrease of their size is proposed. It is shown that under the high vacuum conditions (p<10^-7 torr) the essential role in clusters melting point and lattice parameter shifts is played by the van der Waals forces of cluster-substrate interation. The proposed model satisfactorily accounts for the experimental data., Comment: 6 pages, 3 figures, 1 table

A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was calculated and detailed analysis was carried out. The model allows to characterize the disordered porous medium with the number of nearest neighbors, the area of all mouths that connect pore with the neighboring pores. These paramaters depend on the pore size and porosity and --- in addition to the specific surface area, porosity, and percolation threshold and the distribution function of pore size.

A physical mechanism has been proposed to describe the formation of a stable state of a nonwetting liquid after filling of a porous medium at an increased pressure with the subsequent reduction of the overpressure to zero. It has been shown that the observed transition of the system of nonwetting-liquid nanoclusters to the stable state in a narrow range of filling factors and a narrow temperature interval is due to a decrease in the surface free energy without change in the chemical potential owing to the collective interactions between liquid nanoclusters in the neighboring pores. This effectively corresponds to their mutual attraction. The model makes it possible to describe the observed dependences of the volume of the liquid in pores in the stable state on the filling factor and temperature.

Correlation effects arising during liquid infiltration into hydrophobic porous medium are considered. On the basis of these effects a mechanism of energy absorption at filling porous medium by nonwetting liquid is suggested. In accordance with this mechanism, the absorption of mechanical energy is a result expenditure of energy for the formation of menisci in the pores on the shell of the infinite cluster and expenditure of energy for the formation of liquid-porous medium interface in the pores belonging to the infinite cluster of filled pores. It was found that in dependences on the porosity and, consequently, in dependences on the number of filled pores neighbors, the thermal effect of filling can be either positive or negative and the cycle of infiltration-defiltration can be closed with full outflow of liquid. It can occur under certain relation between percolation properties of porous medium and the energy characteristics of the liquid-porous medium interface and the liquid-gas interface. It is shown that a consecutive account of these correlation effects and percolation properties of the pores space during infiltration allow to describe all experimental data under discussion.