## Space analyticity and integral bounds for solutions to equations of magnetohydrodynamics

In the paper “Space analyticity and bounds for derivatives of solutions to the evolutionary equations of diffusive magnetohydrodynamics”, V. Zheligovsky has given solutions to the three following mutually related problems:

– to carry over the known a priori bounds for arbitrary-order space derivatives of solutions to the Navier–Stokes equation to space-periodic solutions to the equations of diffusive magnetohydrodynamics;

– to derive similar a priori bounds for arbitrary-order space derivatives of the first-order time derivative of the Fourier–Galerkin approximants of the MHD solutions and to prove that the bounds are admitted by weak solutions to the equations of magnetohydrodynamics;

– to reveal a link between these bounds and space analyticity of the MHD solutions at almost all times.

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## Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property The article «Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property» was published in «Engineering. Proceedings» and presented at the 7th International conference on Time Series and Forecasting, Gran Canaria, Spain, 19-21 July 2021. Authors – A. Kushnir and A. Varypaev.

The paper investigates the asymptotic properties of statistical estimates for the vector parameter \mathbf{u} \in R^q of a multidimensional random time series z_{t} \in R^m , t \in \mathbb{Z} , satisfying the strong mixing conditions. The authors have considered estimates \widetilde{\mathbf{u}}_{n}(\overline{z}_{n}) that are solutions of the equations \bigtriangledown_{\mathbf{u}}Q_{n}(\overline{z}_{n};\mathbf{u}) = 0, \overline{z}_{n} = (z^T_{1},...,z^T_{n})^T, where Q_{n}(\overline{z}_n;\mathbf{u}) are some objective functions for which \bigtriangledown_{\mathbf{u}}Q_{n}(\overline{z}_{n};\mathbf{u}) satisfies some constraints. It was proved, that under these constraints, the estimates \widetilde{\mathbf{u}}(\overline{z}_{n}) are \sqrt{n} – consistent and asymptotically normal with a limit covariance matrix \mathbf{D(u) = \Phi^{-1}(u)\Psi(u)\Phi^{-1}(u)} uniquely determined by the objective functions Q_{n}(\overline{z}_{n};\mathbf{u}).

The results of this paper are a generalization of the methods for constructing and analyzing the asymptotic properties of M-estimates, which were previously studied for the case of independent identically distributed observations.

Source: Kushnir, A.; Varypaev, A. Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property // Eng. Proc. 2021, 5, 19. 10.3390/engproc2021005019

## Earthquake Prediction: Old Expectations and New Results

It is known that there is no satisfactory physical model of earthquakes. The paradox of seismicity is known, according to which the implementation of seismic slip according to the generally accepted Reid`s elastic rebound model, due to the corresponding values of temperature and pressure, cannot occur at depths of more than several tens of kilometers. To get around these difficulties, models were proposed for the role of the fluid phase and various types of metamorphic transformations in the occurrence of deeper earthquakes.

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## Computer vision helps estimating the viscosity of lava domes

Lava domes form when a highly viscous magma erupts on the surface. Several types of lava dome morphology can be distinguished depending on the flow rate and the rheology of magma: obelisks, lava lobes, and endogenic structures. The viscosity of magma nonlinearly depends on the volume fraction of crystals and temperature. The paper “A method for magma viscosity assessment by lava dome morphology” published in the Journal of Volcanology and Seismology (Q2; JIF: 0.543) presents a new approach to magma viscosity estimation based on a comparison of observed and simulated dome morphological forms of lava domes. This joint research was performed by scientists from the Institute as well as from the Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, and the Lomonosov Moscow State University and supported by the Russian Science Foundation (Project No. 19-17-00027).

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## Deficit of Large Aftershocks as an Indicator of Afterslip at the Sources of Earthquakes in Subduction Zones

Earthquakes are accompanied by postseismic processes that begin right after the main shock and are manifested in aftershocks and aseismic deformations. The main driving mechanisms of postseismic deformation are viscoelastic relaxation in the crust and in the Earth’s upper mantle and postseismic slips (afterslip), reflecting the frictional properties of the plate interface in the source zone of a large earthquake. Afterslip may occur as aftershocks and/or slow aseismic slips (creep).

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## А modified k-nearest neighbors method and its application to estimation of seismic intensity

In the article published in «Pure and Applied Geophysics», a modified k-nearest neighbors method is introduced, which is designed for statistically meaningful estimation of the field intensity based on locations of events. This method is used to perform a detailed analysis of the seismic intensity field in the region of Japan, shown on the figure, and found spots of increased seismic activity.

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## Active cloaking and illusion of electric potentials in electrostatics

Cloaking (or “camouflage”) and illusion have long appeared in literature for children and science fiction. The “Star Trek” movies used cloaked (invisible to the enemy) spaceships (as presented in the cartoon in Fig. 1). In Charles Perrault’s Cat in Boots, a clever cat asks an ogre to turn into a little mouse and the ogre turns creating an illusion.

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