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Radio-loud quasars at high redshift (z > 4) are rare objects in the Universe and rarely observed with Very Long Baseline Interferometry (VLBI). But some of them have flux density sufficiently high for monitoring of their apparent position. The instability of the astrometric positions could be linked to the astrophysical process in the jetted active galactic nuclei in the early Universe. Regular observations of the high-redshift quasars are used for estimating their apparent proper motion over several years. We have undertaken regular VLBI observations of several high-redshift quasars at 2.3 GHz (S band) and 8.4 GHz (X band) with a network of five radio telescopes: 40-m Yebes (Spain), 25-m Sheshan (China), and three 32-m telescopes of the Quasar VLBI Network (Russia) -- Svetloe, Zelenchukskaya, and Badary. Additional facilities joined this network occasionally. The sources have also been observed in three sessions with the European VLBI Network (EVN) in 2018--2019 and one Long Baseline Array (LBA) experiment in 2018. In addition, several experiments conducted with the Very Long Baseline Array (VLBA) in 2017--2018were used to improve the time sampling and the statistics. Based on these 37 astrometric VLBI experiments between 2017 and 2021, we estimated the apparent proper motions of four quasars: 0901+697, 1428+422, 1508+572, and 2101+600.

Probing the solar corona is crucial to study the coronal heating and solar wind acceleration. However, the transient and inhomogeneous solar wind flows carry large-amplitude inherent Alfven waves and turbulence, which make detection more difficult. We report the oscillation and propagation of the solar wind at 2.6 solar radii (Rs) by observation of China Tianwen and ESA Mars Express with radio telescopes. The observations were carried out on Oct.9 2021, when one coronal mass ejection (CME) passed across the ray paths of the telescope beams. We obtain the frequency fluctuations (FF) of the spacecraft signals from each individual telescope. Firstly, we visually identify the drift of the frequency spikes at a high spatial resolution of thousands of kilometers along the projected baselines. They are used as traces to estimate the solar wind velocity. Then we perform the cross-correlation analysis on the time series of FF from different telescopes. The velocity variations of solar wind structure along radial and tangential directions during the CME passage are obtained. The oscillation of tangential velocity confirms the detection of streamer wave. Moreover, at the tail of the CME, we detect the propagation of an accelerating fast field-aligned density structure indicating the presence of magnetohydrodynamic waves. This study confirm that the ground station-pairs are able to form particular spatial projection baselines with high resolution and sensitivity to study the detailed propagation of the nascent dynamic solar wind structure., Comment: 13 pages, 9 figures

The Hermitian decomposition of a linear operator is generalized to the case of two or more operations. An additive expansion of the product of three octonions into three parts is constructed, wherein each part either preserve or change the sign under the action of the Hermitian conjugation and operation of inversion of the multiplicative order of three hypercomplex numbers, as well as under the composition of specified operations. The product of three octonions, in particular quaternions, with conjugate central factor is presented as the sum of mutually orthogonal triple anticommutator, triple commutator and associator that vanishes in the case of associative quaternions. The triple commutator is treated as a generalization of the cross product to the case of three arguments both for quaternions and octonions. A generalized cross product is introduced as an antisymmetric component of the triple octonionic product that changes sign both for inversion of the multiplicative order of three arguments, and for the Hermitian conjugation of the product considered respectively to the central argument. The definition of the cross product of three hypercomplex numbers deduced from symmetry considerations is compared with the solution of S. Okubo (1993) and the modern solution of T. Dray and M.A. Corinne (2015). It is shown that the derived definition is equivalent to the first solution presented by S.Okubo in an insufficiently perfect form., Comment: 14 pages, 2 figures, 4 tables

This paper is devoted to octonions that are the eight-dimensional hypercomplex numbers characterized by multiplicative non-associativity. The decomposition of the product of three octonions with the conjugated central factor into the sum of mutually orthogonal anticommutator, commutator and associator, is introduced in an obvious way by commuting of factors and alternating the multiplication order. The commutator is regarded as a generalization of the cross product to the case of three arguments both for quaternions and for octonions. It is verified that the resulting additive decomposition is equivalent to the known solution derived and presented by S. Okubo in a cumbersome form., Comment: 10 pages, 15 basic formulas, 1 table

The closest ever fly-by of the Martian moon Phobos, performed by the European Space Agency's Mars Express spacecraft, gives a unique opportunity to sharpen and test the Planetary Radio Interferometry and Doppler Experiments (PRIDE) technique in the interest of studying planet - satellite systems. The aim of this work is to demonstrate a technique of providing high precision positional and Doppler measurements of planetary spacecraft using the Mars Express spacecraft. The technique will be used in the framework of Planetary Radio Interferometry and Doppler Experiments in various planetary missions, in particular in fly-by mode. We advanced a novel approach to spacecraft data processing using the techniques of Doppler and phase-referenced very long baseline interferometry spacecraft tracking. We achieved, on average, mHz precision (30 {\mu}m/s at a 10 seconds integration time) for radial three-way Doppler estimates and sub-nanoradian precision for lateral position measurements, which in a linear measure (at a distance of 1.4 AU) corresponds to ~50 m., Comment: 9 pages, 14 figures. Astronomy and Astrophysics, accepted on 2016/05/31

In this paper a hierarchical model for pixel clustering and image segmentation is developed. In the model an image is hierarchically structured. The original image is treated as a set of nested images, which are capable to reversibly merge with each other. An object is defined as a structural element of an image, so that, an image is regarded as a maximal object. The simulating of none-hierarchical optimal pixel clustering by hierarchical clustering is studied. To generate a hierarchy of optimized piecewise constant image approximations, estimated by the standard deviation of approximation from the image, the conversion of any hierarchy of approximations into the hierarchy described in relation to the number of intensity levels by convex sequence of total squared errors is proposed., Comment: 5 pages, 3 figures, 6 formulas, submitted to the 13th International Conference on Pattern Recognition and Information Processing October 3-5, 2016, Minsk, Belarus