On Sushchansky p-groups

We study Sushchansky p-groups. We recall the original definition and translate it into the language of automata groups. The original actions of Sushchansky groups on p-ary tree are not level-transitive and we describe their orbit trees. This allows us to simplify the definition and prove that these groups admit faithful level-transitive actions on the same tree. Certain branch structures in their self-similar closures are established. We provide the connection with, so-called, G groups that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions.Comment: 14 pages, 3 figure

Constructing networks of quantum channels for state preparation

Entangled possibly mixed states are an essential resource for quantum computation, communication, metrology, and the simulation of many-body systems. It is important to develop and improve preparation protocols for such states. One possible way to prepare states of interest is to design an open system that evolves only towards the desired states. A Markovian evolution of a quantum system can be generally described by a Lindbladian. Tensor networks provide a framework to construct physically relevant entangled states. In particular, matrix product density operators (MPDOs) form an important variational class of states. MPDOs generalize matrix product states to mixed states, can represent thermal states of local one-dimensional Hamiltonians at sufficiently large temperatures, describe systems that satisfy the area law of entanglement, and form the basis of powerful numerical methods. In this work we develop an algorithm that determines for a given linear subspace of MPDOs whether this subspace can be the stable space of some frustration free k-local Lindbladian and, if so, outputs an appropriate Lindbladian. We proceed by using machine learning with networks of quantum channels, also known as quantum neural networks (QNNs), to train denoising post-processing devices for quantum sources. First, we show that QNNs can be trained on imperfect devices even when part of the training data is corrupted. Second, we show that QNNs can be trained to extrapolate quantum states to, e.g., lower temperatures. Third, we show how to denoise quantum states in an unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip, dephasing errors, and random unitary noise. Finally, we develop recurrent QNNs (RQNNs) for denoising that requires memory, such as combating drifts. RQNNs can be thought of as matrix product quantum channels with a quantum algorithm for training and are closely related to MPDOs. The proposed preparation and denoising protocols can be beneficial for various emergent quantum technologies and are within reach of present-day experiments

Classification of Existing Virtualization Methods Used in Telecommunication Networks

This article studies the existing methods of virtualization of different resources. The positive and negative aspects of each of the methods are analyzed, the perspectivity of the approach is noted. It is also made an attempt to classify virtualization methods according to the application domain, which allows us to discover the method weaknesses which are needed to be optimized.Comment: 4 pages, 3 figure

Application of Vortex and Pulsation Coolers in Technologies of Rare Gases Extraction

Two types of gas-dynamic coolers were considered: Rank-Hilsh vortex tubes and resonance tubes, known as devices of Hartmann-Sprenger. These devices have a number of similar physical and structural features: no moving parts, low inertia, environment safety, they can be sources of cold and heat simultaneously, generate pressure pulse, and separate gas mixtures. Gas-dynamic devices can be used in the technologies of rare gases obtaining as coolers of reflux condensers. They use pressure drop and don’t need in additional energy consumption. The temperature drop of mixtures phase equilibrium allows to reduce the concentration of by-products. Due to this, costs of gas concentrates transportation are reduced. Schemes, in which the separation function of the gas-dynamic devices are used, were investigated. The results of tests of step-type coolers in the condition of cryogenic temperatures on methane and helium are presented. An influence of the real gas and a scale factor in the interval of the energy separation chamber’s diameter up to 3 mm was studied

Groups generated by 3-state automata over a 2-letter alphabet, I

An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related to the whole class are formulated. In particular, all finite, abelian, and free groups are classified. In addition, we provide detailed information and complete proofs for several groups from the class, with the intention of showing the main methods and techniques used in the classification.Comment: 37 pages, 52 figure

Tolerance as an important aspect of the professional competence of future specialists

The article outlines tolerance as an important aspect of the professional competence of future specialists. The purpose of the article is disclosed, which substantiates the foundations of the formation of tolerance in students of education as an important aspect of the professional competence of future specialists. The main positions of the formation of tolerance among education seekers are shown and the necessity of an important aspect of the professional competence of future competitive specialists is shown. The definition of tolerance in various aspects is proposed. In order to reveal the essence of professional tolerance, its functions, which are important in our research, are summarized. A typology of tolerance was carried out according to the social spheres of its existence. The article proposes and analyzes three types of orientation of professional tolerance of an individual: intertolerance (external type of tolerance); intratolerance (internal type of tolerance); balanced type of tolerance (clear combination of intratolerance and intertolerance). In the article, the authors define various principles and components of professional tolerance. The criteria of a culturally tolerant personality are singled out. The principles and functions of professional tolerance are considered