Focusing of laser-generated ion beams by a plasma cylinder: similarity theory and the thick lens formula

It is shown that plasma-based optics can be used to guide and focus highly divergent laser-generated ion beams. A hollow cylinder is considered, which initially contains a hot electron population. Plasma streaming toward the cylinder axis maintains a focusing electrostatic field due to the positive radial pressure gradient. The cylinder works as thick lens, whose parameters are obtained from similarity theory for freely expanding plasma in cylindrical geometry. Because the lens parameters are energy dependent, the lens focuses a selected energy range of ions and works as a monochromator. Because the focusing is due to the quasineutral part of the expanding plasma, the lens parameters depend on the hot electron temperature $T_e$ only, and not their density

Asymptotic behaviour of Functional Identities

2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.We calculate the asymptotics of functional codimensions fcn(A) and generalized functional codimensions gfc n (A) of an arbitrary not necessarily associative algebra A over a field F of any characteristic. Namely, fcn(A) ∼ gfcn(A) ∼ dim(A^2) · (dim A^n) as n → ∞ for any finite-dimensional algebra A. In particular, codimensions of functional and generalized functional identities satisfy the analogs of Amitsur’s and Regev’s conjectures. Also we precisely evaluate fcn(UT2(F)) = gfcn(UT2(F)) = 3^(n+1) − 2^(n+1).* Supported by post doctoral fellowship from Atlantic Association for Research in Mathematical Sciences (AARMS), Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and Natural Sciences and Engineering Research Council of Canada (NSERC)

Graded group actions and generalized HH-actions compatible with gradings

We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseudoautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super- or a pseudoinvolution. We study groups of graded pseudoautomorphisms, show that the Jacobson radical of a group graded finite dimensional associative algebra $A$ over a field of characteristic $0$ is stable under graded pseudoautomorphisms, prove the invariant version of the Wedderburn-Artin Theorem and the analog of Amitsur's conjecture for the codimension growth of graded polynomial $G$-identities in such algebras $A$ with a graded action of a group $G$.Comment: 19 page

Performance Evaluation of Distributed Computing Environments with Hadoop and Spark Frameworks

Recently, due to rapid development of information and communication technologies, the data are created and consumed in the avalanche way. Distributed computing create preconditions for analyzing and processing such Big Data by distributing the computations among a number of compute nodes. In this work, performance of distributed computing environments on the basis of Hadoop and Spark frameworks is estimated for real and virtual versions of clusters. As a test task, we chose the classic use case of word counting in texts of various sizes. It was found that the running times grow very fast with the dataset size and faster than a power function even. As to the real and virtual versions of cluster implementations, this tendency is the similar for both Hadoop and Spark frameworks. Moreover, speedup values decrease significantly with the growth of dataset size, especially for virtual version of cluster configuration. The problem of growing data generated by IoT and multimodal (visual, sound, tactile, neuro and brain-computing, muscle and eye tracking, etc.) interaction channels is presented. In the context of this problem, the current observations as to the running times and speedup on Hadoop and Spark frameworks in real and virtual cluster configurations can be very useful for the proper scaling-up and efficient job management, especially for machine learning and Deep Learning applications, where Big Data are widely present.Comment: 5 pages, 1 table, 2017 IEEE International Young Scientists Forum on Applied Physics and Engineering (YSF-2017) (Lviv, Ukraine

Similarity for ultra-relativistic laser plasmas and the optimal acceleration regime

A similarity theory is developed for ultra-relativistic laser-plasmas. It is shown that the most fundamental S-similarity is valid for both under- and overdense plasmas. Optimal scalings for laser wake field electron acceleration are obtained heuristically. The strong message of the present work is that the bubble acceleration regime [see Pukhov, Meyer-ter-Vehn, Appl. Phys. B, vol. 74, 355 (2002)] satisfies these optimal scalings

Electronic structure of CuCl1-xBrx solid solutions: first-principles calculations in the meta-GGA approximation

The electronic structure of CuCl and CuBr compounds and their solid solutions CuCl1–xBrx (x = 0.25, 0.50, 0.75) has been calculated in the framework of the density functional theory. The calculations have been performed in the basis of pseudoatomic orbitals using the simple local approximation (LDA) and the new meta-GGA exchange potential TB09, which, to a large extent, compensates the LDA error in the description of the position of conduction bands in semiconductors. A comparative analysis of the main characteristics of the electronic structure of binary compounds and their solutions has been carried out. It has been found that the composition dependence of the band gap Eg(x) has a small downward bowing with the coefficient b ~ 0.09 eV

ФЕНОМЕН ГЛОБАЛЬНОГО МІСТА: ПРОБЛЕМИ ПОШУКУ ІДЕНТИЧНОСТІ В СУЧАСНОМУ МУЛЬТИКУЛЬТУРНОМУ ПРОСТОРІ (’Global City’ Phenomenon: Search for Identity Problems in Multicultural Space )

У статті висвітлюються основні аспекти соціокультурного виміру поняття «глобальне місто». Аналізуються проблеми пошуку національної та етнічної ідентичності в мультикультурному просторі глобального міста. Узагальнюються основні чинники стосовно проблеми пошуку ідентичності в контексті сучасних викликів політиці мультикультуралізму (The article deals with the main principles of the socio­cultural dimension of «global city.» The authors analyze the problems of national and ethnic identity searching in a multicultural global city space. Paper sums up the problems of identity factor in the context of the modern challenges of multicultural politics

EFFECT OF CA2+ AND AL3+ IONS ON INTERACTION BETWEEN BACTERIA AND MINERAL SORBENTS

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