Finite linear groups, lattices, and products of elliptic curves

Let $V$ be a finite dimensional complex linear space and let $G$ be an irreducible finite subgroup of \GL(V). For a $G$-invariant lattice $\Lambda$ in $V$ of maximal rank, we give a description of structure of the complex torus $V/\Lambda$. In particular, we prove that for a wide class of groups, $V/\Lambda$ is isogenous to a self-product of an elliptic curve, and that in many cases $V/\Lambda$ is isomorphic to a product of mutually isogenous elliptic curves with complex multiplication. We show that there are $G$ and $\Lambda$ such that the complex torus $V/\Lambda$ is not an abelian variety but one can always replace $\Lambda$ by another $G$-invariant lattice $\Delta$ such that $V/\Delta$ is a product if elliptic curves with complex multiplication. We amplify these results with a criterion, in terms of the character and the Schur $\mathbf Q$-index of $G$-module $V$, of the existence of a nonzero $G$-invariant lattice in $V$.Comment: 25 pages. Several examples are adde

Norm closed operator ideals in Lorentz sequence spaces

In this paper, we study the structure of closed algebraic ideals in the algebra of operators acting on a Lorentz sequence space.Comment: 25 page

Simulation model of load balancing in distributed computing systems

The availability of high-performance computing, high speed data transfer over the network and widespread of software for the design and pre-production in mechanical engineering have led to the fact that at the present time the large industrial enterprises and small engineering companies implement complex computer systems for efficient solutions of production and management tasks. Such computer systems are generally built on the basis of distributed heterogeneous computer systems. The analytical problems solved by such systems are the key models of research, but the system-wide problems of efficient distribution (balancing) of the computational load and accommodation input, intermediate and output databases are no less important. The main tasks of this balancing system are load and condition monitoring of compute nodes, and the selection of a node for transition of the user's request in accordance with a predetermined algorithm. The load balancing is one of the most used methods of increasing productivity of distributed computing systems through the optimal allocation of tasks between the computer system nodes. Therefore, the development of methods and algorithms for computing optimal scheduling in a distributed system, dynamically changing its infrastructure, is an important task

MANAGEMENT ACTIVITIES EFFECTIVENESS IN MODERN RUSSIAN INSTITUTION IN THE CONTEXT OF HEAD WORKPLACE MODELING

Purpose: The scientific approach to the organization of labor and the workplace of the institution head involves the search for the most optimal model or technique acceptable to the Russian conditions within the current management culture, traditional views on the nature of managerial work, the scale and effectiveness of management activities. Methodology: Methodological guidelines for the study of workplaces’ organization of credit and financial institutions’ heads are based on the provisions of modern ergonomics and the principles of a system-based approach, allowing justifying as a significant one the environment-oriented approach. Result: The obtained results served as the basis for the development of appropriate recommendations to optimize the current situation in the context of eliminating existing gaps and problems in the credit and financial sector of the Russian economy from the standpoint of optimizing the process of organizing working places for managers of institutions in this profile. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of the Management Activities Effectiveness in Modern Russian Institution in the context of Head Workplace Modeling is presented in a comprehensive and complete manner

Algorithm of Key Words Search Based on Graph Model of Linguistic Corpus

One of the problems of computer corpus linguistics is an automatic determination of keywords inthe text. The solution is a statistical method based on calculation of various frequency characteristics of the text. In this case, the most commonly used model is a “bag of words”, which does not take into account the order of words in the text. In this paper, we propose a graph model of the text that allows us to calculate the frequency characteristics of words in the text not only within the framework of the “word bag” model, but with respect to location of pairs of owls in some common part of the text, for example, in one sentence. To work with such a model, a software model is constructed in the form of a database schema intended for storing various statistical text information. Taking into account such a data model, the article proposes an algorithm for determining the keywords of the text, the implementation of which is performed in the Python programming language. When analyzing a document d of linguistics corpus D, our algorithm creates a list of about 40 words with the largest measure tf-idf, and choise from them 20 words, which are more often used in the document d. We regard these words as vertices of some graph G, and the multiplicity of the edge, connecting the vertices t and t’ is equal to the number of sentences in document d, containing both these words. Approximately 10 vertices of the graph with the greatest degree are selected. The words corresponding to these vertices are taken for key words of document d

Microstructural Features in Multicore Cu–Nb Composites

none5siThe study is devoted to heavily drawn multicore Cu–18Nb composites of cylindrical and rectangular shapes. The composites were fabricated by the melt-and-deform method, namely, 600 in situ rods of Cu–18%Nb alloy were assembled in a copper shell and cold-drawn to a diameter of 15.4 mm (e = 10.2) and then rolled into a rectangular shape the size of 3 × 5.8 mm (e = 12.5). The specimens were analyzed from the viewpoints of their microstructure, microhardness, and thermal stability. The methods of SEM, TEM, X-ray analysis, and microhardness measurements were applied. It is demonstrated that, at higher strain, the fiber texture ⟨110⟩Nb∥ ⟨111⟩Cu∥ DD (drawing direction), characteristic of this material, becomes sharper. The distortions of niobium lattice can be observed, namely, the {110} Nb interplanar distance is broadened in longitudinal direction of specimens and compacted in transverse sections. The copper matrix lattice is distorted as well, though its distortions are much less pronounced due to its recrystallization. Evolution of microstructure under annealing consists mainly in the coagulation of ribbon-like Nb filaments and in the vanishing of lattice distortions. The structural changes in Nb filaments start at 300–400 °C, then develop actively at 600 °C and cause considerable decrease of strength at 700–800 °C.openElena N. Popova, Irina L. Deryagina,Evgeniya G. Valova-Zaharevskaya, Ruello Maria Letizia, Vladimir V. PopovElena N., Popova; Irina L., Deryagina; Evgeniya G., Valova-Zaharevskaya; Ruello, Maria Letizia; Vladimir V., Popo