Algebras with ternary law of composition and their realization by cubic matrices

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle. Given two modules over the algebras with involutions we construct a ternary algebra which is used as a building block for a Lie algebra. We construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices. It is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices. We describe a ternary analog of Lie algebra of cubic matrices of second order which is based on a notion of j-commutator and find all commutation relations of generators of this algebra.Comment: 17 pages, 1 figure, to appear in "Journal of Generalized Lie Theory and Applications

Determination Of Dynamic Characteristics Of Heat Fire Detectors

The proposed methods for determining the dynamic characteristics of heat fire detectors in the time and frequency domains, focused on the use of existing thermal chambers. The proposed method for determining the transition function of the detector is implemented as follows. Heat fire detector creates a thermal effect in the form of a linearly increasing function. The response of the output signal to the influence of this type is measured and approximated using the Heaviside function at regular intervals.It is shown that information on the transition function of a heat fire detector can be used to determine its frequency characteristics by approximating it with Heaviside functions at the same time intervals. This method of determining the frequency characteristics will significantly reduce the time to determine them compared to the classical method, and also eliminate the need for additional equipment.As a result of the studies, the choice of the sampling interval was justified on the example of a class A1 heatfire detector and certain sampling intervals for determining their transition function (τ0≤1.05 s), amplitude-frequency characteristic (τ0≤0.27 s) and phase-frequency characteristic (τ0≤2.0 s).The proposed methods for determining the dynamic characteristics of heat fire detectors open up new opportunities for developing methods for monitoring their technical condition. This is because the information about the transition function of the detector can be used in two ways. The first method involves comparing a certain transition function of the detector with an exemplary one. The second method consists in determining other characteristics of the detector based on information about its transient function and comparing them with standard values

The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in Stochastic Model

Genetically engineered MAPT 10+16 mutation causes pathophysiological excitability of human iPSC-derived neurons related to 4R tau-induced dementia

Human iPSC lines represent a powerful translational model of tauopathies. We have recently described a pathophysiological phenotype of neuronal excitability of human cells derived from the patients with familial frontotemporal dementia and parkinsonism (FTDP-17) caused by the MAPT 10+16 splice-site mutation. This mutation leads to the increased splicing of 4R tau isoforms. However, the role of different isoforms of tau protein in initiating neuronal dementia-related dysfunction, and the causality between the MAPT 10+16 mutation and altered neuronal activity have remained unclear. Here, we employed genetically engineered cells, in which the IVS10+16 mutation was introduced into healthy donor iPSCs to increase the expression of 4R tau isoform in exon 10, aiming to explore key physiological traits of iPSC-derived MAPT IVS10+16 neurons using patch-clamp electrophysiology and multiphoton fluorescent imaging techniques. We found that during late in vitro neurogenesis (from ~180 to 230 days) iPSC-derived cortical neurons of the control group (parental wild-type tau) exhibited membrane properties compatible with "mature" neurons. In contrast, MAPT IVS10+16 neurons displayed impaired excitability, as reflected by a depolarized resting membrane potential, an increased input resistance, and reduced voltage-gated Na+- and K+-channel-mediated currents. The mutation changed the channel properties of fast-inactivating Nav and decreased the Nav1.6 protein level. MAPT IVS10+16 neurons exhibited reduced firing accompanied by a changed action potential waveform and severely disturbed intracellular Ca2+ dynamics, both in the soma and dendrites, upon neuronal depolarization. These results unveil a causal link between the MAPT 10+16 mutation, hence overproduction of 4R tau, and a dysfunction of human cells, identifying a biophysical basis of changed neuronal activity in 4R tau-triggered dementia. Our study lends further support to using iPSC lines as a suitable platform for modelling tau-induced human neuropathology in vitro

Nash equilibrium design in the interaction model of entities in the customs service system

The urgency of the analyzed issue is due to the importance of the use of economic-mathematical tools in the course of modeling the interaction of the entities in the customs service system that is necessary for the development of foreign economic activity (FEA) of any state. The purpose of the article is to identify effective strategies for the interaction between the participants of foreign trade activities with customs brokers. The leading method to the study of this issue is economic-mathematical modeling, allowing studying the process of making decisions while choosing the strategy of cooperation between the customs broker and his client. Results: the article suggests the mathematical model to optimize the management mechanisms of interaction between enterprises, engaged in foreign trade, and customs dealers. The data of this article may be useful in modeling interaction of the entities in the customs service system using the methods of game theory. The model of “customer - customs broker” is implemented as a bimatrix game. Assuming the noncooperativegame the authors solve the problem of finding Nash equilibrium in mixed strategies. © 2016 Fedorenko et al

Photo- and Cathodoluminescence MG-doped Alumina Ceramics

This work was financially supported by the Russian Science Foundation (RSF), project No. 1872-10082

МЕТОДИЧНІ АСПЕКТИ ВИКЛАДАННЯ ДИСЦИПЛІН НАПРЯМКУ «ІНТЕРНЕТ РЕЧЕЙ»

В роботі здійснено огляд комп’ютерних технологій Інтернету речей, короткий аналіз складу і структури інтернету речей, розглянуто властивості і особливості роботи і проектування вбудованих систем керування, як основної складової Інтернету речей. Досліджено запити ІоТ-індустрії щодо випускника закладу вищої освіти, а саме: наявність розуміння структури і процесів в екосистемі, в якій розвиваються виробники компонентів, постачальники готових систем і компанії-інтегратори; володіння системним, цілісним підходом до аналізу і оцінки ситуації та вирішення проблеми; відкритість до нових знань, ідей і технологій; вміння організовувати власну діяльність та виконувати проекти у складі групи, ефективно спілкуватись із замовником, формулювати технічне завдання, розробляти план його виконання, оцінювати та забезпечувати якість виконуваних робіт, представляти результати роботи й обґрунтовувати запропоновані рішення. З огляду на це вивчено ключові питання і проблеми викладання окремих дисциплін напрямку ІоТ та шляхи їх вирішення. Показано, що ефективним є проектне навчання, для реалізації якого було розроблено спеціальний алгоритм створення вбудованих комп’ютерних засобів ІоТ для його використання студентами в процесі вивчення відповідних дисциплін і створення власних проектів. Він характеризується тим, що передбачає дослідження більшості найвідоміших технологій та умов їх застосування і охоплює усі етапи проектування, які використовуються у виробництві. Описано впровадження отриманих результатів досліджень в Київському університеті імені Бориса Грінченка для підготовки фахівців спеціальності «Комп’ютерні науки» в рамках дисциплін «Фізичні процеси в обчислювальних системах» та «Технології проектування вбудованих комп’ютерних систем»

Corrosion resistance of alloys of Hastelloy in chloroaluminate melts

The corrosion of Hastelloy S, Hastelloy X, Haynes 230, Hastelloy N, Hastelloy G35 and Hastelloy C2000 alloys was studied in KCl-AlCl3 melts at 550°С. The rates and the mechanisms of corrosion of the studied materials were determined. The processes taking place during the interaction between alloys and chloroaluminate melts were investigated