On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

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

Assessment of ROS Production in the Mitochondria of Live Cells

Production of reactive oxygen species (ROS) in the mitochondria plays multiple roles in physiology, and excessive production of ROS leads to the development of various pathologies. ROS in the mitochondria are generated by various enzymes, mainly in the electron transporvt chain, and it is important to identify not only the trigger but also the source of free radical production. It is important to measure mitochondrial ROS in live, intact cells, because activation of ROS production could be initiated by changes in extramitochondrial processes which could be overseen when using isolated mitochondria. Here we describe the approaches, which allow to measure production of ROS in the matrix of mitochondria in live cells. We also demonstrate how to measure kinetic changes in lipid peroxidation in mitochondria of live cells. These methods could be used for understanding the mechanisms of pathology in a variety of disease models and also for testing neuro- or cardioprotective chemicals

Z3_3-graded differential geometry of quantum plane

In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given.Comment: 17 page

Monomeric alpha-synuclein exerts a physiological role in brain ATP synthase

Misfolded α-synuclein is a key factor in the pathogenesis of Parkinson's disease (PD). However, knowledge about a physiological role for the native, unfolded α-synuclein is limited. Using brains of mice lacking α-, β-, and γ-synuclein, we report that extracellular monomeric α-synuclein enters neurons and localizes to mitochondria, interacts with ATP synthase subunit α, and modulates ATP synthase function. Using a combination of biochemical, live-cell imaging and mitochondrial respiration analysis, we found that brain mitochondria of α-, β-, and γ-synuclein knock-out mice are uncoupled, as characterized by increased mitochondrial respiration and reduced mitochondrial membrane potential. Furthermore, synuclein deficiency results in reduced ATP synthase efficiency and lower ATP levels. Exogenous application of low unfolded α-synuclein concentrations is able to increase the ATP synthase activity that rescues the mitochondrial phenotypes observed in synuclein deficiency. Overall, the data suggest that α-synuclein is a previously unrecognized physiological regulator of mitochondrial bioenergetics through its ability to interact with ATP synthase and increase its efficiency. This may be of particular importance in times of stress or PD mutations leading to energy depletion and neuronal cell toxicity

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme

MOOCs Usage in Russian Higher Educational Institutions: Why Is Not There Any Increasing Demand for MOOCs During Emergency Distance Learning

The abrupt transition to distance learning during the outbreak of the COVID-19 pandemic triggered an urgent need for online resources at higher education institutes (HIEs). Creating analogues of traditional full-time courses demanded for competencies and time resources. In this case ready-made massive open online courses (MOOCs) were supposed to be the most obvious and fastest solution for HIEs. However, analytics demonstrated that educational institutions did not consider MOOC a promising option. This contradiction served as an incentive to conduct this research, which includes the analysis of both non-reactive (MOOCs platform analytics) and reactive (online survey and interviews with instructors) data. Based on our research, we can conclude that the reasons for not integrating MOOCs at Russian HIEs during the COVID-19 pandemic are the following: the peculiarities of MOOCs format, low motivation of instructors, administrative risks, and the uncertainty of HIEs’ and national policies on MOOCs integration. This article will be useful for those who determine educational policy in Russia, university administrators, methodologists responsible for the development of digital educational technologies in HIEs, as well as researchers of higher education

Joule Heating and Current-Induced Instabilities in Magnetic Nanocontacts

We consider the electrical current through a magnetic point contact in the limit of a strong inelastic scattering of electrons. In this limit local Joule heating of the contact region plays a decisive role in determining the transport properties of the point contact. We show that if an applied constant bias voltage exceeds a critical value, the stationary state of the system is unstable, and that periodic, non-harmonic oscillations in time of both the electrical current through the contact and the local temperature in the contact region develop spontaneously. Our estimations show that the necessary experimental conditions for observing such oscillations with characteristic frequencies in the range $10^8 \div 10^9$ Hz can easily be met. We also show a possibility to manipulate upon the magnetization direction of a magnetic grain coupled through a point contact to a bulk ferromagnetic by exciting the above-mentioned thermal-electric oscillations.Comment: 9 pages, 6 figures, submitted to Physical Review