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

Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Pion Charge Exchange on Deuterium

We investigate quantum corrections to a classical intranuclear cascade simulation of pion single charge exchange on the deuteron. In order to separate various effects the orders of scattering need to be distinguished and, to that end, we develop signals for each order of scattering corresponding to quasi-free conditions. Quantum corrections are evaluated for double scattering and are found to be large. Global agreement with the data is good.Comment: 30 pages, 12 figure

The analyses of socio-economic development tendencies of the capital cities in the modern Russia

© 2016 Taylor & Francis Group, London.This article introduces the approach of the evaluation of socio-economic development of the capital cities. On the basis of the analysis of statistical data in dynamics of the 10-year period, the classification of the cities according to their level of development is given, the found tendencies are explained, the main problems are displayed, and the probable ways of the development of cities are proposed

The cubic chessboard

We present a survey of recent results, scattered in a series of papers that appeared during past five years, whose common denominator is the use of cubic relations in various algebraic structures. Cubic (or ternary) relations can represent different symmetries with respect to the permutation group S_3, or its cyclic subgroup Z_3. Also ordinary or ternary algebras can be divided in different classes with respect to their symmetry properties. We pay special attention to the non-associative ternary algebra of 3-forms (or ``cubic matrices''), and Z_3-graded matrix algebras. We also discuss the Z_3-graded generalization of Grassmann algebras and their realization in generalized exterior differential forms. A new type of gauge theory based on this differential calculus is presented. Finally, a ternary generalization of Clifford algebras is introduced, and an analog of Dirac's equation is discussed, which can be diagonalized only after taking the cube of the Z_3-graded generalization of Dirac's operator. A possibility of using these ideas for the description of quark fields is suggested and discussed in the last Section.Comment: 23 pages, dedicated to A. Trautman on the occasion of his 64th birthda

On the construction of generalized Grassmann representatives of state vectors

Generalized $Z_k$-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors.Comment: 8 page

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

Symmetry of bound and antibound states in the semiclassical limit

We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h. This simple result was inspired by a numerical experiment and we describe the numerical scheme for an efficient computation of resonances in one dimension

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