Monotone matrix maps and Skolem-Noether theorem

Monotone matrix maps induced by a group inverse are considered. The characterization is given in additive and continuous cases. The ring version of the Skolem-Noether theorem is obtained. A series of examples of nonlinear monotone maps is presented.     

Stationary Schr?dinger equation in nonrelativistic quantum mechanics and the functional integral

We formulate a method for representing solutions of homogeneous second-order equations in the form of a functional integral or path integral. As an example, we derive solutions of second-order equations with constant coefficients and a linear potential. The method can be used to find general solutions of the stationary Schr?dinger equation. We show how to find the spectrum and eigenfunctions of the quantum oscillator equation. We obtain a solution of the stationary Schr?dinger equation in the semiclassical approximation, without a singularity at the turning point. In that approximation, we find the coefficient of transmission through a potential barrier. We obtain a representation for the elastic potential scattering amplitude in the form of a functional integral.     

Deformation theory of objects in homotopy and derived categories II: Pro-representability of the deformation functor

This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors to an appropriate bicategory of artinian DG algebras and prove that these extended functors are pro-representable in a strong sense.     

Stabilization of propane combustion in a supersonic air flow using a nonequilibrium longitudinal discharge and a coaxial local low-pressure zone

The results of the experimental investigation of the flow in the vicinity of an electric-discharge module having a low aerodynamic drag and intended for igniting hydrocarbon fuel and stabilizing its burning in a supersonic flow at low initial static temperature and pressure are presented. The distinctive feature of the module is that the combustion zone is not attached to the combustion chamber walls. Due to a certain geometric connection between different regions of the module anode, an interference of shock and expansion waves occurs in its vicinity. This leads to the formation of a local longitudinal low-pressure zone behind the anode, the convergence of individual fuel jetlets injected through orifices in the anode in this zone, the formation precisely there of a longitudinal nonequilibrium discharge, and the intensification of fuel mixing and plasmochemical reactions. The gasdynamic features of supersonic flow past the module are numerically investigated. The dynamics of electrical discharge formation and the combustion zones thus formed are studied under particular conditions. The data on the stagnation temperature distribution in the discharge wake are obtained.     

Effect of electroactive anions on electrochemical behavior of polyaniline

Electrochemical potentiostatic synthesis was used to obtain polyaniline (PAni) modified by new electroactive dopants: dianions of a diammonium salt (2,2′-azine-bis-(3-ethylbenzthiazoline-6-sulfoacid) (ABTS) and ammonium hexachloriridate IrCl₆²⁻ (HCI). Electrochemical behavior of PAni-ABTS and PAni-HCI modified polymers is studied by means of the methods of cyclic voltammetry (CV) and measuring charge-discharge dependences. It is shown that modified PAni-ABTS and PAni-HCI remain electroactive at significantly higher potential sweep rate dependences as compared to PAni doped by HSO₄⁻ (PAni-sulfo). Electrochemical capacity values C are calculated according to the CV data (F/g) and discharge curves (mA h/g) and coulombic efficiency values (ή) of new polymers are determined that cause a considerable increase in the pertinent characteristics of PAni-sulfo. This effect is enhanced in the case of introducing the ABTS and HCI additives into the background electrolyte.     

Experimental and theoretical investigation of γ-butyrolactone decomposition on lithium electrode surface. Effect of Li3N layer

Dependence of gassing upon decomposition of 1 M LiClO₄ electrolyte in γ-butyrolactone (γBL) with various contents of water (0.008 and 0.2% w/w) at a lithium electrode on the current density of charging was studied. Quantum chemical modeling of γBL interaction with lithium surface was performed. The initial stage of γBL decomposition is the formation of a surface organolithium compound, which is hydrolyzed in the subsequent reactions with water.     

Effect of solvents on properties of polymer gel-electrolyte based on polyester diacrylate

New polymer gel electrolytes based on polyester diacrylates and LiClO₄ salt solutions in organic solvents are developed for lithium ion and lithium polymer batteries with a high ionic conductivity up to 2.7 × 10^?3 Ohm^?1cm^?1 at the room temperature. To choose the optimum liquid electrolyte composition, the dependence is studied of physico-chemical parameters of new gel electrolytes on the composition of the mixture of aprotic organic solvents: ethylene carbonate, propylene carbonate, and λ-butyrolacton. The bulk conductivity of gel electrolytes and exchange currents at the gel electrolyte/Li interface are studied using the electrochemical impedance method in symmetrical cells with two Li electrodes. The glass transition temperature and gel homogeneity are determined using the method of differential scanning calorimetry. It is found that the optimum mixture is that of propylene carbonate and λ-butyrolacton, in which a homogeneous polymer gel is formed in a wide temperature range of ?150 to +50°C.     

Deformation theory of objects in homotopy and derived categories I: General theory

This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Defh(E), coDefh(E), Def(E), coDef(E). The first two functors describe the deformations (and co-deformations) of E in the homotopy category, and the last two - in the derived category. We study their properties and relations. These functors are defined on the category of artinian (not necessarily commutative) DG algebras.