Conditions for the solvability of boundary value problems for quasi-elliptic systems in a half-space

We consider boundary value problems in a half-space for a class of quasi-elliptic systems with constant coefficients. We assume that the boundary value problems satisfy the Lopatinskii condition. We obtain necessary and sufficient conditions for their unique solvability in Sobolev spaces.     

Submanifolds of compact operators with fixed multiplicities of eigenvalues

For the first time, a manifold of symmetric real matrices with fixed multiplicities of eigenvalues was considered by Arnold. In the case of compact real self-adjoint operators, similar results were obtained by Japanese mathematicians Fujiwara, Tanikawa, and Yukita. They introduced a special local diffeomorphism “straightening” the Arnold manifold. Later, the properties of the indicated diffeomorphism were studied by Dymarskii. We describe the smooth structure of submanifolds of finite-dimensional and compact operators of the general form in which a selected eigenvalue is associated with a single Jordan block.     

Simulación numérica de la agitación en tanques de almacenamiento de líquidos mediante una estrategia lagrangiana euleriana arbitraria

Sloshing of fluids with a free surface contained in liquid storage tanks is numerically simulated by an arbitrary Lagrangian-Eulerian formulation. The fluid is considered viscous and Newtonian, while the flow is assumed laminar and incompressible. A partitioned and distributed computational code is employed, which solves three instances each time step: (i) the determination of the fluid state, given by the Navier–Stokes equations; (ii) the displacement of the free surface; and (iii) the update of the position of the internal nodes of the mesh, that is deformed as a consequence of the free surface displacement. The purpose of the work is verifying the applicability of the method to sloshing problems with known solutions, as well as the resolution of some practical examples. Numerical examples include validations against analytical solutions, where the wave period and damping rate are well captured, comparisons with reference results from other authors and a sample of sloshing induced by seismic actions.     

On one conjecture in the theory of isochronous Liénard systems

New normal forms are obtained for the center as well as isochronous center of holomorphic Liénard systems.     

Kinetics and mechanism of the reaction between aquacobalamin and isoniazid

Kinetics of the reaction of aquacobalamin (H₂OCbl) with isoniazid (isonicotinic acid hydrazide, INH) in weakly alkaline, neutral, and weakly acidic media was studied using UV–Vis spectroscopy. It is shown that the reversible formation of a complex more stable than those of cobalamin(III) with pyridine and hydrazine occurs during the reaction. A mechanism of the reaction includes reversible stages of binding a neutral INH molecule by cobalamin(III) through an oxygen atom with its subsequent deprotonation, along with the reversible interaction of H₂OCbl and the negatively charged form of INH.     

Activation of molecular oxygen on copper(II) complexes of 5-hydroxy and 5-aminoorotic acids

The fixation and activation of molecular oxygen on copper(II) complexes with 5-hydroxy and 5-aminoorotic acids, leading to oxidation of the ligand.     

New ω-chloroalkyl-substituted isatins and isoindigo

Russian Journal of Organic Chemistry - New 1-(ω-chloroalkyl)isatins were synthesized by alkylation of isatin with α-bromo-ω-chloroalkanes. The reaction of 1-(3-chloropropyl)isatin...     

Peculiarities of temperature behavior of low-molecular fluorooligomers

The peculiarities of the behavior, structure, and properties of low-molecular fluoropolymers (fluorooligomers), namely, industrial fluoroparaffins and derivatives resulting from the thermal processing of ultradisperse powders of FORUM^® trademark, are studied. The results are obtained on the basis of the IR spectroscopic investigation of the products of pyrolysis of the fluorooligomers. The measurement data on rheological properties of the samples upon heating are analyzed.     

Effect of the conditions of activated carbon synthesis from wood on its porous structure and the specific characteristics of double layer supercapacitors with a sulfuric acid-based electrolyte

For supercapacitors with sulfuric acid electrolyte, a promising carbon material was suggested, namely, activated carbon from waste wood. It was shown how the synthesis conditions of activated carbon affect its porous structure and electrochemical characteristics of supercapacitors on its basis. The changes in the porous material under different synthesis conditions were controlled using the highly informative limited evaporation method, which allows us to obtain complete information about the porous structure of the micro- and mesopores of the material within a relatively short period of time. The negative effect of the excess volume of macropores in the electrode on the capacity and energy based on the dry mass of electrodes was shown experimentally and analyzed. The properties of the synthesized material were compared with those of other carbon materials. The best samples of the developed material possess a specific electric capacity of over 390 F/g.