New representation of Dirac-Yang-Mills equations

With the help of the apparatus of tensors with values in the Atiyah-Kähler algebra (the apparatus of lambda tensors), a new representation for the relativistic equation of field theory is proposed. The circle of questions under consideration is standard for investigations concerning the theory of the Dirac equation (in this paper, we treat no problems dealing with second quantization).     

Adjoint equations and their applications

Proceedings of the Steklov Institute of Mathematics -     

Numerical simulation of natural convection in a sessile liquid droplet

Heat transfer in a sessile liquid droplet was studied with numerical methods. A computer code was developed for solving the problem of convection in an axisymmetric hemispherical droplet and in a spherical layer as well. The problem of establishing an equilibrium state in a droplet was solved using several variables: temperature, stream function, and vorticity. Simulation was performed for droplets of water, ethyl alcohol, and model liquids. Variable parameters: intensity of heat transfer from droplet surface, Rayleigh and Marangoni dimensionless criteria, and the characteristic temperature difference. It was revealed that the curve of convective flow intensity versus heat transfer intensity at droplet surface has a maximum. A dual-vortex structure was obtained in a stationary hemispherical profile of liquid droplet for the case of close values for thermocapillary and thermogravitational forces. Either thermocapillary or thermogravitational vortex might be dominating phenomena in the flow structure.     

Angular Benzoperylenetetracarboxylic Bisimides

Benzoperylene derivatives with two angularly attached dicarboxylic imide rings, which were prepared by the Diels–Alder‐Reaction, exhibit strong fluorescence and their free peri positions allow either control of the UV/Vis spectra through their substituents or form anchor positions for the attachment of functional units. The angular chromophore 3 may be used both for fluorescent labeling such as for primary amines or enzymes or as building blocks for more complex assemblies where they may act as energy donors for FRET or electron acceptors in PET such as for photovoltaic solar cells.     

The Degree of Decidable Categoricity of a Model with Infinite Solutions for Complete Formulas

Algebra and Logic - We construct a decidable prime model in which the degree of a set of complete formulas is equal to 0', infinitely many tuples of elements comply with every complete formula,...     

Electret-thermal and dielectric analyses of electrically active colloids

The nature and mechanism of interfacial electrical interaction in organic colloids containing an active solid phase and a polar liquid phase are studied. Such systems are shown to offer specific properties. Specifically, high electrical forces producing gradients of the potential of the self-electric internal field arise at the liquid-solid interface. In the presence of free charges and ionic conductivity channels, this field can induce currents in such systems. When investigating the colloid system of the human venous blood, it is found that the internal field causes mesoscopic inhomogeneity in the structure of the aqueous components of the plasma and cytoplasm. It is shown that the concentration of free water molecules in the liquid phase of the system is maximal in group I blood and the physically nonuniform properties of combined water show up to the greatest extent in group IV blood. This finding is corroborated by the dispersion of the dielectric polarization in blood of different groups.     

A High‐Pressure Polymorph of Phosphorus Nitride Imide

Phosphorus nitride imide, PN(NH), is of great scientific importance because it is isosteric with silica (SiO₂). Accordingly, a varied structural diversity could be expected. However, only one polymorph of PN(NH) has been reported thus far. Herein, we report on the synthesis and structural investigation of the first high‐pressure polymorph of phosphorus nitride imide, β‐PN(NH); the compound has been synthesized using the multianvil technique. By adding catalytic amounts of NH₄Cl as a mineralizer, it became possible to grow single crystals of β‐PN(NH), which allowed the first complete structural elucidation of a highly condensed phosphorus nitride from single‐crystal X‐ray diffraction data. The structure was confirmed by FTIR and ³¹P and ¹H solid‐state NMR spectroscopy. We are confident that high‐pressure/high‐temperature reactions could lead to new polymorphs of PN(NH) containing five‐fold‐ or even six‐fold‐coordinated phosphorus atoms and thus rivalling or even surpassing the structural variety of SiO₂.     

Model of filmwise vapor condensation on curved surfaces

A three-dimensional unsteady model of filmwise vapor condensation on a curved surface that takes into account the mass forces, the surface tension, and the friction on the surface of the condensate film is developed. This model generalizes the previous models of the filmwise vapor condensation. An evolution equation is derived for a condensate-layer thickness. Numerical algorithms are developed for solving the evolution equation. The condensation of ethanol vapor moving in a round tube is calculated. The effect of the tube diameter on the intensity of condensation is analyzed.