On the classical solutions of the liouville equation in a four-dimensional euclidean space

In terms of Fueter analytic functions, a classical solution of the Liouville equation in a fourdimensional Euclidean space depending on two arbitrary complex functions is obtained and discussed.     

Investigations of 2-substituted imidazoles. 2. Synthesis and electrophilic substitution of 1-methyl-2-(thienyl-2)imidazole. A convenient method of methylation of 2-R-imidazoles

We have synthesized 2-(thienyl-2)imidazole and its N-methyl derivative. The latter product was obtained by nitration, bromination, acylation, and formylation, occurring as a rule on the thiophene ring. A general method for methylating 2-R-imidazoles with methyl iodide KOH-dimethoxy ethane is proposed.For Communication 1 see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1414–1418, October, 1991.     

Synthesis and methylation products of 4(5)-(2-furyl)imidazole

Bromination of 2-acetylfuran with copper(II) bromide in a mixture of ethyl acetate and chloroform leads selectively to furacyl bromide, the nucleophilic substitution of bromine in which by OAc and subsequent use of the Weidenhagen reaction enabled the synthesis of 4(5)-(2-furyl)imidazole. On N-methylation of this imidazole in KOH–acetone 2 isomers are formed, the 1-methyl-4- and 1-methyl-5-(2-furyl)imidazoles. It was established that, unlike alkylation of 4(5)-phenylimidazole, the main product of the reaction is 1-methyl-5-(2-furyl)imidazole.     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

Electroluminescent characteristics of InGaAsSb/GaAlAsSb heterostructure Mid-IR LEDs at high temperatures

The electroluminescent characteristics of an InGaAsSb/GaAlAsSb heterostructure LED emitting at 1.85 μm are studied in the temperature range 20–200°C. It is shown that the emission power exponentially drops as P ≅ 0.4exp(2.05 × 10³/T) with a rise in temperature primarily because of an increase in the Auger recombination rate. It is found that band-to-band radiative recombination goes in parallel with recombination through acceptor levels, the latter causing the emission spectrum to broaden. With a rise in temperature, the activation energy of the acceptor levels decreases by the law ΔE≅ 32.9 − 0.075T and the maximum of the LED’s emission spectrum shifts toward the long-wavelength range (hν _max = 0.693 − 4.497 × 10⁻⁴ T). Based on the dependence E _g = hν _max − 0.5kT and experimental data, an expression is derived for the temperature variation of the bandgap in the In_0.055Ga_0.945AsSb active area, E _g ≅ 0.817 − 4.951 × 10⁻⁴ T, in the range 290 K < T < 495 K. The resistance of the heterostructure decreases exponentially with rising temperature as R ₀ ≅ 5.52 × 10⁻²exp(0.672/2kT), while cutoff voltage U _cut characterizing the barrier height of a p−n junction decreases linearly with increasing temperature (U _cut = −1.59T + 534). It is found that the current through the heterostructure is due to the generation-recombination mechanism throughout the temperature interval.     

Multilayer coaxial fiber dielectric elastomers for actuation and sensing

A simple dip-coating technique was employed to manufacture coaxial actuators with multiple layers of alternating dielectric and conducting layers. A thin rubber string was coated with an electrode–insulator–electrode structure, giving rise to a thin, fiber-like actuator with coaxial geometry. The process was repeated to achieve a compact multilayer actuator with up to three coaxial dielectric layers. Mechanical and electromechanical characterization of the actuators is presented, showing actuation strains up to 8% and proper voltage–thickness scaling behavior. Also presented is a capacitance vs. extension plot, demonstrating that these structures can be used for compact and accurate capacitive strain sensing.     

Tape polymer materials for anti-corrosion insulation of pipelines

The article discusses peculiar features of polymer tape coatings for protecting pipelines and main methods of applying them in a field environment. It is shown that the design of polymer tape coating depends on operational conditions, the conditions of the coating application, and the method of pipeline construction. The main Russian and Western insulating materials are reviewed and some of the technical characteristics of these materials are presented.     

Method of frustrated total reflection in spectroscopy of surface polaritons in almost perfectly conducting metals

The standard technique for surface polaritons excitation by a prism coupling in Otto configuration is applied for investigation of almost perfectly conducting (pec) metals like tantalum irradiated by a collimated He-Ne laser radiation (λ ₀ = 632.8 nm). In pec metals the imaginary part of the relative dielectric permittivity (ɛ″) is quite larger than the modulus of the real part of the same quantity (ɛ′ < 0, ɛ″ ≫ | ɛ′ |). Under this condition the single Lorentz dip of the reflectivity coefficient is proven to exist and is given in an analytical form, which follows from simplification of the usual multilayer Fresnel formula. In the case of a deterministically curved metal surface an approximate solution to the reduced Rayleigh integral equation appropriate for the Otto configuration is also given. These two theoretical deductions are compared with experimental data that have been produced by us for the reflectivity into the prism region from a bulk tantalum sample.