Study of the Thermal Behavior of Wedge-Shaped Samples of HfB<Subscript>2</Subscript>–45 vol % SiC Ultra-High-Temperature Composite in a High-Enthalpy Air Flow

By spark plasma sintering, HfB₂–45 vol % SiC ultra-high-temperature ceramic was prepared, from which wedge-shaped samples were cut. The behavior of the samples was examined in a flow of dissociated air produced by an induction plasmatron, where the surface temperature of the leading edges of the samples reached ~2700°C. The dependence of the temperature distribution gradient on the distance from the leading edges of the samples was experimentally investigated. For the samples after the experiments, the elemental and phase compositions were determined, and features of the surface microstructure in various regions of the sample and on its polished surface were studied.     

Pyrroloindoles. 8. Electrophilic substitution in the 1H,5H-pyrrolo[2,3-f]indole and 3H,6H-pyrrolo[3,2-e]indole series

The principles of the electron density distribution in 1H,5H-pyrrolo [2,3-f]indole and 3H,6H-pyrrolo[3,2-e]indole molecules were determined on the basis of quantumchemical calculations. These results were confirmed by the results of the investigated electrophilic-substitution reactions. The reaction centers of these compounds proved to be the same positions as in indole, viz., the 3 and 7 and 1 and 8 positions, respectively. The impossibility of 1,8-disubstitution in the angular heteroring was demonstrated in the case of bulky substituents; this was explained by a steric effect.See [1] for communication 7.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1086–1091, August, 1983.     

μSR-study of reactivity of substituent ions and point-like defects in quartz monocrystals

SR-method has been used for studying reactions of muonium as an analogue of a light hydrogen isotope with impurity atoms and point-like defects. The relaxation rate of muonium polarization _Mu was measured for 11 samples with different concentrations of impurity atoms and defects. The rate constants of reactions of muonium with Fe, Al, Li, Ba, Cu, Mn, Ti and Pb atoms in quartz were defined.     

The Hilbert–Poincaré Series for Some Algebras of Invariants of Cyclic Groups

Let be a linear representation of a finite group over a field of characteristic 0. Further, let R be the corresponding algebra of invariants, and let P (t) be its Hilbert–Poincaré series. Then the series P (t) represents a rational function (t)/(t). If R is a complete intersection, then (t) is a product of cyclotomic polynomials. Here we prove the inverse statement for the case where is an almost regular (in particular, regular) representation of a cyclic group. This yields an answer to a question of R. Stanley in this very special case. Bibliography: 3 titles.     

Word maps and word maps with constants of simple algebraic groups

In the present paper, we consider word maps w: G ^m → G and word maps with constants w _Σ: G ^m → G of a simple algebraic group G, where w is a nontrivial word in the free group F _m of rank m, w _Σ = w ₁ σ ₁ w ₂ ··· w _r σ _r w _{r + 1}, w ₁, …, w _{r + 1} ∈ F _m , w ₂, …, w _r ≠ 1, Σ = {σ ₁, …, σ _r | σ _i ∈ G Z(G)}. We present results on the images of such maps, in particular, we prove a theorem on the dominance of “general” word maps with constants, which can be viewed as an analogue of a well-known theorem of Borel on the dominance of genuine word maps. Besides, we establish a relationship between the existence of unipotents in the image of a word map and the structure of the representation variety R(Γ_w, G) of the group Γ_w = F _m /<w>.     

HF-plasmatron experiment and numerical simulation of heat transfer in underexpanded dissociated-nitrogen jets

Experiments on heat transfer in underexpanded supersonic jets of high-enthalpy nitrogen are performed on the VGU-4 induction high-frequency plasmatron at a pressure of 10.4 GPa in a compression chamber. At gas flow rates of 2.4 and 3.6 g/s and HF generator powers of 45 and 64 kW the heat fluxes to the copper, stainless steel, MPG-7 graphite, and quartz surfaces are measured at the stagnation point of a water-cooled cylindrical, flat-ended model, 20 mm in diameter. In the same regimes the stagnation pressures are measured. The effect of the surface catalyticity with respect to nitrogen atom recombination on the heat flux is demonstrated and the qualitative catalyticity scale of the studied materials is established. In the supersonic regimes nonequilibrium nitrogen plasma flow in the discharge channel of the plasmatron and the underexpanded jet flow past the model are numerically simulated for the experimental conditions. The experimental and calculated data on the stagnation pressures and the heat fluxes to cooled surfaces of the metals, graphite, and quartz are compared.