On the construction and calculation of optimal nonlifting critical airfoils

Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM for a given thickness ratio and tail angle _t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM and for various _t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM 1, 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding and _t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.     

The classical ruin problem on a finite solvable group

For the classical ruin problem (a special case of a cyclic group), we use an explicit expression for the characteristic function of the time of first hitting an arbitrary subset of a finite solvable group by a random walk, from a fixed subset, to obtain a new proof of the well-known formula which allows one to estimate the characteristic function of the ruin probability (hitting the identity of a group) at theth- trial.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 361–366, March, 1993.     

Path integral evaluation of the Eta function

In a three-dimensional model in which the gauge group does not commute with the Lorentz group, we demonstrate how the phase associated with the one-loop effective action (the function) can be computed by considering a quantum mechanical path integral.     

Optimization of reliability and longevity of cylindrical shells subject to corrosive wear

The problem of the optimal (with respect to the minimum average rate of weight loss in a structure) design of a smooth cylindrical shell loaded by an axial compressive force and under corrosive wear, the rate of which depends exponentially on the stresses, is solved. The problem is solved analytically using apparatus of the method of Lagrange multipliers.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 59–63, 1987.     

A study of the (Δ, C)-equivalence of certain numerical matrices

We study the properties of (,C)-transforms of numerical matrices. It is proved that the set of invertible -matrices for a fixed (x) forms a group. On the basis of the properties obtained it is proved that semiscalar equivalence of two nonsingular equivalent polynomial matrices with the same invariant factor is equivalent to the (, C)-equivalence of the matrices of values of the last rows of the left generators of these matrices in Smith form.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 25–29.     

Use of synchronization methods for measurement of fluctuations in ultralow-noise solid-state microwave oscillators

The amplitude and frequency fluctuations of a synchronized oscillator and the fluctuations of the phase difference between input and output are examined. Synchronization methods are demonstrated for measurement of the frequency fluctuations of ultralow-noise low-power microwave oscillators, for which conventional methods are unsuitable. The methods are verified.Presented at All-Union Coordinating Conference Low-Frequency Noise in Semiconductor Devices (Chernogolovka, Moscow Region, June, 1991).St. Petersburg State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 12, pp. 1153–1162, December, 1993.     

Unusual coordination of the in(3+) atom in the decahydrated complex Na3{In[N(CH2COO)3]2}·9H2O

All-Union Scientific-Research Institute of Chemical Reagents and Ultrapure Chemical Substances. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 2, pp. 163–166, March–April, 1991.     

Mössbauer spectroscopic investigations on the pressure (shock wave) dependence of phase generation and carbide precipitation in C80W2 steel

Results of phase generation and carbide formation after a shock wave treatment of the C80W2 steel are reported. It is shown that the reactions follow the energy supply to the steel by shock wave treatment.     

Solid-state thermal polymerization of the heterocyclic HC7N7 acid

The preparation of a new type of thermally stable (up to 385°C) heterocyclic polymer, containing a five-membered fused ring system, is described. The ultraviolet, visible, and infrared spectra indicate that this solid-state polymerization probably proceeds via formation of an azomethine-type intermolecular crosslink, rather than via opening of the C₄N₄ ring system. The reaction is facilitated by the presence of reactive protons, which act as an efficient catalyst for this nucleophilic addition to the nitrile group. It is suggested that this type of solid-state polymerization may possibly be carried out on a single HC₇N₇ crystal resulting in a fully ordered macroscopic polymer single crystal.