Decomposable symmetric designs

The first infinite families of symmetric designs were obtained from finite projective geometries, Hadamard matrices, and difference sets. In this paper we describe two general methods of constructing symmetric designs that give rise to the parameters of all other known infinite families of symmetric designs. The method of global decomposition produces an incidence matrix of a symmetric design as a block matrix with each block being a zero matrix or an incidence matrix of a smaller symmetric design. The method of local decomposition represents incidence matrices of a residual and a derived design of a symmetric design as block matrices with each block being a zero matrix or an incidence matrix of a smaller residual or derived design, respectively.     

Simulated annealing algorithm for the robust spanning tree problem

This paper addresses the robust spanning tree problem with interval data, i.e. the case of classical minimum spanning tree problem when edge weights are not fixed but take their values from some intervals associated with edges. The problem consists of finding a spanning tree that minimizes so-called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in Kouvelis and Yu (Robust Discrete Optimization and Its Applications, Kluwer Academic, Norwell, 1997), the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem.     

Groups whose lattice of centralizers is a sublattice of the subgroup lattice

An earlier conjecture suggests that the lattice of centralizers is modular in the title groups. We prove it to hold for two classes of groups whose lattice of centralizers has finite length — groups with the normalizer condition and locally finite groups.Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 475–513, September–October, 1994.     

Renormalization group in the theory of developed turbulence. The problem of justifying the Kolmogorov hypotheses for composite operators

In this paper, the stochastic theory of developed turbulence is considered within the framework of the quantum field renormalization group and operator expansions. The problem of justifying the Kolmogorov-Obukhov theorem in application to the correlation functions of composite operators is discussed. An explicit expression is found for the critical dimension of a general-type composite operator. For an arbitrary UV-finite composite operator, the second Kolmogorov hypothesis (the viscosity-independence of the correlator) is proved and the dependence of various correlators on the external turbulence scale is determined. It is shown that the problem involves an infinite number of Galilean-invariant scalar operators with negative critical dimensions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 122–136, January, 1997.     

Experimental study of the discrete component in the noise spectrum of supersonic flows

The discrete component in the noise spectrum of an inefficient supersonic stream flowing into a flooded space is studied experimentally. The effect of a discrete tone on the average parameters of the initial and main portions of the stream is examined. It is found that the lengthl ₀ of the supersonic part of the stream decreases linearly as the level L* of the discrete component acting on the base of the stream is increased. It is also shown experimentally that the oscillations in the density jumps at the ends of the first and second cells of the stream take place out of phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 163–166, July–August, 1976.     

Nonsteady supersonic flow over spiked bodies

In longitudinal supersonic flow over spiked cylinders nonsteady regimes can occur in which a separation zone is periodically generated at the spike, grows vigorously in size, and then vanishes. Several authors [1–6] have investigated the physical pattern of flow with separation zone fluctuations (using shadowgraphs) and have determined the boundaries of existence of the nonsteady regime as a function of the ratio between the spike length and diameter of the cylinder. The authors, however, did not systematically study the dependence of the pulsation frequency on the freestream Mach and Reynolds numbers or on the relative diameter and tip angle of the spike. We have undertaken such an investigation. We are concerned primarily with the influence of the dimensionless parameters on the Strouhal number Sh of the separation zone pulsations at a spike attached to the front of a flat-ended cylinder. Earlier investigations [4–6] have been carried out using motion pictures with film speeds up to 32·10³ frames/sec. In the present study we used high-speed motion pictures with a speed of 6.25· 10⁵ frames/sec. This speed allowed us to determine the precise sequence of phases of the pulsations and their relative durations, as well as the speed at which the boundaries of the separation zone move.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 118–124, September–October, 1976.     

Effect of angle of attack on supersonic flow past axisymmetric blunt bodies with surface injection

The effect of angles of attack in the interval 0 40° on the flow pattern and the aerodynamic characteristics of a body of power-law shape (equation of the generator in the cylindrical coordinate system r=zⁿ, n=0.125) is investigated for supersonic flow without injection and with intense subsonic localized injection from the surface. As a result of numerical calculations it is established that the use of Newton's theory for determining the coordinates of the gas stagnation point behind the shock in flow past an impermeable body of the shape in question leads to serious errors, and an expression for determining the location of this point is given. It is shown that for three-dimensional flow the flow pattern and the surface pressure distribution are sharply different from the case=0. It is established that on the parameter interval in question intense injection considerably reduces the aerodynamic drag without loss of static stability, which is important in connection with the solution of the problem of gas-stable aircraft control.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–101, September–October, 1987.     

The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

Experimental investigation of nonstationary flow in cavities in a supersonic flow

An experimental investigation was made into the flow and pressure pulsations in cylindrical cavities open toward a supersonic flow and set up at zero angle of attack (i.e., the cavity axis and the direction of the flow coincide).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 180–183, September–October, 1979.