Analysis of Decomposition Algorithms with Benders Cuts for p-Median Problem

In this paper the algorithms for solving the p-median problem based on the Benders decomposition are investigated. A family of problems hard for solving with such algorithms is constructed and then generalized to a special NP-hard case of the p-median problem. It is shown that the effectiveness of the considered algorithms depends on the choice of the optimal values of the dual variables used in Benders cuts. In particular, the depth of the cuts can be equal to one.     

Frequencies of Free Oscillations of a Truncated Spherical Sector Covered with a Thin Elastic Spherical Shell

An analytic solution of the problem concerning the frequencies and shapes of free axially symmetric oscillations of a truncated spherical sector filled with an ideal compressible fluid is constructed. A spherical wall of smaller radius and the radial wall of the sector are absolutely rigid. A thin elastic shell whose edge is clamped in the radial wall is located on a spherical boundary of larger radius. The outer surface of the shell borders vacuum. The phenomenon of an anomalous decrease in the fundamental frequency as the spherical walls approach each other is discovered. An approximate formula for determination of the lowest fundamental frequencies, which are approximately proportional to the square root of the difference of the radii of spherical walls for small values of this difference, is constructed and tested numerically. Bibliography: 13 titles.     

Reaction Medium and Kinetics of N-Vinylsuccinimide Copolymerization

Studies in the field of radical copolymerization of N-vinylsuccinimide were summarized, theeffect of the reaction medium on the process kinetics was examined. Factors governing the relative activity ofthe monomers were revealed, and ways to control the reactivity of N-vinylsuccinimide in binary copolymerizations were suggested.     

Frequencies of Free Acoustic Oscillations in a Fluid Separating Rigid and Elastic Tube Walls of Finite Length

A solution of the problem of determining the frequencies and mode shapes of free nonsymmetric oscillations in an annular volume filled with an ideal compressible fluid is constructed. The inner tube and the end plane walls are ideally rigid. A thin elastic shell with edges clamped to the end walls is located on the outer tube boundary. A phenomenon of a decrease in the fundamental frequency as the thickness of a fluid layer adjacent to the elastic wall decreases is confirmed. Bibliography: 8 titles.     

Radiative corrections to the Lagrangian of the electromagnetic field

The single-loop corrections to the Lagrangian of a uniform, constant electromagnetic field are found which include the anomalous magnetic moment and electric dipole moment of the electron. The imaginary part of the effective Lagrangian, which determines the probability of electron-positron pair production is found. The asymptotic behavior of the effective action is studied for supercritical magnetic fields H » H₀ = m²/e with the dependence of the anomalous magnetic moment on H taken into account.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 37–42, March, 1987.