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.     

Effective equation of nonlinear pulse evolution in a randomly anisotropic medium

Propagation of a light pulse through a weakly inhomogeneous optical fiber is analyzed. The non-linear envelope equation describing the evolution of polarized pulses is determined by statistical properties of inhomogeneities in the optical fiber. The isotropic Manakov system of equations is shown to be applicable in the presence of high-frequency small-scale defects in the fiber. In the presence of only large-scale inhomogeneities, the signal dynamics are described by an anisotropic system of equations.     

Estimation of the number of iterations in integer programming algorithms using the regular partitions method

We review the results of studying integer linear programming algorithms which exploit properties of problem relaxation sets. The main attention is paid to the estimation of the number of iterations of these algorithms by means of the regular partitions method and other approaches. We present such estimates for some cutting plane, branch and bound (Land and Doig scheme), and L-class enumeration algorithms and consider questions of their stability. We establish the upper bounds for the average number of iterations of the mentioned algorithms as applied to the knapsack problem and the set packing one.     

Features of the complexation of octadecane-2,4-dione and lanthanide ions in Langmuir monolayers

Monolayers of octadecane-2,4-dione on the surfaces of EuCl₃ and TbCl₃ solutions in the concentration range of 1 × 10^–4 to 5 × 10^–3 M at pH 5.8 are studied. It is found that the limiting area of octadecane-2,4-dione molecule in a monolayer dependence on Eu³⁺ and Tb³⁺ concentration is of extreme nature. The formation of complex compounds in the ligand monolayer is postulated, and structures are proposed for these compounds at different concentrations of metal ions.     

Extreme outages caused by polarization mode dispersion

We study the dependence on fiber birefringence of the bit-error rate (BER) caused by amplifier noise in a linear optical fiber telecommunication system. We show that the probability-distribution function of the BER obtained by averaging over many realizations of birefringent disorder has an extended tail that corresponds to anomalously large values of BER. We specifically discuss the dependence of the tail on such details of pulse detection at the fiber output as setting the clock and filtering procedures.     

Solving a Bicriteria Problem of Optimal Service Centers Location

The problem of service centers location is formulated as a bicriteria optimization problem of finding a dominating set in graph. We investigate the properties of this problem and propose the methods for its solving. The results of computational experiment for instances with random data are presented.     

Synthesis and Study of Copper(II) Complexes with Aspartic Acid,Serine, and Valine

Binary and ternary copper(II) complexes with aspartic acid (H₂Asp), serine (HSer), and valine (HVal) were prepared by electrochemical and chemical procedures. The purity of the compounds was confirmed by elemental and thermogravimetric analyses. According to the IR spectra, all the complexes contain a five-membered chelate ring in which the Cu(II) atom is bonded with the oxygen atom of the carboxy group and nitrogen atom of the amino group. This is also confirmed by the ESR spectra.__________Translated from Zhurnal Obshchei Khimii, Vol. 75, No. 4, 2005, pp. 541–544.Original Russian Text Copyright © 2005 by Kryukova, Frolov, Kolokolov, Bolotin, Panyushkin.