A Genetic Algorithm for Solving a Capacitated p-Median Problem

Facility-location problems have several applications, such as telecommunications, industrial transportation and distribution. One of the most well-known facility-location problems is the p-median problem. This work addresses an application of the capacitated p-median problem to a real-world problem. We propose a genetic algorithm (GA) to solve the capacitated p-median problem. The proposed GA uses not only conventional genetic operators, but also a new heuristic “hypermutation” operator suggested in this work. The proposed GA is compared with a tabu search algorithm.     

Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi

We study the asymptotic expansion of the first Dirichlet eigenvalue of certain families of triangles and of rhombi as a singular limit is approached. In certain cases, which include isosceles and right triangles, we obtain the exact value of all the coefficients of the unbounded terms in the asymptotic expansion as the angle opening approaches zero, plus the constant term and estimates on the remainder. For rhombi and other triangle families such as isosceles triangles where now the angle opening approaches π, we have the first two terms plus bounds on the remainder. These results are based on new upper and lower bounds for these domains whose asymptotic expansions coincide up to the orders mentioned. Apart from being accurate near the singular limits considered, our lower bounds for the rhombus improve upon the bound by Hooker and Protter for angles up to approximately 22° and in the range (31°,54°). These results also show that the asymptotic expansion around the degenerate case of the isosceles triangle with vanishing angle opening depends on the path used to approach it.     

Basins of Attraction of Periodic Oscillations in Suspension Bridges

We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations.     

Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or Rn and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of Rn results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem.     

A Borsuk–Ulam Theorem for Maps from a Sphere to a Generalized Manifold

H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds.     

Oscillator strength of a two-dimensional D ion in magnetic fields

In the present paper we determine the oscillator strength of two-dimensional (2D) D⁻ ions under the influence of a static magnetic field. The results are important for the analysis of the optical transitions observed in semiconductor quantum wells. We have applied the ab initio procedure Hyperspherical Adiabatic Approach, based on the use of hyperspherical coordinates. This approach uses an adiabatic separation of the total wave function that allows accurate energies determination from molecular-like potential curves. The convergence is obtained in a systematic way by the inclusion of non-adiabatic couplings without the need of adjustable parameters.     

Should Epstein strip arrangement be changed?

The paper describes effect of texture on the anisotropy of magnetic properties and shows that an Epstein strip arrangement including strips cut in a direction 45° to the rolling direction gives property values that are closer to the average values than the traditional RD+TD arrangement.