Lot-sizing with fixed charges on stocks: the convex hull

In this paper, we examine a variant of the uncapacitated lot-sizing model of Wagner–Whitin that includes fixed charges on the stocks. Such a model is natural in a production environment where stocking is a complex operation, and appears as a subproblem in more general network design problems.

Linear-programming formulations, a dynamic program, the convex hull of integer solutions and a separation algorithm are presented. All these turn out to be very natural extensions of the corresponding results of Barany et al. (Math. Programming Stud. 22 (1984) 32) for the uncapacitated lot-sizing problem. The convex hull proof is based on showing that an extended facility location formulation is tight and by projecting it onto the original space of variables.     

Corrosion products on steel 20 in aerated hydrazine solutions: Mössbauer study

Composition of corrosion layers on steel 20 in aerated solutions with hydrazine concentrations less than 11 ppm was studied at 50, 60, and 80°C in dynamic conditions by transmission Mössbauer spectroscopy and X-ray diffraction as supplementary technique. Corrosion rates were determined by gravimetric method. A comparison with corrosion in water at 80°C was made. The observed layers have not any protective character. For 0.1 m/s linear velocity, they are composed by nonstoichiometric magnetite, (Fe_3?x O₄,x=0.02–0.04) with lepidocrocite (γ-FeOOH) as secondary phase at 50°C. Haematite (α-Fe₂O₃) is observed at 60 and 80°C with a 19 nm particle size. It becomes smaller for higher velocity (0.7 m/s).     

Banach-stone theorems and separating maps

LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH ⁻¹ are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries 4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex. Research supported by the Fundació Caixa Castelló, MI/25.043/92     

Parallelization of population-based multi-objective meta-heuristics: An empirical study

In single-objective optimization it is possible to find a global optimum, while in the multi-objective case no optimal solution is clearly defined, but several that simultaneously optimize all the objectives. However, the majority of this kind of problems cannot be solved exactly as they have very large and highly complex search spaces. Recently, meta-heuristic approaches have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. Most of these meta-heuristics use a population of solutions, and hence the runtime increases when the population size grows. An interesting way to overcome this problem is to apply parallel processing. This paper analyzes the performance of several parallel paradigms in the context of population-based multi-objective meta-heuristics. In particular, we evaluate four alternative parallelizations of the Pareto simulated annealing algorithm, in terms of quality of the solutions, and speedup.     

A finite difference approach to the equations of age-dependent population dynamics

We establish the convergence of the finite difference scheme for the nonlinear equations of population dynamics proposed by Guertin and MacCamy. The applicability of the discrete equations to establish qualitative properties of the solution to the continuous problem is also illustrated.     

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.     

On the interpretation of the racemic states of the B 2 phase of banana-shaped mesogens

We show that the racemic states of the B 2 phase of liquid crystals composed of banana-shaped molecules do not satisfy the Curie principle. Thus it is argued that these states cannot exist in bulk samples and the homochiral states constitute the only stable microscopic structures. A reinterpretation of the racemic states with the same macroscopic optical behaviour is proposed in terms of mixtures of the homochiral structures.     

Nonlinear stability and convergence of finite-difference methods for the “good” Boussinesq equation

Summary The good Boussinesq equationu _tt =–u _xxxx +u _xx +(u ²) _xx has recently been found to possess an interesting soliton-interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the good Boussinesq equation. Numerical experimentas are also reported.