David Hull

Journal of Optimization Theory and Applications -     

Sul calcolo delle variazioni

[Estratto da una lettera al Prof. G. Bagnera]     

Heuristic Algorithms and Scatter Search for the Cardinality Constrained P||Cmax Problem

We consider the generalization of the classical P||C_max problem (assign n jobs to m identical parallel processors by minimizing the makespan) arising when the number of jobs that can be assigned to each processor cannot exceed a given integer k. The problem is strongly NP-hard for any fixed k > 2. We briefly survey lower and upper bounds from the literature. We introduce greedy heuristics, local search and a scatter search approach. The effectiveness of these approaches is evaluated through extensive computational comparison with a depth-first branch-and-bound algorithm that includes new lower bounds and dominance criteria.     

How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main argument brought in favor of this statement.     

A non-isothermal Ginzburg–Landau model in superconductivity: Existence,uniqueness and asymptotic behaviour

In this paper we study a Ginzburg–Landau model which describes the behaviour of a superconducting material including thermal effects. We extend the traditional formulation of the problem, by introducing the temperature as an additional state variable. Accordingly, together with the Gor’kov–Eliashberg system, we introduce an evolution equation for the absolute temperature. We examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature, neglecting the electromagnetic field. For this problem existence and uniqueness of the solution are shown. Finally we analyze the asymptotic behaviour of the solutions, proving that the system possesses a global attractor.     

Symmetry character of collective states in 104Pd populated in the EC-β+ decay of 104Ag

The states of ¹⁰⁴Pd, populated in the EC-β⁺ decay of the ground ( J ^π = 5⁺) and metastable ( J ^π = 2⁺) states of ¹⁰⁴Ag, have been investigated in the framework of the proton-neutron interacting boson model, extending a previous analysis to take into account the newly appeared experimental data. All positive-parity states up to an excitation energy of 3 MeV and spin in the range J = 1-6, fed by more than 0.3% in the decay of the parent nucleus, have been considered. As a result, strong evidence has been found for interpreting most of these states as states of collective nature having a quite pure full- or mixed-symmetry character and, in particular, for identifying the 1⁺ level at 2276 keV as the lowest 1⁺ mixed-symmetry state.     

Polynomial Stability to Three-Dimensional Magnetoelastic Waves

In this work we show that the energy associated to the linear three-dimensional magneto-elastic system decays polynomially to zero as time goes to infinity, provided the initial data is smooth enough.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.