Metaheuristics for the team orienteering problem

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.     

On spectral geometry of minimal parallel submanifolds

We consider the problem of characterizing some minimal submanifolds using the spectrum⁰Spec of the Laplace-Beltrami operator acting on fucntions. In particular we characterize then-dimensional compact minimal totally real parallel submanifolds immersed in the complex projective spaceCP ⁿ, 3≤n≤6, by their⁰Spec in the class of all compact totally real minimal submanifolds ofCP ⁿ. Moreover, we characterize the Clifford torus by its⁰Spec in the class of all compact minimal submanifolds of the Euclidean sphereS ⁿ⁺¹(1). Authors supported by funds of the University of Lecce and the M.U.R.S.T.     

Rounding Error Analysis in Solving M-Matrix Linear Systems of Block Hessenberg Form

The problem of solving large M-matrix linear systems with sparse coefficient matrix in block Hessenberg form is here addressed. In previous work of the authors a divide-and-conquer strategy was proposed and a backward error analysis of the resulting algorithm was presented showing its effectiveness for the solution of computational problems of queueing theory and Markov chains. In particular, it was shown that for block Hessenberg M-matrices the algorithm is weakly backward stable in the sense that the computed solution is the exact solution of a nearby linear system, where the norm of the perturbation is proportional to the condition number of the coefficient matrix. In this note a better error estimate is given by showing that for block Hessenberg M-matrices the algorithm is even backward stable.     

Segments and Hilbert schemes of points

Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order (as, for example, the degrevlex order) in the Hilbert scheme of points in Pⁿ. In this context, we look into the properties of several types of “segment” ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.     

CuPc molecules adsorbed on Au(1 1 0)-(1 × 2): growth morphology and evolution of valence band states

We present the growth morphology, the long-range ordering, and the evolution of the valence band electronic states of ultrathin films of copper phthalocyanine (CuPc) deposited on the Au(1 1 0)-(1 × 2) reconstructed surface, as a function of the organic molecule coverage. The low energy electron diffraction patterns present a (5 × 3) reconstruction from the early adsorption stages. High-resolution UV photoelectron spectroscopy data show the disappearance of the Au surface states related to the (1 × 2) reconstruction, and the presence of new electronic features related to the molecule-substrate interaction and to the CuPc molecular states. The CuPc highest occupied molecular orbital gradually emerges in the valence band, while the interface electronic states are quenched, upon increasing the coverage.     

Interpreting technical evidence from spectral imaging of paintings by Édouard Manet in the Courtauld Gallery

The paintings by Édouard Manet in The Courtauld Gallery Déjeuner sur l'herbe (1863–68), Marguerite de Conflans en Toilette de Bal (1870–1880), Banks of the Seine at Argenteuil (1874), and A Bar at the Folies–Bergère (1882) were investigated for the first time using a range of non-invasive in situ analyses. The aims of the study were to investigate the painting techniques and materials used for this group of works and to critically evaluate the technical evidence derived from the integrated use of imaging techniques and portable spectroscopic methods in this context. The paintings were investigated by means of macro X-ray fluorescence (MA-XRF), reflection spectral imaging, portable UV–Vis–NIR spectroscopy, portable Raman spectroscopy, and reflection FTIR. MA-XRF and reflection spectral imaging allowed visualising elements in the compositions that were not visible using traditional methods of technical study. For example, MA-XRF analysis of Déjeuner sur l'herbe revealed elements of the development of the composition that provided new evidence to consider its relationship to other versions of the composition. The study also highlighted questions about the interpretation of elemental distribution maps and spectral images that did not correspond to the reworking visible in X-radiographs. For example, in A Bar at the Folies–Bergère Manet made numerous changes during painting, which were not clearly visualised with any of the techniques used. The research has wider implications for the study of Impressionist paintings, as the results will support technical studies of works by other artists of the period who used similar materials and painting methods.     

On the Spectral Rigidity of Hopf Manifolds

We characterize Hopf manifolds of complex dimension 3 (resp. 2) in the class of compact locally conformal Kaehler manifold ( resp. Hermitian manifold ) by the spectrum of the Laplacian acting on functions.     

Surface characterization of synthetic and mineral carbonate fluoroapatites

As part of a larger project concerning the sorption capacities of carbonate fluoroapatites, the physical and surface properties of the synthetic carbonate fluoroapatite and mineral francolite retained for this work have been carefully examined. The average particle size of the powdered samples, determined by laser granulometry, is around 30 microm. Their specific surface areas, measured according to the N(2) BET method, are 8.8+/-0.1 and 13.9+/-0.1 m(2).g(-1), respectively, for the synthetic and the mineral compound. The solubility of both solids has been studied under undersaturation initial conditions. The synthetic compound has a solubility product of 10(-103+/-2), but the mineral francolite, which is highly substituted and poorly crystalline, is more soluble and dissolves incongruently. The amphoteric properties of the hydrous carbonate fluoroapatites surfaces have also been investigated through zeta-potential measurements and potentiometric titrations in KNO(3) medium at 25 degrees C. The experimental data have been interpreted using the computer program FITEQL 3.2, applying either the nonelectrostatic or the constant capacitance model. For both solids, the values of the surface acidity constants determined with the two models are very close, suggesting a weak contribution of the electrostatic interactions. Moreover, the more acidic surface of the synthetic compound compared to that of the mineral one is assigned to the differences in crystallinity and chemical composition between the two solids.     

Magnetite, a model system for mixed-valence oxides, does not show charge ordering

We have investigated the charge ordering (CO) in magnetite below the Verwey transition. A new set of half-integer and mixed-integer superlattice reflections of the low-temperature phase have been studied by x-ray resonant scattering. None of these reflections show features characteristic of CO. We demonstrate the absence of CO along the c axis with the periodicity of either the cubic lattice q=(001) or the doubled cubic lattice q=(001/2). This result suggests that the Verwey transition is caused by strong electron-phonon interaction instead of an electronic ordering on the octahedral Fe atoms.     

Anchoring sulphur-headgroup organic molecules at Cu(1 0 0): Tailoring the interface electronic states

Sulphur-headgroup organic molecules have been chemisorbed on Cu(1 0 0) as self-assembled monolayers (SAMs) in highly-ordered two-fold symmetry structures, and the electronic states induced at the interface have been measured by photoemission: a close similarity of the main interface states for methane-thiolate and mercaptobenzoxazole on Cu(1 0 0) in the same p(2 × 2)-phase is observed. The bonding states for methane-thiolate/Cu(1 0 0) in the p(2 × 2) and c(2 × 2) structures have been compared to ab-initio calculation of the total density of states (DOS) for the S/Cu(1 0 0) system in the same phases. The major role of the S-Cu bonding to determine the density of state evolution at the interface is brought to light. The observed differences in the two phases depend mainly on the charge distribution associated to the different molecular packing, with a minor role of the radical group.