The Dial-a-Ride Problem (DARP): Variants,modeling issues and algorithms

The Dial-a-Ride Problem (DARP) consists of designing vehicle routes and schedules for n users who specify pick-up and drop-off requests between origins and destinations. The aim is to plan a set of m minimum cost vehicle routes capable of accommodating as many users as possible, under a set of constraints. The most common example arises in door-to-door transportation for elderly or disabled people. The purpose of this article is to review the scientific literature on the DARP. The main features of the problem are described and classified and some modeling issues are discussed. A summary of the most important algorithms is provided.AMS classification: 90B06, 90C27, 90C59     

Operator kernel estimates for functions of generalized Schrödinger operators

We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.

     

Structural characterization of nanopatterned surfaces

In this work, chemically and topographically nanopatterned surfaces were produced by a top-down processing approach for biosensing devices. The nanopatterning was the result of the combination of plasma polymerisation (pp) of biofunctional materials and colloidal lithography techniques. The morphological and chemical properties induced by the plasma deposition-etching treatment were characterised by optical method combining ellipsometry and Fourier Transform Infrared spectroscopy studies. This method supported by atomic force microscopy measurements, allowed the full optical characterization of each step of the top-down process. The optical characterization of the end-up nanopatterned samples demonstrated that the chosen process is able to produce well-defined nanostructured surfaces with controlled chemical and morphological properties.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Localized proton spectroscopy without water suppression: removal of gradient induced frequency modulations by modulus signal selection

Most Magnetic Resonance Spectroscopy (MRS) localization methods can generate gradient vibrations at acoustic frequencies and/or magnetic field oscillation, which can cause a time-varying magnetic field superimposed onto the static one. This effect can produce frequency modulations of the spectral resonances. When localized MRS data are acquired without water suppression, the associated frequency modulations are manifested as a manifold of spurious peaks, called sidebands, which occur symmetrically around the water resonance. These sidebands can be larger than the small metabolite resonances and can present a problem for the quantitation of the spectra, especially at short echo times. Furthermore, the resonance lineshapes may be distorted if any low frequency modulations are present. A simple solution is presented which consists of selecting the modulus of the acquired Free Induction Decay (FID) signal. Since the frequency modulations affect only the phase of the FID signal, the obtained real spectrum of the modulus is free from the spurious peaks where quantitative results may be directly obtained. Using this method, the distortions caused by the sidebands are removed. This is demonstrated by processing proton MRS spectra acquired without water suppression collected from a phantom containing metabolites at concentrations comparable to those in human brain and from a human subject using two different localization methods (PRESS and Chemical Shift Imaging PRESS-(CSI)). The results obtained illustrate the ability of this approach to remove the spurious peaks. The corrected spectra can then be fit accurately. This is confirmed by the results obtained from both the relative and the absolute metabolites concentrations in phantoms and in vivo.     

Mössbauer study of Brazilian soapstone

Steatite mineral rocks, soapstone, have been studied by X-ray diffraction, optical microscopic analysis (modal analysis), electron probe micro analysis and Mössbauer spectroscopy for characterization, mineral percentages and chemical composition. Mössbauer spectra show both, magnetic interactions corresponding to magnetite and doublets corresponding to talc. chlorite, dolomite and tremolite. The temperature dependence of the quadrupole splitting in dolomite has been explained in terms of crystal field interaction.     

Lower bounds on the cluster size distribution

We rigorously prove that the probabilityP _n that the origin of ad-dimensional lattice belongs to a cluster of exactlyn sites satisfiesP _n > exp(–n ^(d–1)/d ) whenever percolation occurs. This holds for the usual (noninteracting) percolation models for any concentrationp > p _c , as well as for the equilibrium states of lattice spin systems with quite general interactions. Such a lower bound applies also if no percolation occurs, but if it appears in some other phase of the system.