A fast solver for linear systems with displacement structure

We describe a fast solver for linear systems with reconstructible Cauchy-like structure, which requires O(rn ²) floating point operations and O(rn) memory locations, where n is the size of the matrix and r its displacement rank. The solver is based on the application of the generalized Schur algorithm to a suitable augmented matrix, under some assumptions on the knots of the Cauchy-like matrix. It includes various pivoting strategies, already discussed in the literature, and a new algorithm, which only requires reconstructibility. We have developed a software package, written in Matlab and C-MEX, which provides a robust implementation of the above method. Our package also includes solvers for Toeplitz(+Hankel)-like and Vandermonde-like linear systems, as these structures can be reduced to Cauchy-like by fast and stable transforms. Numerical experiments demonstrate the effectiveness of the software.     

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

This paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company’s pharmacy to patients’ homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks.     

Competition between evaporation and fission: Stochastic aspects

The new neutronrich isotope ²²⁸ Rn was produced by spallation reactions induced by 600 MeV protons in a ²³² Th target and identified by massseparation and decay spectroscopy. The Zassignment was confirmed via KX-rays and the genetic relationship to the wellknown daughter product ²²⁸ Fr. The halflife of ²²⁸ Rn is 65±2 s. Energies and relative intensities of prominent γ-rays are presented for the first time from the decay of both the new isotope ²²⁸ Rn and ²²⁷ Rn.     

Quantum electrodynamics analysis of optical binding in counterpropagating beams and effect of particle size

A general expression for optical binding energy between particles of any size, in counterpropagating beams with and without interference, is derived using quantum electrodynamics. The effect of particle size on the optically induced interparticle energy surface, which has been the subject of recent research, is explored. Significant changes in this surface when particle size approaches the wavelength of the optical field are revealed. Finally, optically induced particle arrays that may be fabricated with these potentials are briefly discussed.     

Bernstein-Type Inequalities for Rational Functions with Prescribed Poles

We establish Bernstein-type inequalities for rational functionswith prescribed poles in the Chebyshev norm on the unit circlein the complex plane. Generalizations of polynomial inequalitiesof Erds-Lax and Turán are also obtained for such rational functions with restricted zeros.