Self-induced systems

A minimal Cantor system is said to be self-induced whenever it is conjugate to one of its induced systems. Substitution subshifts and some odometers are classical examples, and we show that these are the only examples in the equicontinuous or expansive case. Nevertheless, we exhibit a zero entropy self-induced system that is neither equicontinuous nor expansive. We also provide non-uniquely ergodic self-induced systems with infinite entropy. Moreover, we give a characterization of self-induced minimal Cantor systems in terms of substitutions on finite or infinite alphabets.     

A branch-and-cut-and-price approach for the pickup and delivery problem with shuttle routes

The Pickup and Delivery Problem with Shuttle routes (PDPS) is a special case of the Pickup and Delivery Problem with Time Windows (PDPTW) where the trips between the pickup points and the delivery points can be decomposed into two legs. The first leg visits only pickup points and ends at some delivery point. The second leg is a direct trip – called a shuttle – between two delivery points. This optimization problem has practical applications in the transportation of people between a large set of pickup points and a restricted set of delivery points.     

Polymerization of water soluble cationic vinyl monomers

This paper summarizes investigations on the radical polymerization of cationic vinyl monomers with respect to the peculiarities of the reaction in aqueous solution, the synthesis of model polymers and polyelectrolytes with regular structure as well as to a new process of stabilized precipitation polymerization. The rate of polymerization depends on the ionic strength of the solution. Random copolymers of diallyldimethylammonium chloride and acrylamide with variable charge density but equal molecular weight were synthesized by a feeding technique. Block copolymers consisting of charged and uncharged monomelic units with different hydrophilicity are available using macroazoinitiators. The novel polymers are powerful stabilizers in the precipitation polymerization of water soluble cationic vinyl monomers in aqueous salt solution leading to a dispersion of fine polymer particles. Polyampholytes with alternating positively and negatively charged monomelic units in the backbone were obtained by cyclocopolymerization of diallylanmine compounds and derivatives of maleic acid.     

Quantum Nuclear Delocalization and its Rovibrational Fingerprints

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex . The equilibrium structure of is planar and T-shaped, one He atom solvating the quasi-linear He−H⁺−He core. The dynamical structure of , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent chomophore, but freely orbits the central proton, forming a three-dimensional torus around the chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.