Bounds and Heuristics for the Shortest Capacitated Paths Problem

Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a set of paths of least total length, linking given pairs of vertices in G, and satisfying capacity constraints on the arcs of G.We formulate the SCPP as a 0-1 linear program and study two Lagrangian relaxations for getting lower bounds on the optimal value. We then propose two heuristic methods. The first one is based on a greedy approach, while the second one is an adaptation of the tabu search meta-heuristic.     

Derivation of Feynman–Kac and Bloch–Torrey Equations in a Trapping Medium

Methodology and Computing in Applied Probability - We derive rigorously the fractional counterpart of the Feynman–Kac equation for a transport problem with trapping events characterized by...     

Limit theorems for Hilbert space-valued linear processes under long range dependence

Let ${\left(X_k\right)}_{k\in \mathbb{Z}}$ be a linear process with values in a separable Hilbert space $\mathbb{H}$ given by $X_k={\sum }_{j=0}^{\infty }{(j+1)}^{?N}{\epsilon }_{k?j}$ for each $k\in \mathbb{Z}$, where $N:\mathbb{H}\to \mathbb{H}$ is a bounded, linear normal operator and ${\left({\epsilon }_k\right)}_{k\in \mathbb{Z}}$ is a sequence of independent, identically distributed $\mathbb{H}$-valued random variables with $E{\epsilon }_0=0$ and $E6{\epsilon }_0{6}^2<\infty$. We investigate the central and the functional central limit theorem for ${\left(X_k\right)}_{k\in \mathbb{Z}}$ when the series of operator norms ${\sum }_{j=0}^{\infty }6{(j+1)}^{?N}{6}_{op}$ diverges. Furthermore, we show that the limit process in case of the functional central limit theorem generates an operator self-similar process.     

Influence of the modified Becke-Johnson exchange potential on thermoelectric properties: application to Mg2Si

The electronic and transport properties of Mg(2)Si are calculated using the density-functional and semi-classical Boltzmann transport theories. A detailed comparison of the efficiency of the Perdew, Burke, and Ernzerhof (PBE) and the modified Becke-Johnson (m-BJ) exchange potentials on the prediction of these properties is presented. We show that the m-BJ potential is able to predict the Mg(2)Si thermoelectric properties with better agreement with the experimental data than the PBE potential. These findings are correlated with a small modification of the valence orbitals of the materials and the opening of the gap.     

The wave-particle dualism in 1992: A summary

We review the past and present theoretical and experimental situations relating to wave-particle dualism. New tests aimed at enlightening the individual behavior as awave, then as aparticle, of asingle quantum mechanical system in the same experimental run are presented. The related epistemological, philosophical, and historical backgrounds are presented in a twofold exposition taking into account thepositivistic standard Copenhagen interpretation as well as therealist de Broglian point of view.     

Viscosity of aqueous mixtures of silver and thallium nitrates with calcium or cadmium nitrates from pure fused salt to pure water

Fused salt-water systems extending from pure fused salt to pure water have been less studied than dilute aqueous solutions, despite their practical and theoretical importance. Even fewer studies have been made regarding the influence of the temperature upon transport properties. The present publication brings new interesting information on the viscous flow properties of the following two fused nitrate-water systems containing monovalent and divalent cations: AgNO₃–TINO₃–M(NO₃)₂–H₂O where M=Ca or Cd, with the TINO₃ and M(NO₃)₂ mole fractions in the anhydrous salt fixed at 0.436 and 0.100, respectively. The parameters in the Arrhenius, Eyring, Batschinski and the Abraham and Abraham equations are found to be well correlated with the properties of the components of the melts. The temperature effect allows a discussion to be made in terms of structural features such as holes and free volumes.     

New triterpenoids from the stem barks of Drypetes tessmanniana

The MeOH extract of the stem barks of Drypetes tessmanniana (Euphorbiaceae) afforded two new triterpene derivatives characterized as 3beta-O-(E)-3,5-dihydroxycinnamoyl-11-oxo-olean-12-ene and 3beta,6alpha-dihydroxylup-20(29)-ene together with seven known compounds. Their structures were established on the basis of spectral analysis.     

Some chemical transformations of carbohydrates in aqueous medium

The interest of combining the use of carbohydrates as synthons and the use of water as the reaction medium is emphasized by briefly reviewing some examples of contributions in this field achieved in our Lyon and Orsay laboratories.