Étude mécanistique et structurale des résines R/F

The follow-up of the advance of the reaction of polymerization of resorcinol with formaldehyde in acid or basic medium by NMR shows that the structure of the obtained xerogel in both cases is the same one. Indeed, the junction between the aromatic nuclei is of type OCH₂OCH₂. While basing itself on the structure of the xerogel, we propose the mechanism for the polymerization reaction between resorcinol and formaldehyde.     

Almost Sure Exponential Stability of Large-Scale Stochastic Nonlinear Systems

ABSTRACT

This contribution deals with the study of the almost sure exponential stability of large-scale stochastic systems with multiplicative noises. Under a Lipschitz-like assumption, it is proven that this stability is guaranteed if each “diagonal” subsystem is almost surely exponentially stable.     

Critical extreme points of the 2-edge connected spanning subgraph polytope

In this paper we study the extreme points of the polytope P(G), the linear relaxation of the 2-edge connected spanning subgraph polytope of a graph G. We introduce a partial ordering on the extreme points of P(G) and give necessary conditions for a non-integer extreme point of P(G) to be minimal with respect to that ordering. We show that, if is a non-integer minimal extreme point of P(G), then G and can be reduced, by means of some reduction operations, to a graph G' and an extreme point of P(G') where G' and satisfy some simple properties. As a consequence we obtain a characterization of the perfectly 2-edge connected graphs, the graphs for which the polytope P(G) is integral. Received: May, 2004 Part of this work has been done while the first author was visiting the Research Institute for Discrete Mathematics, University of Bonn, Germany.     

Transient heat and mass transfer and long-term stability of a salt-gradient solar pond

In this work, the problem of transient heat and mass transfer and long-term stability of a SGSP has been numerically investigated using a 2D-transient-variable properties model and a finite-control-volume numerical method. The pond, which was assumed initially stabilized with linear temperature and salinity profiles, has been subject to real weather conditions. The numerical model has been satisfactorily validated against measured temperature data. Numerical results have clearly shown that the solar heating effect appears considerably more pronounced during the hot seasons (spring and summer) than during the cold ones (winter and autumn). The existence of two critical zones, one beneath the water surface and the other one located near the pond bottom, has clearly been established at a very early time of operation. It has been found that such critical zones have progressively become more vulnerable in time. Also, the solar heating effect, the heat losses through the free surface as well as the water transparency have an important influence on the pond stability characteristics and its temporal evolution. The presence of a heat extraction with its cooling effect tends to stabilize the pond. Such a beneficial effect, which is mainly observed in the bottom region of the pond, has been found to be more pronounced during the summer than during the winter time. Results have also shown that the pond with good transparency water would likely be more susceptible to develop instabilities than the one with poorer transparency water. Such an effect appears to be more important inside the lower critical zone.     

KNi3(AsO4)(As2O7)

The structure of the title compound, potassium trinickel arsenate diarsenate, is built up from corner‐ and edge‐sharing NiO₆ octahedra, AsO₄ tetrahedra and As₂O₇ groups, giving rise to a polyhedral connectivity which produces large tunnels running along the crystallographic [010] direction. The K⁺ cations are located within these tunnels.     

Analyzing the Effects of Topological Defect (TD) on the Energy Spectra and Thermal Properties of LiH,TiC and I2 Diatomic Molecules

In this study, the impacts of TD on the energy spectra and thermal properties of LiH, TiC and I₂ diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) method. The energy spectra and eigenfunction are obtained respectively. The energy spectra is used to obtain the partition function which is then used to evaluate the thermal properties of the system is evaluated accordingly. We find that the energy spectra in the presence of the TD differ from their flat Minkowski spacetime analogue. The effects of the deformation parameter and TD on the thermal properties of the system is also analysed in detail. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation as the deformation parameter and topological defect approaches unity. The results of our study can be applied in the astrophysical situation where these modifications exist in the understanding of spectroscopical data and it may be used as a probe of the presence of a cosmic string or a global monopole in the Universe.     

Two-edge connected spanning subgraphs and polyhedra

This paper studies the problem of finding a two-edge connected spanning subgraph of minimum weight. This problem is closely related to the widely studied traveling salesman problem and has applications to the design of reliable communication and transportation networks. We discuss the polytope associated with the solutions to this problem. We show that when the graph is series-parallel, the polytope is completely described by the trivial constraints and the so-called cut constraints. We also give some classes of facet defining inequalities of this polytope when the graph is general.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and CP Rail and the German Research Association (Deutsche Forschungsgemeinschaft SFR 303).