Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations

In the first part of this paper, we give a survey on convergence rates analysis of quasi-Newton methods in infinite Hilbert spaces for nonlinear equations. Then, in the second part we apply quasi-Newton methods in their Hilbert formulation to solve matrix equations. So, we prove, under natural assumptions, that quasi-Newton methods converge locally and superlinearly; the global convergence is also studied. For numerical calculations, we propose new formulations of these methods based on the matrix representation of the dyadic operator and the vectorization of matrices. Finally, we apply our results to algebraic Riccati equations.     

Structure initiale et propriétés de liquéfaction statique d'un sableInitial structure and static liquefaction properties of sand.

Based on the use of two different preparation procedures for reconstituting triaxial samples of sand, i.e. wet tamping and dry pluviation, significant differences in associated mechanical behaviour are observed on a reference sand with respect to the phenomenon of ‘static’ liquefaction. Wet tamping favours the initiation of liquefaction instability, whereas dry pluviation favours a more stable behaviour, less susceptible to liquefaction. Microscopic observation of corresponding sand specimens allows us to identify two well differentiated structures, i.e., for wet tamping, an irregular structure with predominance of aggregates (aggregated grains) and macropores, very contractant and unstable and, for dry pluviation, a more regular structure, without macropores, more dilatant and more stable. These observations show the importance of further characterization, based on the introduction of appropriate parameters, of the initial structure of sandy materials, strongly dependant upon their mode of formation (natural or artificial). To cite this article: N. Benahmed et al., C. R. Mecanique 332 (2004).     

Structural,elastic, electronic,optical and thermoelectric properties of the Zintl-phase Ae3AlAs3 (Ae = Sr,Ba)

First-principles calculations were performed to investigate the structural, elastic, electronic, optical and thermoelectric properties of the Zintl-phase Ae₃AlAs₃ (Ae = Sr, Ba) using two complementary approaches based on density functional theory. The pseudopotential plane-wave method was used to explore the structural and elastic properties whereas the full-potential linearised augmented plane wave approach was used to study the structural, electronic, optical and thermoelectric properties. The calculated structural parameters are in good consistency with the corresponding measured ones. The single-crystal and polycrystalline elastic constants and related properties were examined in details. The electronic properties, including energy band dispersions, density of states and charge-carrier effective masses, were computed using Tran-Blaha modified Becke-Johnson functional for the exchange-correlation potential. It is found that both studied compounds are direct band gap semiconductors. Frequency-dependence of the linear optical functions were predicted for a wide photon energy range up to 15 eV. Charge carrier concentration and temperature dependences of the basic parameters of the thermoelectric properties were explored using the semi-classical Boltzmann transport model. Our calculations unveil that the studied compounds are characterised by a high thermopower for both carriers, especially the p-type conduction is more favourable.     

Cellulose Acetate-g-Polycaprolactone Copolymerization Using Diisocyanate Intermediates and the Effect of Polymer Chain Length on Surface,Thermal, and Antibacterial Properties

The need for biodegradable and biocompatible polymers is growing quickly, particularly in the biomedical and environmental industries. Cellulose acetate, a natural polysaccharide, can be taken from plants and modified with polycaprolactone to improve its characteristics for a number of uses, including biomedical applications and food packaging. Cellulose acetate-g-polycaprolactone was prepared by a three-step reaction: First, polymerization of ε-caprolactone via ring-opening polymerization (ROP) reaction using 2-hydroxyethyl methacrylate (HEMA) and functionalization of polycaprolactone(PCL) by introducing NCO on the hydroxyl end of the HEMA-PCL using hexamethyl lenediisocyanate(HDI) were carried out. Then, the NCO–HEMA-PCL was grafted onto cellulose acetate (using the “grafting to” method). The polycaprolactone grafted cellulose acetate was confirmed by FTIR, the thermal characteristics of the copolymers were investigated by DSC and TGA, and the hydrophobicity was analyzed via water CA measurement. Introducing NCO-PCL to cellulose acetate increased the thermal stability. The contact angle of the unreacted PCL was higher than that of cellulose acetate-g-PCL, and it increased when the chain length increased. The CA-g-PCL50, CA-g-PCL100, and CA-g-PCL200 showed very high inhibition zones for all three bacteria tested (E. coli, S. aureus, and P. aeruginosa).     

Fixed point theorem in ordered Banach spaces and applications to matrix equations

In this paper, we give an important generalization of Lakshmikantham’s theorem (Theorem 2.1 in Nonlinear Anal Theory Methods Appl 3448–3458, 2009). Our main result asserts the existence of fixed point for a class of nonlinear operators defined in an ordered Banach space, and gives a new monotone Newton-like method to compute this fixed point. We also apply our new result to some important matrix equations.     

A new isoflavone glycoside from the aerial parts of <Emphasis Type="Italic">Retama sphaerocarpa</Emphasis>

A new isoflavone glycoside, genistein 7-O-xylosyl 8-C-glucoside (1), was isolated from the leaves of Retama sphaerocarpa. Its structure was elucidated by spectroscopic methods.