Synthesis of linear and hyperbranched sugar‐grafted polysiloxanes using N‐hydroxysuccinimide‐activated esters

A straightforward method for the preparation of polysiloxanes grafted with carbohydrate side groups is described. Two kinds of backbones have been functionalized, namely one‐dimensional, linear polysiloxanes, and hyperbranched poly(siloxysilane)s based on cyclotetrasiloxanes. The method enables us to keep a good integrity of the polysiloxane backbone. The introduction of intermediate activated esters as side groups on the polysiloxane backbone ensures a complete homogeneity of the reaction medium during sugar grafting in dimethyl sulfoxide, and consequently an easy grafting with the unprotected amino sugar. Solubility of the resulting polysiloxanes has been tested in various solvents. The sugar‐grafted polysiloxanes are good candidates for applications such as silicone formulations, hydrophilic silicone elastomers, interactions with metallic nanoparticles, and suspension stabilization, or as starting point for the design of more complex polysiloxanes for molecular recognition. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3607–3618     

Are dualities appropriate for duality theories in optimization?

We raise some questions about duality theories in global optimization. The main one concerns the possibility to extend the use of conjugacies to general dualities for studying dual optimization problems. In fact, we examine whether dualities are the most general concepts to get duality results. We also consider the passage from a Lagrangian approach to a perturbational approach and the reverse passage in the framework of general dualities. Since a notion of subdifferential can be defined for any duality, it is natural to examine whether the familiar interpretation of multipliers as generalized derivatives of the performance function associated with a dualizing parameterization of the given problem is still valid in the general framework of dualities.     

A (1→4)-β-D-Glucuronan Excreted by a Mutant of the Rhizobium Meliloti M5N1 Strain

Abstract

A mutant of the R. meliloti M5N1 strain has been selected. This strain, R. meliloti M5N1 CS (NCIMB 40472), excretes an extracellular material composed of 2-O-Ac-β-GlcpA, 3-O-Ac-β-GlcpA, 2,3-di-O-Ac-β-GlcpA and three species of β-GlcpA residues 1→4 linked. For the culture conditions used, the weight average molecular weight of the polymer varied in the range of 6 × 10⁴ < Mw < 4 × 10⁵. High molecular weight glucuronate forms thermoreversible gels at 5 g L^?l. In the presence of divalent cation such as Ca²⁺ or trivalent cations such as Cr³⁺ or Fe^{3 +}, cross linking of the polymer occurs. This polysaccharide is the first exocellular (1→4)-β-D-glucuronan produced by a R. meliloti strain.     

On the Convergence of Descent Algorithms

It is proved that any cluster point of a sequence defined by a steepest descent algorithm in a general normed vector space is a critical point. The function is just assumed to be continuously differentiable. The class of algorithms we consider encompasses several choices such as the Cauchy steplength and the Curry steplength.     

Magnetic and magnetooptical properties of Au/Cu-wedge/15-Å-NiFe sandwiches

The results of an investigation of the magnetic and magnetooptical properties of Au/Cu-wedge/15-Å-NiFe sandwiches are reported. Oscillations of the equatorial Kerr effect as a function of the copper wedge thickness are observed. The period of these oscillations is found to be of the order of 5–6 Å. The experimentally observed oscillations of the equatorial Kerr effect are attributed to a quantum size effect. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 33–36 (10 January 1998)     

Classes caractéristiques pour les cônes projectifs et homologie d'intersection

Sans résumé En hommage à Jean Louis Verdier     

Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

We show that three important topics in nonlinear analysis and optimization are intimately related: the theory of perturbations, the notion of well-posedness and variational principles in the sense of Ekeland, Borwein–Preiss and Deville–Godefroy–Zizler. The concept of genericity and the new notion of flexible perturbation play a key role in these connections. This notion enables one to consider topologies on spaces of functions which have been introduced recently. A link between the Asplund and Ekeland–Lebourg methods and the Palais–Smale condition, another important topic in nonlinear analysis, is pointed out.     

Design and demonstration of a high-energy booster amplifier for a high-repetition rate petawatt class laser system

We have successfully developed a high-energy, high-repetition rate Ti:sapphire laser system that delivers 33 J before compression at 0.1 Hz. The final booster amplifier is based on a 100 mm diameter Ti:sapphire crystal pumped with 72 J of energy in six beams delivered by three frequency-doubled high-repetition rate Nd:glass lasers. This system is, to the best of our knowledge, the first demonstrated petawatt class laser system running at a high repetition rate.