A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

We present some reflections on the application of the Lagrangian formalism for continuous media locally uniform subjected to internal irreversible evolutions. The Lagrangian density, defined as the time derivative of a non-equilibrium thermodynamic potential, [Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. P. Germain’s Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter’s Behaviour, 2000], contains all the symmetry properties of the system. The generalised Lagrange co-ordinates correspond to the state and internal variables of the time derivative of the generalised Gibbs potential. The latter being used within the framework of the De Donder’s method, must also account for the memory effect of the physical medium.This first part is devoted to the thermodynamic framework called the distribution of non-linear relaxations approach (DNLR) developed by C. Cunat on the basis of the generalised Gibbs’ relation.     

Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot

In this paper it is shown that a class ofn-dimensional nonholonomic chained systems can bestabilized using the invariant manifold approach. First, we derive aninvariant manifold for this class of systems and we show that, once onit, all the closed-loop trajectories tend to the origin under a linearsmooth time-invariant state feedback. Thereafter, it is shown that thismanifold can be made attractive by means of a discontinuoustime-invariant state feedback. Finally, a mobile robot is taken as anexample demonstrating the effectiveness of our study.     

Preliminary Communications Thermotropic liquid crystal behaviour of 5,5'-[(4-hexadecyloxyphenyl)ethynyl]-2,2'-bipyridine

5,5'-[(4-Hexadecyloxyphenyl)ethynyl]-2,2'-bipyridine was synthesized by a palladium(O) cross-coupling reaction. Its thermotropic liquid crystalline behaviour was analysed using differential scanning calorimetry, polarizing microscopy, and X-ray diffraction. Three enantiotropic tilted smectic phases were identified upon heating: S_F, S_I, and S_C.     

Exponential mean square stability of partially linear stochastic systems

The purpose of this paper is to state sufficient conditions for the existence of linear feedback laws which render the equilibrium solution of a composite partially linear stochastic system (the linear part of which is deterministic) exponentially stable in mean square.     

Reactions des complexes chlorure cuivreux - PhnP(OPh)3-n (n=0,1,2) avec des composes a halogene positif : les cyano-3 bromo-3 pyrrolidinediones-2,5.

Copper (I) complexes of phosphorus ligands react with 3-cyano 3-bromo pyrrolidine 2,5-diones give phosphoranes and complexes of copper (I)-halogens.     

The Fundamental Blossoming Inequality in Chebyshev Spaces—I: Applications to Schur Functions

A classical theorem by Chebyshev says how to obtain the minimum and maximum values of a symmetric multiaffine function of n variables with a prescribed sum. We show that, given two functions in an Extended Chebyshev space good for design, a similar result can be stated for the minimum and maximum values of the blossom of the first function with a prescribed value for the blossom of the second one. We give a simple geometric condition on the control polygon of the planar parametric curve defined by the pair of functions ensuring the uniqueness of the solution to the corresponding optimization problem. This provides us with a fundamental blossoming inequality associated with each Extended Chebyshev space good for design. This inequality proves to be a very powerful tool to derive many classical or new interesting inequalities. For instance, applied to Müntz spaces and to rational Müntz spaces, it provides us with new inequalities involving Schur functions which generalize the classical MacLaurin’s and Newton’s inequalities. This work definitely demonstrates that, via blossoms, CAGD techniques can have important implications in other mathematical domains, e.g., combinatorics.     

Biomimetic oxidation of catechol employing complexes formed in situ with heterocyclic ligands and different copper(II) salts

In the present work, catecholase activity is presented. The complexes were prepared by condensation of the organic ligand pyrazolyl L ₁ –L ₄ and copper(II) ion in situ. The pyrazolyl compounds L ₁ –L ₄ used in this study are: L ₁ is (3,5-dimethyl-pyrazol-1-ylmethyl)-(4-methyl-pyridin-2-yl)-pyrazol-1-ylmethyl-amine; L ₂ is 1-{4-[(3,5-dimethyl-pyrazol-1-ylmethyl)-pyrazol-1-ylmethyl-amino]-phenyl}-ethanone; L ₃ is 1-{4-[(3,5-dimethyl-pyrazol-1-ylmethyl)-[1,2,4]triazol-1-ylmethyl-amino]-phenyl}-ethanone, and L ₄ is 2-[(3,5-dimethyl-pyrazol-1-ylmethyl)-[1,2,4]triazol-1-ylmethyl-amino]-6-methyl-pyrimidin-4-ol, and copper ions salts Cu(II) are (Cu(CH₃COO)₂, CuCl₂, Cu(NO₃)₂ and CuSO₄). In order to determine factors influencing the catecholase activity of these complexes, the effect of ligand nature, ligand concentration, nature of solvent and nature of counter anion has been studied. The best activity of catechol oxidation is given by the combination formed by one equivalent of ligand L ₂ and one equivalent of Cu(CH₃COO)₂ in methanol solvent which is equal to 9.09 µmol L^?1 min^?1. The Michaelis–Menten model is applied for the best combination, to obtain the kinetic parameters, and we proposed the mechanism for oxidation reaction of catecholase.     

Influence of the formulation of catalysts deposited on cordierite monoliths for acetic acid oxidation

Monolithic catalysts are prepared by washcoating cordierite monoliths with different sols (Pt/Al₂O₃, Pt/CeO₂, Pt/ZrO₂, Pt/Al₂O₃CeO₂, Pt/Al₂O₃ZrO₂, and Pt/CeO₂ZrO₂). These sols are prepared by a sol–gel process and characterized by specific surface area (S_BET), inductively coupled plasma, hydrogen chemisorption, high-resolution transmission electron microscopy, field emission scanning electron microscopy, oxygen storage capacity, X-ray diffraction, temperature-programmed reduction, CO₂ chemisorption, and the model reaction of 3,3-dimethylbutene isomerization. The catalytic performances of the monolithic catalysts are then evaluated for the acetic acid oxidation. The nature of catalyst coating has been found to influence the adherence with the cordierite monolith and the presence of cerium in the catalyst appears to increase the adherence of the latter. Pt/CeO₂, Pt/Al₂O₃CeO₂, and Pt/CeO₂ZrO₂ are found to be the most reducible catalysts (oxygen storage capacity and temperature-programmed reduction) and to have the lowest acidities (3,3-dimethylbutene isomerization). CO₂ chemisorption shows that these catalysts possess a good basicity. From the relation established between the catalytic activity and the redox and acid–base properties it has been concluded that the reducibility is the key factor for a good catalytic activity although the basicity has a significant influence on the catalytic performance.