Solid Lipid Nanoparticles (SLNs): Preparation and Properties of Calix[4]resorcinarene Derived Systems.

Solid Lipid Nanoparticles (SLNs) have been prepared fromc-2,c-8,c-14,c-20-tetraundecyl-4,6,10,12,16,18,22,24-octahydroxyresorc[4]areneas colloidal suspensions. Photon Correlation Spectroscopy studies revealed aparticle hydrodynamic diameter of 150 nm. Non-contact mode Atomic ForceMicroscopy allows observation of the particles as slightly flattened sphericalobjects of 236 (±40) nm diameter and 145 (±40) nm height. Thestudy of the preparation parameters showed that shear force does not affectthe hydrodynamic size of the SLNs. In contrast, the viscosity and the pH ofthe aqueous phase, the amphiphile concentration in the organic phase and thevolume of organic phase used, all lead to variation in the size of the particles.In term of post preparation parameters only the ionic strength has been shownto affect significantly the particle size; while the pH of the storing solution,microwave, ultrasonic and thermal treatments do not. Short and long-termstability studies have been performed to measure the effect of the ionic strengthon the stability of the particles. The use of carbohydrate cryoprotectants does notallow re-dispersion of the colloidal suspension after freeze-drying.     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

Approximation diophantienne sur les courbes elliptiques à multiplication complexe

Let $\text{E}$ be an elliptic curve with complex multiplication, defined over $\text{Q}$. We consider linear forms on $\text{Lie}\text{(}\text{E}{}^{\mathrm{n}}\text{)}$ with coefficients in the CM field of $\text{E}$. Within this framework, we present a new measure of linear independence for elliptic logarithms in (logb)(loga)ⁿ. Like recent advances in this domain (works by Ably, David, Hirata-Kohno), our result is best possible in terms of the height of the linear forms (logb) while providing a better estimate in the height of algebraic points considered (loga), removing a term in logloga. To cite this article: M. Ably, É. Gaudron, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Degenerate nonlinear hyperbolic conservation laws: Non classical geometrical theory

Kinetic selection principles have been shown to be useful and physically reasonable in nonlinear hyperbolic problems with large amplitude phase transitions. We refer to Abeyaratne and Knowles, [A-K], for discussion on the subject. They also have been used for degenerate nonlinear problems, where the genuine nonlinearity property of Lax is violated. This is the framework of Liu, [Li], in the kinetic situation of Hayes and Le Floch, [H-L], where their so-called non classical shocks may be seen as small amplitude phase transitions. Here, we describe the local geometry generated by the generic non genuinely nonlinear assumption. A geometric kinetic criterion can be used to select indeterminate simple waves and obtain the well-posedness of the local Riemann problem. A particular case is the entropic kinetic criterion of Hayes and Le Floch.

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Sunto Principi di selezione cinetica sono stati mostrati utili e fisicamente ragionevoli in problemi iperbolici con transizioni di fase di grande ampiezza. Ci riferiamo ad Abeyaratne e Knowles, [A-K], per discussioni sull'argomento. Detti principi sono stati usati per problemi nonlineari degeneri, dove la proprietà di genuina nonlinearità di Lax è violata. Questo è la prospettiva di Liu, [Li], nella situazione cinetica di Hayes e Le Floch, [H-L], dove i loro così detti urti non classici possono essere considerati come transizioni di fase di piccola ampiezza. Qui, descriviamo la geometria locale generata dall'ipotesi generica genuinamente nonlineare. Un criterio di geometria cinetica può essere usato per selezionare onde semplici indeterminate ed ottenere la buona posizione per il problema locale di Riemann. Un caso particolare è il criterio di entropia cinetico di Hayes e Le Floc.

     

Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004     

Lagrangian flows: The dynamics of globally minimizing orbits

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].Reprinted by permission of Addison Wesley Longman Ltd.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.