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.     

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.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

Twistor Geometry for Hyperkähler Metrics on Complex Adjoint Orbits

We study the hyperkähler geometry of complex adjoint orbits from the point of view of twistor theory. We introduce, for complex semisimple adjoint orbits, the associated spectral curve and construct the twistor space as a union of certain regular adjoint orbits; we also exhibit the family of twistor lines. Furthermore, we show how our methods may be applied for describing hyperkähler metrics associated to more general spectral curves. In particular, we give an algebraic characterisation of the twistor lines.     

Variations of constants and red-shift in 6D cosmology

On the basis of the general class of solutions of 6D vacuum Einstein equations and using well-known results of the 6D geometric model of electroweak and gravitational interactions, the variations of fundamental physical constants and their influence on the observed red-shift of galaxies are investigated. By considering the interpretation of extra components of the 6D metric as reproducing the properties of matter in the 4D curved space-time, the effective quantities of matter are obtained. In particular, the states of dust and radiation are shown. The corresponding 5D models were also investigated.     

Unreasonable effectiveness of symmetry in physics

We prove that in some reasonable sense, every possible physical law can be reformulated in terms of symmetries. This result explains the well-known success of the group-theoretic approach in physics.     

Enumeration of three-dimensional convex polygons

A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ ^d withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections with statistical mechanics. Of course, polygons on ℤ ^d are defined up to a translation, and the relevant statistic is their perimeter. A SAP on ℤ ^d is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher dimension. We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's result, which explains combinatorially the form of the generating function. We then compute the generating function for convex SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However, our method suggests that the generating function for convex SAPs on ℤ ^d is always a quotient ofdifferentiably finite power series.