Thermal Behaviour of Perfluoropolyether w/o Percolative Microemulsions

The thermal properties of a perfluoropolyether (PFPE) W/O microemulsion were investigated by Differential Scanning Calorimetry (DSC) both on freezing the liquid samples and upon their melting. PFPE systems as a function of increasing volume fraction (Φ=water+surfactant/total), were studied along a dilution line with a water/surfactant molar ratio W/S=11. The percolative nature of these systems emerged directly from the spreading of the exothermic peaks associated with the freezing of the dispersed phase. This behaviour was found to depend on whether the starting temperature of the DSC measure was at, below or above the percolative threshold temperature of the given sample. A low temperature 'needle-like' peak was found around 143 K, immediately after the glass transition due to the oil continuous phase. The low temperature peak was also present in other percolative, three-component microemulsions. The higher order phase transition at the percolation temperature was also evidenced. This revised version was published online in August 2006 with corrections to the Cover Date.     

Simultaneous determination of two components by spectrofluorimetric techniques

A procedure is described for the resolution of two-component mixtures by use of data from variable-angle fluorescence spectrometry. The experimental data are treated by multilinear regression. The method is applied to the resolution of mixtures of fluorescein and dichlorofluorescein at the ng ml^?1 level; mean errors are < 4%.     

Exact Max-SAT solvers for over-constrained problems

We present a new generic problem solving approach for over-constrained problems based on Max-SAT. We first define a Boolean clausal form formalism, called soft CNF formulas, that deals with blocks of clauses instead of individual clauses, and that allows one to declare each block either as hard (i.e., must be satisfied by any solution) or soft (i.e., can be violated by some solution). We then present two Max-SAT solvers that find a truth assignment that satisfies all the hard blocks of clauses and the maximum number of soft blocks of clauses. Our solvers are branch and bound algorithms equipped with original lazy data structures, powerful inference techniques, good quality lower bounds, and original variable selection heuristics. Finally, we report an experimental investigation on a representative sample of instances (random 2-SAT, Max-CSP, graph coloring, pigeon hole and quasigroup completion) which provides experimental evidence that our approach is very competitive compared with the state-of-the-art approaches developed in the CSP and SAT communities. Research partially supported by projects TIN2004-07933-C03-03 and TIC2003-00950 funded by the Ministerio de Educación y Ciencia. The second author is supported by a grant Ramón y Cajal.     

Local Łojasiewicz exponents,Milnor numbers and mixed multiplicities of ideals

Let be a finite analytic map. We give an expression for the local Łojasiewicz exponent and for the multiplicity of g when the component functions of g satisfy certain condition with respect to a set of n monomial ideals I ₁,..., I _n . We give an effective method to compute Łojasiewicz exponents based on the computation of mixed multiplicities. As a consequence of our study, we give a numerical characterization of a class of functions that includes semi-weighted homogenous functions and Newton non-degenerate functions. Work supported by DGICYT Grant MTM2006-06027.     

Third-Order Differential Subordinations for Analytic Functions Associated with Generalized Mittag-Leffler Functions

In this paper, third-order differential subordination results are obtained for analytic functions associated with an operator defined by the normalized form of the generalized Mittag-Leffler functions. Some particular cases involving Mittag-Leffler and hyperbolic functions are also considered.     

Connections on the Total Space of a Holomorphic Lie Algebroid

The main purpose of the paper is the study of the total space of a holomorphic Lie algebroid E. The paper is structured in three parts. In the first section, we briefly introduce basic notions on holomorphic Lie algebroids. The local expressions are written and the complexified holomorphic bundle is introduced. The second section presents two approaches on the study of the geometry of the complex manifold E. The first part contains the study of the tangent bundle \(T_{\mathbb {C}}E=T'E\oplus T''E\) and its link, via the tangent anchor map, with the complexified tangent bundle \(T_{\mathbb {C}}(T'M)=T'(T'M)\oplus T''(T'M)\). A holomorphic Lie algebroid structure is emphasized on \(T'E\). A special study is made for integral curves of a spray on \(T'E\). Theorem 2.8 gives the coefficients of a spray, called canonical, obtained from a complex Lagrangian on \(T'E\). In the second part of section two, we study the holomorphic prolongation \(\mathcal {T}'E\) of the Lie algebroid E. In the third section, we study how a complex Lagrange (Finsler) structure on \(T'M\) induces a Lagrangian structure on E. Three particular cases are analysed by the rank of the anchor map, the dimensions of manifold M, and those of the fibres. We obtain the correspondent on E of the Chern–Lagrange nonlinear connection from \(T'M\).     

Types d'orbites et dynamique minimale pour les applications continues de graphesOrbit types and minimal dynamics for graph maps

We define the type of a periodic orbit of a graph map. We consider the class of ‘train-track’ representatives, that is, those graph maps which minimise the topological entropy of the topological representatives of a given free group endomorphism. We prove that each type of periodic orbit realised by an efficient representative is also realised by any representative of the same free group endomorphism. Moreover, the number of periodic orbits of a given type is minimised by the efficient representatives. To cite this article: Ll. Alsedà et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 479–482.     

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N _c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z ^1/3. This improves Lieb’s upper bound N _c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).