Structure of foliations of codimension greater than one

We study the structure of a foliation of high codimension which admits a transverse foliation. We introduce four families of open saturated sets. These open sets have a simple characterization and allow us to establish a structure theorem as in codimension 1.     

On the Solutions of a Singular Nonlinear Periodic Boundary Value Problem

In this paper, we consider the following singular nonlinear problem

The spectrum and the law of large numbers for infinite-dimensional nonstationary stochastic processes

Helley's 1st and 2nd theorems for trace class-valued distributions are established. Using these theorems the concept of spectrum for an infinite dimensional nonstationary stochastic process is introduced, and a law of large numbers for processes which admit a spectrum is obtained.     

N-free posets as generalizations of series-parallel posets

N-Free posets have recently taken some importance and motivated many studies. This class of posets introduced by Grillet [8] and Heuchenne [11] are very related to another important class of posets, namely the series-parallel posets, introduced by Lawler [12] and studied by Valdes et al. [21]. This paper shows how N-free posets can be considered as generalizations of series-parallel posets, by giving a recursive construction of N-free posets. Furthermore we propose a linear time algorithm to recognize and decompose any N-free poset. This yields some very naturel problems, namely: which are the properties(such as linear time algorithm for some invariant) of series-parallel posets that are kept for N-free posets?     

A halogen anion sensor based on the hydrophobic entrapment of a fluorescent probe in silica sol-gel thin films

A halogen anion (Cl⁻, Br⁻, I⁻) sensor has been designed, based on the entrapment of a fluorescent molecule in a sol-gel silica film deposited on a glass substrate. A key factor is the use of the newly synthesized hydrophobic fluorophore, N-dodecyl-6-methoxyquinolinium, so as to avoid the problem of leaching. This probe allows detection and measurement of chloride concentrations in the physiological range (100 mM) coupled with a response time less than 1 s. The fluorescence quenching data are fitted to a model which assumes two quenching sites.     

Interval dimension and MacNeille completion

Equality between the interval dimensions of a poset and its MacNeille completion, announced in [7], has been obtained by the authors as a byproduct of their study of Galois lattices in [8]. The purpose of this note is to give a direct proof, similar to the classical proof of Baker's result stating that the dimension (in the Dushnik-Miller sense) of a poset and its MacNeille completion are the same.Supported by French PRC Math-Info.