Constructing Hierarchical Set Systems

In this note, it is shown that by applying ranking procedures to data that allow, for any three objects a₁, a₂, b in a collection X of objects of interest, to make consistent decisions about which of the two objects a₁ or a₂ is more similar to b, a family of cluster systems can be constructed that start with the associated Apresjan Hierarchy and keep growing until, for k = #X–1, the full set of all subsets of X is reached. Various ideas regarding canonical modifications of the similarity values so that these cluster systems contain as many clusters as possible for small values of k (and in particular for k := 0) and/or are rooted at a specific element in X, possible applications, e.g. concerning (i) the comparison of distinct dissimilarity data defined on the same set X or (ii) diversity optimization, and new tasks arising in ranking statistics are also discussed.Received November 15, 2003     

N-H..S hydrogen bonds

Infrared spectra of some compounds containing weak and medium-strong NH..S hydrogen bonds have been investigated. Spectroscopic and structural data have been correlated and compared with those obtained for NH..O and NH..N systems. At the same strength, the N..S distance is 0.51 and 0.36 Å longer than the corresponding N..O and N..N distances, respectively.     

Example of diffusion in a disordered Lorentz gas

We prove a diffusion law for a disordered Lorentz gas obtained by modification of a model of Gates, Gerst, Kac in Ref. 1, even though the motion is not a Markovian one in the technical sense of the word.     

Fluoration de telomeres polyhalogenes par le fluorure de potassium: synthese d'olefines perfluorees

Action of potassium fluoride on chlorofluorinated telomers of general formula Cl-(CFCl-CF₂)_n-CCl₃ leads to a mixture of perfluorinated cis isomers of internal olefins with the more substitued isomer being preponderant. The influence of temperature and solvant has also been studied. Only reactions carried out in tetramethylene sulfone or preferably in dimethylsulfoxide lead to perfluorinated alkenes. We suggest a mechanism with elimination followed by fluorination.     

Phosphoranes bicycliques a liaison PH : Bases de Lewis potentielles

By reaction of Borane Dimethyl Sulfide on the bicyclophosphorane $\text{1}$ the adduct $\text{2}$ is obtained with 56 % yield; by-products $\text{3}$ and $\text{4}$ are characterized .     

Anionic polymerization of 2-vinylpyridine initiated by symmetrical organomagnesium compounds in tetrahydrofuran

Anionic polymerization of 2-vinylpyridine has been studied, initiated either by dialkyl and diaryl magnesium or by living oligomers in tetrahydrofuran solution at 20°C. Spectrophotometric observations indicate the existence of stable active species with different structures. Kinetic data for propagation and viscosimetric measurements on two-ended polymers agree with a cyclic structure of living polymers and lead us to the conclusion of the existence of reactive negative “tripleions.”     

Isomerisation de l'ion moleculaire de derives substitues polycycliques du benzodioxinne-1,4

Three fragmentations (loss of phenyl, hydrogen and a RCO radical) of benzocyclobutene derivatives of differently substituted 1,4-benzodioxin were studied. In some cases these molecules, deuteriated in a specific position, revealed the existence of several isomers of the molecular ion.