L p -pinching and the geometry of compact Riemannian manifolds

We prove a Harnack-type inequality inf|S|/sup|S|>1?ε(W, M, V) satisfied by the sections of a Riemannian vector bundleW lying in the kernel of a Schrödinger operator ∨*∨+V underL ^p -pinching assumptions on the potentialV and derive various topological and geometric consequences. For instance, we prove a fibration theorem which gives a classification of almost non-negatively curved compact manifolds by the first Betti number. In the case of almost non-positively curved compact manifolds, we prove that the minimal volume must vanish whenever the isometry group is not finite and give conditions implying that it is abelian.     

Bisphenol-A polycarbonate–poly(butylene terephthalate) transesterification. IV. Kinetics and mechanism of the exchange reaction

The kinetic aspects of the bisphenol-A polycarbonate–polybutylene terephthalate exchange reaction are considered as a function of temperature and of the PC/PBTP ratio. The most likely mechanism is a direct reversible ester-ester interchange reaction catalyzed by titanium residues present in commercial PBTP.     

Symmetry of nonrigid molecules and isomerization processes

Starting from the concept of a totally flexible molecule, rigidity is introduced by restricting progressively the allowed permutations. Each nonrigid isomer is then characterized by its Longuet-Higgins group ? of allowed permutation inversions. For a given ? all nonrigidity types correspond to all possible choices of the symmetry subgroup ? of the skeleton. The structure of ? also allows a characterization of the isomerization processes studied in chemical kinetics. In both situations, isomerization mechanisms may be associated with generators and are, in the simplest situations, represented by Cayley graphs.     

Crystallization and melting of aqueous gelatin

Gelation and melting of aqueous gelatin were investigated by differential scanning calorimetry. This phenomenon can be analyzed as a conventional crystallization process assuming predetermined primary nucleation and unidirectional growth. The results were interpreted in terms of the fringed micelle model. Calculated values of the diameter of the renatured collagen fibril were found in excellent agreement with those determined previously by electron microscopy.     

Synthèse d'acétals de désoxy-3-hydroxyamino-3-furannoses. Note de laboratoire

Synthesis of 3-Deoxy-3-(hydroxyamino)furanose Acetals Reduction of sugar ketoximes with NaBH₃CN under acidic conditions constitutes a good synthetic pathway to deoxy(hydroxyamino)sugar derivatives. These compounds which are useful building blocks for the preparation of analogs of various classes of biologically important carbohydrates are reasonably stable.     

Analyse spectrale des formes automorphes et séries d'Eisenstein

Sans résumé     

Internal symmetry groups of non-rigid molecules

Hougen has established, for quasi-rigid molecules, the relationship between permutationinversions acting on the molecular Hamiltonians written in Cartesian co-ordinates and permutation-rotations (perrotations) of symmetry acting on nuclear equilibrium configurations. We extend these relations to the case of non-rigid molecules. For this, we introduce kinetic perrotations which act on nuclear equilibrium configurations in the same way as do Altmann's isodynamic operators. We show that isodynamic operators do not always form a group. Moreover, their action cannot be extended to the electrons. They cannot be used for the classification of molecular wave functions. This classification is achieved by using the group of Longuet-Higgins and the group of the corresponding feasible perrotations.     

Evidence of Brillouin scattering in an ytterbium-doped double-clad fiber laser

We have designed and performed an experiment that permitted direct observation of Brillouin backscattering in an Yb-doped double-clad fiber laser. Fifteen Brillouin-shifted frequencies were observed for the first time to our knowledge. We clearly demonstrate that stimulated Brillouin scattering is directly responsible for both fast transient dynamics of the laser and reduction of the laser's pulse width.     

Iron(II) carboxylate complexes based on a tetraimidazole ligand as models of the photosynthetic non-heme ferrous sites: synthesis, crystal structure, and Mössbauer and magnetic studies

The preparations, X-ray structures, and detailed physical characterization are presented for new complexes involving an iron(II) center, a tetraimidazole ligand (TIM), and different carboxylates. [Fe(TIM)(C(6)H(5)CH(2)CO(2))](ClO(4)) (1) crystallizes in the Pbca space group with a = 10.8947(13), b = 20.343(2), and c = 22.833(3) A, Z = 8, and V = 5060.6(11) A(3). [Fe(TIM)(CH(3)CO(2))](ClO(4)) (2) crystallizes in the Ia space group with a = 17.117(2), b = 10.3358(12), and c = 25.658(3) A, beta = 90.301(13) degrees, Z = 8, and V = 4539.5(9) A(3). In both structures, the iron(II) is hexacoordinated to the four N(imidazole) donors of the TIM ligand and the two O donors of a bidentate carboxylate. The flexibility of the carboxylate bidentate coordination, symmetrical or more or less asymmetrical, associated with the steric demand of the TIM ligand results in a remarkable versatility of the Fe(II)N(4)O(2) coordination geometry. The diversity in carboxylate bidentate coordination modes has allowed us to clearly show the importance of the structural and electronic effects, through IR and M?ssbauer spectroscopy, of this apparently tenuous carboxylate shift. Comparison of the structural and M?ssbauer properties of these complexes with the non-heme ferrous site of photosynthetic systems (i) shows that the metric parameters of site 2b, including the symmetrically chelated bidentate carboxylate, are closer to those of the non-heme ferrous site in the bacterial reaction centers of Rhodopseudomonas viridis and R. sphaeroides and (ii) suggests that the ligand environment of the non-heme ferrous center of PS 2 is close to the axially distorted octahedral symmetry resulting from an asymmetrical bidentate coordination of the -CO(2) motif, as in complex 1.