CR-submanifolds of complex hyperbolic spaces satisfying a basic equality

The first author introduced a Riemannian invariant denoted by δ and proved in [4] that everyn-dimensional submanifold of the complex hyperbolicm-space ℂH ^m (4c) of constant holomorphic sectional curvature 4c<0 satisfies a basic inequality , whereH ² denotes the squared mean curvature of the submanifold. The main purpose of this paper is to completely classify properCR-submanifolds of complex hyperbolic spaces which satisfy the equality case of this inequality. Dedicated to Leopold Verstraelen on his fiftieth birthday     

Clustering for routing in densely populated areas

This paper introduces a new approach for generating school bus routes in a dense urban area. First, a districting algorithm is used to determine clusters including appropriate numbers of students. Then, for each cluster, a route and the stops along this route are determined. Numerical results are reported and compared with those obtained previously. Although the algorithm has been developped and tested in a specific context, it could easily be extended to more general vehicle routing problems.     

Long optically controlled delays in optical fibers

Optically controlled delay lines in optical fibers are demonstrated by use of the group-velocity control of signal pulses based on stimulated Brillouin scattering. We achieve continuous time delay within the range of 150 ns, much larger than the width of the 40 ns signal pulse, using cascaded fiber segments joined by unidirectional optical attenuators. In the meantime, we also observe a large amount of pulse broadening, which agrees well with a theoretical prediction based on linear theory.     

Femtosecond optical vortices in air

We examine the robustness of ultrashort optical vortices propagating freely in the atmosphere. We first approximate the stability regions of femtosecond spinning pulses as a function of their topological charge. Next, we numerically demonstrate that atmospheric optical vortices are capable of conveying high power levels in air over hundreds of meters before they break up into filaments.     

Structural change of the heme pocket due to disulfide bridge formation is significantly larger for neuroglobin than for cytoglobin

Human neuroglobin (hNgb) and human cytoglobin (hCygb), two recently discovered members of the vertebrate globin family, are known to be able to form an intramolecular disulfide bridge. Using electron paramagnetic resonance (EPR), we show that formation of a disulfide bridge in ferric hNgb causes a considerable change in the heme pocket structure, whereas this is not so clear for ferric hCygb. The structural results can be related nicely to earlier histidine and dioxygen affinity studies of the ferrous proteins.     

Batalin-Vilkovisky Algebras and Cyclic Cohomology of Hopf Algebras

We show that the Connes–Moscovici negative cyclic cohomology of a Hopf algebra equipped with a character has a Lie bracket of degree -2. More generally, we show that a cyclic operad with multiplication is a cocyclic module whose simplicial cohomology is a Batalin–Vilkovisky algebra and whose negative cyclic cohomology is a graded Lie algebra of degree -2. This generalizes the fact that the Hochschild cohomology algebra of a symmetric algebra is a Batalin–Vilkovisky algebra.     

Distributed measurement of chromatic dispersion by four-wave mixing and Brillouin optical-time-domain analysis

A new nondestructive method for measuring the spatial distribution of chromatic dispersion along an optical fiber is presented. It is based on using Brillouin optical time-domain analysis to probe the power distribution of the four-wave mixing generated by two continuous-wave lasers. The results obtained prove that this new method is capable of providing better performance than comparable techniques. Furthermore, sensing the variations of Brillouin gain maximum produces additional information about the fiber, such as presence of strain and concentration of GeO2.