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.     

Jack Polynomials in Superspace

This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were constructed. Orthogonal eigenfunctions are now obtained by diagonalizing the first nontrivial element of a bosonic tower of commuting conserved charges not containing this Hamiltonian. Quite remarkably, the expansion coefficients of these orthogonal eigenfunctions in the supermonomial basis are stable with respect to the number of variables. The second and more direct approach amounts to symmetrize products of non-symmetric Jack polynomials with monomials in the fermionic variables. This time, the orthogonality is inherited from the orthogonality of the non-symmetric Jack polynomials, and the value of the norm is given explicitly.     

On-fiber photodegradation after solid-phase microextraction of p,p'-DDT and two of its major photoproducts,p,p'-DDE and p,p'-DDD

The potential of performing photochemical studies in solid phase microextraction (SPME) fibers, "photo-SPME", to study the photodegradation of p,p'-DDT and two of its major degradation products, p,p'-DDE and p,p'-DDD, is shown. Analyses were carried out by gas chromatography mass spectroscopy detection. DDT was extracted from aqueous solutions using five different commercial coatings. The fibers were then exposed to UV light emitted by a low-pressure mercury lamp. After 30 min of irradiation, the degradation of DDT only occurred in polydimethylsiloxane fibers. The on-fiber degradation kinetics of p,p'-DDT was studied from 2 to 60 min. A large number of photoproducts were generated and their kinetic behavior was studied. In order to clarify the possible photoreaction pathways for DDT, individual water solutions containing p,p'-DDD or p.p'-DDE were prepared and photo-SPME was performed for each compound at different irradiation times. On the basis of the photoproducts identified, some photodegradation pathways are proposed. Finally, aqueous photodegradation studies followed by SPME were performed and compared to the photo-SPME. This work will show the enormous potential of photo-SPME to perform photodegradation studies.     

New Examples of Willmore Surfaces in S n

A surface x: M S ⁿ is called a Willmore surface if it is a criticalsurface of the Willmore functional _M (S – 2H ²)dv, where H isthe mean curvature and S is the square of the length of the secondfundamental form. It is well known that any minimal surface is aWillmore surface. The first nonminimal example of a flat Willmoresurface in higher codimension was obtained by Ejiri. This example whichcan be viewed as a tensor product immersion of S ¹(1) and a particularsmall circle in S ²(1), and therefore is contained in S ⁵(1) gives anegative answer to a question by Weiner. In this paper we generalize theabove mentioned example by investigating Willmore surfaces in S ⁿ (1)which can be obtained as a tensor product immersion of two curves. We inparticular show that in this case too, one of the curves has to beS ¹(1), whereas the other one is contained either in S ²(1) or in S ³(1). In the first case, we explicitly determine the immersion interms of elliptic functions, thus constructing infinetely many newnonminimal flat Willmore surfaces in S ⁵. Also in the latter casewe explicitly include examples.     

Lipschitz Kernel of a Closed Set-Valued Map

This paper deals with Lipschitz selections of set-valued maps with closed graphs. First, we characterize Lipschitzianity of a closed set-valued map in the differential games framework in terms of a discriminating property of its graph. This allows us to consider the -Lipschitz kernel of a given set-valued map as the largest -Lipschitz closed set-valued map contained in the initial one, to derive an algorithm to compute the collection of Lipschitz selections, and to extend the Pasch–Hausdorff envelope to set-valued maps.