Synthesis of optical standard frequencies in the S, C and L telecommunication bands by use of four-wave mixing in semiconductor optical amplifiers

The generation of standard reference frequencies close to the ITU channels is essential for the calibration and maintenance of DWDM systems. This work describes a method to synthesize frequency references in the range from 187.1 to 205.1 THz (1462-1602 nm). The method is based on the generation of four equispaced frequencies (by the process of four-wave mixing in a semiconductor amplifier) of which two are locked to absorption lines of the acetylene ¹²C₂H₂ (1511-1542 nm).     

Hopf Algebras of Dimension 12

We conclude the classification of Hopf algebras of dimension 12 over an algebraically closed field of characteristic zero.     

First application of the real space linear muffin-tin orbital atomic sphere approximation method for calculating Fermi contact hyperfine fields

In this work we apply the recently developed first-principles real space linear muffin-tin orbital atomic sphere approximation (RS-LMTO-ASA) scheme to calculate the hyperfine field for 3d impurities (V, Cr, Mn andFe) in Cu. We obtain the Fermi contact term at the impurities andat four shells of host atoms around the impurities. We compare our results with theoretical values obtained using the KKR-Green-function method andwith NMR measurements. The overall agreement is excellent, confirming the reliability of the RS-LMTO-ASA approach as means of obtaining information on hyperfine fields.     

Isomer shifts in Zr2Fe and Zr3Fe

The⁵⁷Fe isomer shifts in the crystalline compounds Zr₂Fe and Zr₃Fe are calculated. We use the standard first-principles linear-muffin-tin-orbital formalism in the atomic sphere approximation (LMTO-ASA) to obtain the electronic structure of the compounds. The electronic structure of pure Fe was also calculated with the same formalism, where the local spin density approximation for the exchange correlation term is used. We found that the calculated isomer shift values are in good agreement with the experimental values for Zr₂Fe and Zr₃Fe found in the literature.     

Local and global average degree in graphs and multigraphs

A vertex v of a graph G is called groupie if the average degree t_v of all neighbors of v in G is not smaller than the average degree t_G of G. Every graph contains a groupie vertex; the problem of whether or not every simple graph on ≧2 vertices has at least two groupie vertices turned out to be surprisingly difficult. We present various sufficient conditions for a simple graph to contain at least two groupie vertices. Further, we investigate the function f(n) = max min_v (t_v/t_G), where the maximum ranges over all simple graphs on n vertices, and prove that f(n) = 1/42n + o(1). The corresponding result for multigraphs is in sharp contrast with the above. We also characterize trees in which the local average degree t_v is constant.     

Minimal colorings for properly colored subgraphs

We give conditions on the minimum numberk of colors, sufficient for the existence of given types of properly edge-colored subgraphs in ak-edge-colored complete graph. The types of subgraphs we study include families of internally pairwise vertex-disjoint paths with common endpoints, hamiltonian paths and hamiltonian cycles, cycles with a given lower bound of their length, spanning trees, stars, and cliques. Throughout the paper, related conjectures are proposed.Research supported by a European Union PECO grant under identification number CIPA3510PL929589, while on leave at University Paris-XI     

Pickering emulsions with controllable stability

We prepare solid-stabilized emulsions using paramagnetic particles at an oil/water interface that can undergo macroscopic phase separation upon application of an external magnetic field. A critical field strength is found for which emulsion droplets begin to translate into the continuous-phase fluid. At higher fields, the emulsions destabilize, leading to a fully phase-separated system. This effect is reversible, and long-term stability can be recovered by remixing the components with mechanical agitation.     

The accuracy of ab initio molecular geometries for systems containing second-row atoms

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis on a collection of 31 molecules (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozen-core approximation with calculations where all electrons are correlated.     

Distribution of amines in water/AOT/n-hexane reverse micelles: influence of the amine chemical structure

The distribution of different aliphatic and aromatic amines: n-butylamine (n-BA), isobutylamine (i-BA), tert-butylamine (t-BA), piperidine (PIP), N,N-dimethylaniline (DMA) and N-methylaniline (MA) in water/sodium 1,4-bis(2-ethylhexyl)sulfosuccinate(AOT)/n-hexane reverse micelles was investigated by steady-state fluorescence measurements. The partition constants were measured by an indirect method based on the effect that amine partitioning exert on the bimolecular rate of the reaction between a microphase incorporated fluorophore (Ru(bpy)2+(3)) and the quencher, (Fe(CN)3-(6)). For MA, that can act as a quencher of the fluorophore a direct method was used. The results show that primary amines have larger partition constants than the secondary ones. For tertiary amines the distribution constants were practically negligible. Laser flash photolysis experiments confirmed that tertiary amines, both aliphatic and aromatic, are not incorporated to the micellar pseudophase. The effect of the amine structure on the partition constant was analyzed through linear solvation free energy relationships (LSER) using solute parameters and compared with those obtained for alcohols. Hydrogen bond interactions with the AOT polar heads appear to be the main driving force for the distribution of amines between the organic and micellar pseudophases, whereas the size of the alkyl or aromatic group tends to hinder it.