Normal subgroups of

We classify the normal subgroups of of index less than 960; they are all congruence subgroups.

     

Quantitative stability of variational systems: III.ε-approximate solutions

We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.     

Sur de nouvelles phases séléniées ternaires du molybdène

The synthesis and the crystal properties of new selenides of formula M_xMo₃Se₄ are described. If M = Zn, Ag, Cd, Sn and Pb, they are stoichiometric with x = 0.6; if M = Fe, Mn, Cr, V, Ti, triclinic solid solutions are observed with 0.5 < x < 0.7; if M = Cu, Co, Ni, rhombohedral solid solutions are obtained with 0 < x < 1.4 for M = Cu, 0 < x < 0.7 for M = Co and 0 < x < 0.8 for M = Ni All these phases can be deduced from the Mo₃Se₄ structure by introducing metal atoms into the tunnels between the “Mo₆Se₈” metal atom cluster configuration.     

Synthesis and photophysical properties of meso-substituted bisporphyrins: comparative study of phosphorescence quenching for dioxygen sensing

The 4,6-bis(10-mesityl-5,15-di-p-tolylporpyrinyl)dibenzothiophene (H4DPSN) free base was obtained in five steps from commercially available materials. The metalation of DPSN2- with zinc(II), copper(II), and palladium(II) led to three new homobimetallic systems, (Zn)2DPSN, (Cu)2DPSN, and (Pd)2DPSN, respectively. The cofacial structures of these molecules offer the possibility of having dioxygen molecules inside the cavity for a period of time, allowing dynamic (collisional) phosphorescence quenching to be more efficient. The bimolecular excited-state deactivation rate constant for deactivation by dioxygen (kQ: (Pd)2DPB, 2.98x10(9); (Pd)2DPSN, 3.99x10(9); (Pd)2DPX, 6.94x10(9); (Pd)TPP, 8.95x10(9); (Pd)2DPS, 8.95x10(9) M-1 s-1) of (Pd)2DPSN, which exhibits an intense phosphorescence at 699 nm, was compared to those observed for (Pd)TPP, (Pd)2DPS, (Pd)2DPX, and (Pd)2DPB (TPP2-=tetraphenylporphyrin dianion, DPS4-=4,6-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]dibenzothiophene tetraanion, DPX4-=4,5-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]-9,9-dimethylxanthene tetraanion, and DPB4-=1,8-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]biphenylene tetraanion). These collision-induced deactivation data were interpreted by estimating a series of physical parameters such as the surface area and bisporphyrin radii, the diffusion coefficient of the bismacrocycles, and the theoretical deactivation efficiency for the five compounds addressing the role of steric hindrance of the macrocycles on each other and the aryl groups at the meso positions. For sensing purposes, (Pd)2DPX is characterized by a Stern-Volmer constant kSV of 2.91x10(6) M-1, placing the lower detection limit for [O2] in solution at 0.58 ppm, which is better than that for (Pd)TPP (kSV=2.31x10(6) M-1; lower detection limit of 0.73 ppm), the classically used monoporphyrin complex.     

Electronic and vibrational second-order nonlinear optical properties of protein secondary structural motifs

A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.     

Photodegradation of Polychlorinated Dibenzo-p-dioxins in Liquid Samples by Near UV Light Irradiation

Photodegradation of 1,2,3,4-tetrachlorodibenzo-p-dioxin (1,2,3,4-TCDD) in hexane solution was studied under controlled near-UV light exposure in the spectral region from 325 to 269 nm. GC-MS was used to detect the amount of unreacted dioxin and to characterize the relevant degradation products. Irradiation experiments carried out at a constant light energy (700 mJ) showed that the percentage of 1,2,3,4-TCDD left in the solution after irradiation changed from about 55 to 75%, with a minimum of 55% at 310 nm. Further irradiation experiments carried out at two wavelengths, namely 310 and 269 nm, and light energy ranging from 0 to 4000 mJ, showed that the photodegradation reaction of the TCDD always followed a pseudo-first-order kinetic, with a rate constant of 8 × 10⁻⁴and 5 × 10⁻⁴mJ⁻¹, respectively. These experiments also showed that trichloro- and dichloro-dibenzo-p-dioxins were produced with less than 15% of the initial quantity of TCDD, leading to the conclusion that the dechlorination process is a minor photolysis pathway.