Stability of a Cubically Convergent Method for Generalized Equations

In Geoffroy et al, Acceleration of convergence in Dontchev's iterative method for solving variational inclusions Serdica Math. J. 29 (2003), pp. 45–54] we showed the convergence of a cubic method for solving generalized equations of the form 0 ∈ f(x) +- G(x) where f is a function and G stands for a set-valued map. We investigate here the stability of such a method with respect to some perturbations. More precisely, we consider the perturbed equation y ∈ f(x) +- G(x) and we show that the pseudo-Lipschitzness of the map (f +- G)⁻¹ is closely tied to the uniformity of our method in the sense that the attraction region does not depend on small perturbations of the parameter y. Finally, we provide an enhanced version of the convergence theorem established by Geoffroy, et al.     

Maharam's problem

We solve Maharam's problem [D. Maharam, An algebraic characterization of measure algebras, Ann. Math. 48 (1947) 154–167. [3]], also known as the Control Measure Problem. We construct a non-zero exhaustive submeasure on the algebra of clopen sets of the Cantor set that is not absolutely continuous with respect to a measure. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Photoinduced magnetism caused by charge-transfer excitations in tetracyanoethylene-based organic magnets

The photoinduced magnetism in Mn-tetracyanoethylene (TCNE) molecule-based magnets is ascribed to charge-transfer excitations from manganese to TCNE. Charge-transfer energies are calculated using density functional theory; photoinduced magnetization is described using a model Hamiltonian based on a double-exchange mechanism. Photoexciting electrons from the manganese core spins into the lowest unoccupied orbital of TCNE with photon energies around 3 eV increase the magnetization through a reduction of the canting angle of the manganese core spins for an average electron density on TCNE less than one. When photoexciting with a smaller energy, divalent TCNE molecules are formed. The delocalization of the excited electron causes a local spin flip of a manganese core spin.     

Entropy-driven formation of the gyroid cubic phase

We show, by computer simulation, that tapered or pear-shaped particles, interacting through purely repulsive interactions, can freely self-assemble to form the three-dimensionally periodic, gyroid cubic phase. The Ia3d gyroid cubic phase is formed by these particles on both compression of an isotropic configuration and expansion of a smectic A bilayer arrangement. For the latter case, it is possible to identify the steps by which the topological transformation from nonintersecting planes to fully interpenetrating, periodic networks takes place.     

Synthesis, crystal structure and reactivity of uranium(IV) complexes with p-tert-butylcalix[4]arene ligands

Reactions of UCl4 with 25,27-dimethoxy-5,11,17,23-tetra-tert-butylcalix[4]arene (H2Me2calix) in THF or pyridine at 80 degrees C gave [UCl2(Me2calix)L2] [L = THF (1) or pyridine (2)]. Similar treatment of U(acac)(4) (acac = MeCOCHCOMe) with H2Me2calix in THF or pyridine afforded [U(acac)2(Me2calix)] (3). The bis-calixarene compound [U(Me2calix)(H2calix)] (4) was obtained by reaction of U(OTf)4 or U(OTf)3 with H2Me2calix in pyridine at 110 degrees C. Treatment of UCl4 with H2Me2calix in pyridine at 110 degrees C gave [Mepy][UCl2(Hcalix)(py)2] (5) resulting from demethylation and acid cleavage of the methoxy groups of the calixarene ligand of 2. Adventitious traces of air were responsible for the formation of [Hpy][Mepy]4[{UCl(calix)}3(mu3-O)][UCl6] (6) during the reaction of UCl4 and H2Me2calix, and of [{U(Me2calix)(mu3-O)LiCl(THF)}2] (7) during the reaction of 2 with tBuLi. The X-ray crystal structures of 1.2THF, 2.2py, 3.0.25L (L = THF and py), 4.2py, 5, 6.3py and 7.THF have been determined.     

Host-guest interaction between cyclen based macrotricyclic ligands and phosphate anions. A potentiometric investigation

The host-guest interaction between orthophosphate, pyrophosphate and triphosphate anions and three cyclen based macrotricyclic ligands possessing ortho- (TOC), meta- (TMC) and para-xylenyl (TPC) linkers was investigated by potentiometric measurements. The ternary species present in solution and their stability constants have been determined. The different behaviours are explained in terms of hydrogen bond formation and coulombic attraction between the organic host and the inorganic guest. The selectivity, illustrated with species distribution diagrams, is discussed. The results unambiguously showed the importance of the distance between the two cyclen cores and emphasized the increasing of the triphosphate species selectivity together with the cavity size of the ligand. A comparison of the present results with those obtained with their mono-bridged homologues is also discussed.     

Chemical composition and in vitro antifungal and antioxidant activity of the essential oil and methanolic extract of Teucrium sauvagei Le Houerou

The chemical composition and the in vitro antifungal and antioxidant activity of the essential oil and the methanolic leaf extracts of Teucrium sauvagei Le Houerou, an endemic medicinal plant growing in Tunisia, have been studied. More than 35 constituents having an abundance >or=0.2% were identified in the oil. beta-Eudesmol, T-cadinol, alpha-thujene, gamma-cadinene, and sabinene were the prevalent constituents. Results of the antifungal activity tests indicated that the methanolic extract inhibited the in vitro growth of seven dermatophytes, whereas the essential oil showed average inhibition against only three dermatophytes. In vitro antioxidant properties of the essential oil and the methanolic extract were determined by DPPH (2,2-diphenyl-1-picrylhydrazyl) and ABTS (2,2'-azinobis(3-ethylbenzothiazoline-6-sulphonic acid)) assays and compared to those of the synthetic antioxidant Trolox. Due to their antifungal and antioxidant properties, the essential oil and the methanolic extract of T. sauvagei may be of use as natural preservative ingredients in food and/or pharmaceutical industries.     

The colors of polydiacetylenes: a commentary

Polydiacetylenes (PDA) can take several colors, mostly "red" and "blue", and blue-to-red color transitions are usually considered as transitions from a well ordered state to a disordered one. Recent work on single isolated PDA chains shows that this is not correct: red chains can be quasi-perfect quantum wires. The transition is between two different chain conformations, and each may, or may not, be perfectly ordered. Disorder, when it occurs, is a side-product of the transformation.     

Iterative solving of generalized equations with calm solution mappings

We present an iterative procedure for solving, in finite dimensions, generalized equations of the form

(∗)     

Polarization dependence of L- and M-edge resonant inelastic X-ray scattering in transition-metal compounds

The resonant inelastic x-ray scattering (RIXS) cross section at the L and M edges of transition-metal compounds is studied using an effective scattering operator. The intensities of the elastic peak and for spin-flip processes are derived. It is shown how the polarization dependence can be used to select transitions. Comparisons are made with experiment. A detailed analysis of the polarization and angular dependence of L- and M-edge RIXS for divalent copper compounds, such as the high-Tc superconductors, is given.