Computation of the Maslov index and the spectral flow via partial signatures

Given a smooth Lagrangian path, both in the finite and in the infinite dimensional (Fredholm) case, we introduce the notion of partial signatures at each isolated intersection of the path with the Maslov cycle. For real-analytic paths, we give a formula for the computation of the Maslov index using the partial signatures; a similar formula holds for the spectral flow of real-analytic paths of Fredholm self-adjoint operators on real separable Hilbert spaces. As applications of the theory, we obtain a semi-Riemannian version of the Morse index theorem for geodesics with possibly conjugate endpoints, and we prove a bifurcation result at conjugate points along semi-Riemannian geodesics. To cite this article: R. Giambò et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

Supersymmetry and bosonization in three dimensions

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

Infrared and Raman spectroscopic investigation of Eu3+-doped mono and Di-urethanesil hybrid siliceous materials

The general features of two series of sol-gel derived materials, designatedurethanesils (Ut), have been investigated by infrared and Raman spectroscopies with the goal of elucidating the chemical environment of the Eu³⁺ cations. The host frameworks of the two families of ormolytes studied have been represented by m-Ut(350) and d-Ut(300), where m stands for mono, d stands for di, 350 and 300 are the average molecular weights of the organic precursors (poly(ethylene glycol) methyl ether, PEGME, and poly(ethylene glycol), PEG, respectively). The hybrid matrix of the mono-xerogels is composed by a siliceous backbone bonded by means of urethane linkages (-NHC (=O)O-) to pendant methyl end capped oligopolymer chains with approximately 7 oxyethylene units, whereas that of the di-xerogels is based on a siliceous network grafted through urethane groups to both ends of poly(oxyethylene) segments containing about 6 (OCH₂CH₂) repeat units. Both classes of materials have been doped with europium triflate (Eu(CF₃SO₃)₃). The doped samples have been identified by m-Ut(350)_nEu(CF₃SO₃)₃ and d-Ut(300)_nEu(CF₃SO₃), where n is the molar ratio of (OCH₂CH₂) repeat units per Eu³⁺ ion. Materials with n ranging from ∞ to 5 have been analyzed. The spectral data obtained provide evidence that the cations begin to coordinate to the ether oxygen atoms of the oligopolymer chains at n=40 in the mono-urethanesils and at n=10 in the di-urethanesils. In mono-urethanesils samples with n>40 and in di-urethanesils materials with n>10, the Eu³⁺ coordinate exclusively to the carbonyl oxygen atoms of the urethane linkages. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

Solvent-dependent host–guest complexation of two homologous merocyanines by a water-soluble calix[8]arene: Spectroscopic analysis and structural calculations

The sulfonated calixarene I₈C₁₂ acts as a host for homologous merocyanines Mc1 and Mc2 in organic solvents, exhibiting neither selectivity towards the guest dyes nor solvent dependence of the complexation equilibria. In water, on the contrary, only the lower homologue, Mc1, is solubilized in the presence of the calixarene. A combination of UV–visible and fluorescence spectroscopic and photophysical analysis and MD structural simulation of the calixarene-dye complexes was employed to account for the observations, and suggests that a radical change in the complexation mode occurs upon moving from an organic to an aqueous environment.     

Paraxial designing of planar waveguide variable-index focusing elements: Part 2—lenses of elliptical symmetry

A paraxial ray-optics formalism proposed for designing radially symmetric variable-index lenses is extended to the case of lenses of elliptical symmetry of the index profile.     

Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006