Short-term memories with a stochastic perturbation

We investigate short-term memories in linear and weakly nonlinear coupled map lattices with a periodic external input. We use locally coupled maps to present numerical results about short-term memory formation adding a stochastic perturbation in the maps and in the external input.     

Relaxation dynamics of excited states of Tm3+ in SrGdGa3O7 crystals activated with Tm3+ and Tb3+

3 H₄ and ³F₄ states of Tm in SrGdGa₃O₇ single crystal was evaluated. Tm-Tb energy transfer reduces effectively the lifetime of terminal level in a potential ³H₄-³F₄ laser transition but gives rise to parasitic nonradiative relaxation of the initial ³H₄ level. SrGdGa₃O₇ crystal single doped with thulium possesses combination of properties advantageous for laser oscillations near 1.9 μm, namely high rate of cross relaxation process leading to population buildup on the initial ³F₄ level and relatively high crystal field splitting of the ground ³H₆ level. Received: 25 April 1996/Revised version: 10 October 1996     

Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

We prove the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller ow on (any connected component of a stratum of) the moduli space of Abelian differentials on compact Riemann surfaces are all distinct. By previous work of Zorich and Kontsevich, this implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface. Work carried out within the Brazil–France Agreement in Mathematics. Avila is a Clay Research Fellow. Viana is partially supported by Pronex and Faperj.     

Mild Transformation of Telluro and Seleno Esters into Carboxylic Acid and Esters

Te-Butyl Telluroesters and Se-Butyl Selenoesters are hydrolyzed to carboxylic acids under very mild conditions by reaction with copper(II) chloride dihydrate. When the reaction is performed in ethanol or methanol, using anhydrous copper(II) chloride a transesterification occurred leading to the oxygenated esters in good yield.     

Cooperative emission study in ytterbium-doped Y2SiO5

Ytterbium ions infrared and visible cooperative luminescences, resulting from YAG laser and selective site excitations, in (6%) Yb-doped Y₂SiO₅ thin film are analyzed. Magnetically coupled Yb-Yb ion pairs seem to play a major role in energy transfer and cooperative emission, confirming the prevalence of superexchange mechanisms.     

On certain curves of genus three in characteristic two

We study curves of genus 3 over algebraically closed fields of characteristic 2 with the canonical theta characteristic totally supported in one point. We compute the moduli dimension of such curves and focus on some of them which have two Weierstrass points with Weierstrass directions towards the support of the theta characteristic. We answer questions related to order sequence and Weierstrass weight of Weierstrass points and the existence of other Weierstrass points with similar properties. – Dedicated to the treasured memory of our coauthor, Paulo Henrique Viana     

Infrared spectrum, DFT: pBP86/DN** and NCA vibrational calculations of 2-methylthiosemicarbazide copper(II) nitrate [Cu(2MeTSC)2(NO3)2

To elucidate tentative assignments of metal-ligand modes of thiosemicarbazide complexes, a structural study and a assignment of the normal vibrations of 2-methylthiosemicarbazide copper(II) nitrate, [Cu(2MeTSC)(2)(NO(3))(2)] have been done through the ab initio DFT: pBP86/DN** procedure, and through the normal coordinate analysis (NCA). In the vibrational calculations, the elongated CuONO(2) bonds of the nitrate groups were considered in the CS and CN tautomers of the complex. DFT calculations had revealed that the infrared spectra can be well interpreted through the CN tautomer, failing in the prediction of the -NO(2) group wavenumbers. A little difference stabilization energy for the tautomers were found: for the CN tautomer was E=-3487,36376a.u., and for the CS tautomer, E=-3473,93598a.u. The observed combination bands at 1763.0 and at 1754.0 cm(-1) are an indicative that the -NO(3)(-) groups acts as monodentate ligands. Calculations had confirmed the experimental assignment of the infrared spectrum.     

New insight in the structure–luminescence relationships of Ca9Eu(PO4)7

The double phosphate Ca₉Eu(PO₄)₇, obtained by solid state reaction, was found to be isotypic with Ca₃(PO₄)₂, with space group R3c and unit cell parameters a=10.4546(1) Å, c=37.4050(3) Å, V=3540.67(9) Å³, Z=6. The structure parameters refined using the Rietveld method showed that europium shares positions M1, M2 and M3 with calcium, contradicting previously published Mössbauer results. Low temperature luminescence under selective excitation of Eu³⁺ in Ca₉Y_1−xEu_x(PO₄)₇ and in Ca₉Eu(PO₄)₇ samples was studied, confirming the Eu³⁺ distribution into these sites. At 10 K, ⁵D₀→⁷F₀ emission lines of Eu³⁺ were observed at 578.5, 579.5, 580.1 nm for the M3, M1 and M2 sites, respectively. High temperature X-ray powder diffraction evidenced a second-order phase transition around 573 °C.     

On the quantum polarization and entanglement of superpositions of two two-mode coherent states

This work discusses the entanglement and quantum polarization of superpositions of two-mode coherent states of the types |ψ₁〉 = N₁(|α, β〉 + |β, α〉) and |ψ₂〉 = N₂(|−α, −α〉 + |α, α〉). We use the concurrence to measure their entanglements and the quantum Stokes parameters and the Q function in order to analyze their polarization and degree of polarization.     

Temperature‐dependent Raman spectra of Ba2BiSbO6 ceramics

In this work, we have performed Raman scattering measurements in Ba₂BiSbO₆ ceramics in the temperature range from 10 to 573 K. The Raman spectra were examined using group theory to analyze the decomposition of the reducible representation of the vibrational modes and with a virtual octahedral model. At room temperature, five modes were observed. At low temperatures, the spectra subtly showed the rhombohedral–monoclinic phase transition, which was identified by changes in the Raman intensity of the bending and symmetrical stretching SbO₆ octahedral modes. The cubic–rhombohedral phase transition was not clearly evident in the high‐temperature Raman data. Copyright © 2009 John Wiley & Sons, Ltd.