Hopf Algebras, Renormalization and Noncommutative Geometry

We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations. Received: 14 August 1998/ Accepted: 5 October 1998     

Interacting branching process as a simple model of innovation

We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/τ at each generation. In contrast with mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For τ = ∞, surviving processes exhibit a bottleneck before exploding superexponentially-a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p→0.     

Ultrafast melting of a charge-density wave in the Mott insulator 1T-TaS2

Femtosecond time-resolved core-level photoemission spectroscopy with a free-electron laser is used to measure the atomic-site specific charge-order dynamics of the charge-density?wave in the Mott insulator 1T-TaS2. After strong photoexcitation, a prompt loss of charge order and subsequent fast equilibration dynamics of the electron-lattice system are observed. On the time scale of electron-phonon thermalization, about 1?ps, the system is driven across a phase transition from a long-range charge ordered state to a quasiequilibrium state with domainlike short-range charge and lattice order. The experiment opens the way to study the nonequilibrium dynamics of condensed matter systems with full elemental, chemical, and atomic-site selectivity.     

Structural and electronic effects in metallocene catalysts studied by x‐ray techniques

A series of metallocenes, namely, [Cp₂ZrCl₂], [(MeCp)₂ZrCl₂], [(nBuCp)₂ZrCl₂], [(iBuCp)₂ZrCl₂], [(tBuCp)₂ZrCl₂], [Et(Ind)₂ZrCl₂], [Et(IndH₄)₂ZrCl₂], and [MeSi₂(Ind)₂ZrCl₂)] were analyzed by extended x‐ray absorption fine structure (EXAFS) and x‐ray photoelectron spectroscopy (XPS). Complementary techniques, UV–vis spectroscopy and cyclic and differential pulse voltammetry, were employed to characterize the organometallic complexes. The catalysts were evaluated in ethylene polymerization, having methylaluminoxane (MAO) as the cocatalyst, and the resulting polymers were characterized by gel permeation chromatography. The structural and electronic effects caused by the coordination sphere around the metal center and their effects on the catalytic activity and polymer characteristics are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Phase transition in ammonium hexafluorovanadate (III)

Heat capacity of ammonium hexafluorovanadate (NH₄)₃ [VF₆] has been measured with a miniaturized adiabatic calorimeter from 20 to 300 K. A phase transition was found at 280.44 ± 0.05 K with the associated entropy change Δ_trs S = 24.9 ± 0.5 JK^?1 mol^?1. The entropy transition is accounted for by the orientational order-disorder changes of hexafluorovanadate ion and ammonium ion occupying respective octahedral sites, as in the cases of (NH₄)₃AlF₆ and (NH₄)₃FeF₆ crystals. Changes in infrared spectra relative to v₃ vibrational mode of [VF₆]^3? ion can be explained by an orientational disorder of the anions in the high-temperature phase (HTP). The dependence of cubic root of the unit-cell volume of a family of ammonium cryolites on their transition temperatures is discussed in relation to the nature of interactions which induce the phase transition.     

The CH3D absorption spectrum in the 1.58 μm transparency window of methane: Empirical line lists at 81 K and 294 K and temperature dependence

In spite of its low isotopic abundance in methane (about 5×10⁻⁴), CH₃D contributes greatly to the very weak absorption in the 1.58 μm methane transparency window. This methane window deserves to be characterized in details because it is important for planetary applications in particular for Titan and the giant planets. In this work, we recorded the CH₃D spectrum by high sensitivity differential absorption spectroscopy (α_min≈5×10⁻⁸ cm⁻¹) both at room temperature and at 81 K. A list of more than 9000 lines was constructed from the 81 K spectrum for the 6099–6530 cm⁻¹ region. In order to get the temperature dependence of the line intensities, the low energy values have to be determined. The rovibrational assignments available in the literature provide low energy values for about 380 strong transitions of the region. This is insufficient to characterize the temperature dependence of the CH₃D absorption between 6200 and 6400 cm⁻¹. In this interval, a list of 5500 lines was constructed from the room temperature spectrum. The empirical energy values of the transitions were derived from the ratio of the intensities at 81 K and 294 K. The exact and empirical lower state energies included in the final line lists provided as Supplementary Material, allow for accounting for the temperature dependence of the CH₃D spectrum in the entire 6099–6530 cm⁻¹ region.Our measurements have been compared to the spectroscopic parameters and assignments available in the literature in particular those adopted in the HITRAN database. Improvements and corrections are proposed for the wavenumber calibration and for some lower state energies.     

Preparation and basic physical properties of BiTeI single crystals

A modified Bridgman method is described, which makes it possible to prepare homogeneous BiTeI crystals using excess iodine. At room temperature the values of the electrical conductivity of the crystals range around 2000 ^–1 cm^–1, the Hall constant value about 0·09 cm^–3 coul^–1, the Seebeck coefficient about 50 V K^–1. In connection with the assumption of super-stoichiometric iodine content we expect there exist point defects in the crystals, where Te atoms are replaced with I atoms, which gives rise to electric conductivity. On the basis of the temperature dependence of the electron mobility one can suppose a mixed mechanism of the scattering of the free carriers by the acoustic branch of lattice vibrations and by ionized impurities.     

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.Preprint Université de Bourgogne-mai 1990     

Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals

We give criteria for the Cohen-Macaulay and Gorenstein property of Rees algebras of height 2 non-singular equimultiple prime ideals in terms of explicite representations of the associated graded rings. As consequences, we show that in general, the Cohen-Macaulay resp. Gorenstein property of such Rees algebras does not imply the Cohen-Macaulay resp. Gorenstein property of the base ring and that these properties depend upon the characteristic. Dedicated to the memrory of Professor Lê Van Thiêm Professor Lê Van Thiêm was the first directorof Hanoi Institute of Mathematics