Inversionless Amplification in a Three-Level System Driven by a Single Field

The three-level system subjected to electromagnetic fields is investigated. It is shown that when one of two fields is strong (the pumping field), the system can amplify the second (probe) field even if no population inversion is created, but some phase relations are satisfied. The conditions necessary for inversionless amplification to take place are discussed. The connection between this effect and stimulated Raman emission is shown. Numerical simulations for each one of the discussed cases were performed.     

On algebraic equations satisfied by correlators in Wess-Zumino-Witten models

Apart from the Knizhnik-Zamolodchikov differential equations, correlation functions in Wess-Zumino-Witten models of conformal field theory satisfy a certain system of algebraic equations. We show that hypergeometric solutions of KZ equations constructed in [3] do satisfy these algebraic equations.     

Determinant bundles and Virasoro algebras

We consider the interplay of infinite-dimensional Lie algebras of Virasoro type and moduli spaces of curves, suggested by string theory. We will see that the infinitesimal geometry of determinant bundles is governed by Virasoro symmetries. The Mumford forms are just invariants of these symmetries. The representations of Virasoro algebra define (twisted)D-modules on moduli spaces; theseD-modules are equations on correlators in conformal field theory.To the memory of Vadik Knizhnik (20. 2. 1962–25. 12. 1987)     

Interplay of Antiferromagnetic Coupling and Spin Crossover in Dinuclear Iron(II) Complexes

This article reports on the study of the interplay between magnetic coupling and spin transition in 2,2′-bipyrimidine (bpym)-bridged iron(II) dinuclear compounds. Coexistence of both phenomena has been observed in [Fe(bpym)(NCS)₂]₂bpym, [Fe(bpym)(NCSe)₂]₂bpym and [Fe(bt)(NCS)₂]₂bpym (bpym = 2,2′-bipyrimidine, bt = 2,2′-bithiazoline) by the action of external physical factors namely pressure or electromagnetic radiation. Competition between magnetic exchange and spin crossover has been studied in [Fe(bpym)(NCS)₂]₂bpym at 6.3 kbar. LIESST experiments carried out in [Fe(bpym)(NCSe)₂]₂bpym and [Fe(bt)(NCS)₂]₂bpym at 4.2 K have shown that is possible to achieve dinuclear molecules with different spin states in this class of compounds. This revised version was published online in August 2006 with corrections to the Cover Date.     

When is a non-self-adjoint Hill operator a spectral operator of scalar type?

We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator $H=?{\mathrm{d}}^2/\mathrm{d}{x}^2+V$ in $L^2(\mathbb{R})$ to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. To cite this article: F. Gesztesy, V. Tkachenko, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Kinetic study of the gas-phase reaction of OH with Br2

An experimental, temperature-dependent kinetic study of the gas-phase reaction of the hydroxyl radical with molecular bromine (reaction 1) has been performed by using a pulsed laser photolysis/pulsed-laser-induced fluorescence technique over a wide temperature range of 297-766 K, and at pressures between 6.68 and 40.29 kPa of helium. The experimental rate coefficients for reaction 1 demonstrate no correlation with pressure and exhibit a negative temperature dependence with a slight negative curvature in the Arrhenius plot. A nonlinear least-squares fit with two floating parameters of the temperature-dependent k(1)(T) data set using an equation of the form k(1)(T) = AT(n) yields the recommended expression k(1)(T) = (1.85 x 10(-9))T(-0.66) cm(3) molecule(-1) s(-1) for the temperature dependence of the reaction 1 rate coefficient. The potential energy surface (PES) of reaction 1 was investigated with use of quantum chemistry methods. The reaction proceeds through formation of a weakly bound OH...Br(2) complex and a PES saddle point with an energy below that of the reactants. Temperature dependence of the reaction rate coefficient was modeled by using the RRKM method on the basis of the calculated PES.     

A new stepwise synthesis of a family of propylamines derived from diatom silaffins and their activity in silicification

A new method for the stepwise synthesis of propylamines containing fragments of N-methyl propylamine as found in diatom bioextracts is presented and their activity in silicic acid condensation is described.