Indirect Methods For Determination of The Protective Effects of Coating Films on The Surface of Crystals

The extents of the protective effects of coating films on the surface of crystals were determined. Three different samples were made with different quantities of coating fluid (Sepifilm LP 010 in 10% aqueous solution). Since the atomizing rate was constant, the coating time increased in parallel with the volume of coating fluid applied. The direct measurement of film thickness and smoothness is very difficult, and therefore indirect methods were used. Dimenhydrinate was chosen as model drug; this is a heat-sensitive antihistamine with a low melting point. This temperature can be reached during the tableting process. The behaviour of samples on exposure to heat was examined by differential scanning calorimetry. The water uptakes of the samples were determined with an Enslin apparatus. Plasticity was studied with an instrumented tablet machine. These indirect methods (thermal conductivity, water uptake and plasticity measurements) revealed connections between the results of the various experiments. An overlong coating time decreased the protective effect of the coating film. This revised version was published online in August 2006 with corrections to the Cover Date.     

Convexity of Domains of Riemannian Manifolds

In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy.     

Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Quantum chaos and fractals with atoms in cavities

We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning |δ|1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of |δ| to be equal to |αp₀|, is found numerically and described analytically (with α to be the normalized recoil frequency and p₀ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion z_out, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion z_in that the probability of detecting any value of z_out in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.     

Remarks on exact controllability for Stokes and Navier–Stokes systems

This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Extraction-ability and -selectivity of tetra-aza-crown ethers for transition metal cations

In order to investigate the relative effects of the differences between the structures and lipophilicities of 1, 10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TA-18-crown-6) and the tetrabenzyl derivative of 1,10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TBTA-18-crown-6) on their extraction-abilities and -selectivities for transition metal cations, constants of the overall extraction (logK _ex) of 1:1 (M:L) complexes, the distribution (K _D) for two diluents (CH₂Cl₂ and CHCl₃) with different dielectric constants have been determined at 25 ± 0.1 °C. The magnitude of logK _ex is largely determined by that of K _D. The equilibrium constants of TA-18-crown-6 have been compared with those of TBTA-18-crown-6. It is found that:(i) logK _ex sequences of TA-18-crown-6 and TBTA-18-crown-6 for transition metals in CH₂Cl₂ lie in order: Fe³⁺ > Cu²⁺ > Mn²⁺ > Co²⁺ > Cd²⁺ > Ni²⁺ > Zn²⁺ and Fe³⁺ > Cu²⁺ > Co²⁺ > Mn²⁺ > Ni²⁺ > Cd²⁺ > Zn²⁺ respectively; (ii) the stability sequences of two types of tetra-aza-crown ethers with the transition metal cations in CHCl₃ are the same as follows: Fe³⁺ > Ni²⁺ > Cu²⁺ > Co²⁺ > Zn²⁺ > Cd²⁺ > Mn²⁺, and (iii) unusual selectivities are observed for transition metal-tetra-aza-crowns, e.g. the high Fe³⁺/M ⁿ⁺ selectivity factors (S_f) of TA-18-crown-6, except for the competitive-extractions for the special case in CHCl₃ of TBTA-18-crown-6, it was found that the Mn²⁺/M ⁿ⁺ values were relatively higher according to the other transition metal cations. A systematic sequence in these two types of solvents is not found for a given transition metal cation in terms of the variation of selectivity with the tetra-aza-crown ethers. The results provide alternatives for the rational design of other specific ligands on the transition metal cations.     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.