Synthesis and Characterization of Acetone Hydrazones

1‐Isopropylidene‐2‐methylhydrazine ( 1 ), 1‐isopropylidene‐2‐hydroxyethylhydrazine ( 2 ) and 1‐isopropylidene‐2‐formylhydrazine ( 3 ) were synthesized by reaction of the corresponding hydrazine with an excess of acetone in the presence of a drying agent (anhydrous sodium sulfate or barium oxide). All compounds 1 – 3 were characterized by elemental analysis, coupled gas chromatography‐mass spectrometry (GC–MS), multinuclear NMR spectroscopy (¹H, ¹³C and ¹⁵N) and vibrational spectroscopy (infrared and Raman). Compounds 1 and 2 are liquid at room conditions and their density was measured by means of a picnometer, however, (at room conditions) compound 3 is a solid and its crystal density and structure were determined by low temperature X‐ray diffraction techniques (monoclinic, P2₁/n, Z = 4, a = 5.666(1) Å, b = 6.254(1) Å, c = 15.277(4) Å, β = 91.30(2)°, V = 541.2(2) ų). The structure of hydrazone 3 is discussed in detail and compared to that of monoformylhydrazine. Finally, the (gas phase) structure of compound 3 was optimized using DFT calculations (B3LYP/6‐31+G(d, p)) and its NBO charges are reported.     

Geometric Optics and Long Range Scattering¶for One-Dimensional Nonlinear Schrödinger Equations

With the methods of geometric optics used in [2], we provide a new proof of some results of [10], to construct modified wave operators for the one-dimensional cubic Schr?dinger equation. We improve the rate of convergence of the nonlinear solution towards the simplified evolution, and get better control of the loss of regularity in Sobolev spaces. In particular, using the results of [9], we deduce the existence of a modified scattering operator with small data in some Sobolev spaces. We show that in terms of geometric optics, this gives rise to a “random phase shift” at a caustic. Received: 23 May 2000 / Accepted: 8 January 2001     

Large Deviations for Stochastic Volterra Equations in the Plane

We prove a Large Deviation Principle for the family of solutions of Volterra equations in the plane obtained by perturbation of the driving white noise. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof uses the method developped by Azencott for diffusion processes. The main ingredients are exponential inequalities for different classes of two-parameter stochastic integrals; these integrals are related to the representation of the stochastic term in the differential equation as a representable semimatringale.     

Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation

Summary. Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation For p>5 , the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of solutions of the equation, the dynamics of suitably perturbed solitary waves are examined. Among other conclusions, we find that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics. Received March 28, 2000; accepted August 24, 2000 %%Online publication November 15, 2000 Communicated by Thanasis Fokas     

Kemp Elimination Reaction Catalyzed by Electric Fields

The Kemp elimination reaction is the most widely used in the de novo design of new enzymes. The effect of two different kinds of electric fields in the reactions of acetate as a base with benzisoxazole and 5-nitrobenzisoxazole as substrates have been theoretically studied. The effect of the solvent reaction field has been calculated using the SMD continuum model for several solvents; we have shown that solvents inhibit both reactions, the decrease of the reaction rate being larger as far as the dielectric constant is increased. The diminution of the reaction rate is especially remarkable between aprotic organic solvents and protic solvents as water, the electrostatic term of the hydrogen bonds being the main factor for the large inhibitory effect of water. The presence of an external electric field oriented in the direction of the charge transfer (z axis) increases it and, so, the reaction rate. In the reaction of the nitro compound, if the electric field is oriented in an orthogonal direction (x axis) the charge transfer to the NO₂ group is favored and there is a subsequent increase of the reaction rate. However, this increase is smaller than the one produced by the field in the z axis. It is worthwhile mentioning that one of the main effects of external electric fields of intermediate intensity is the reorientation of the reactants. Finally, the implications of our results in the de novo design of enzymes are discussed.     

Host/Guest Interactions and NMR Spectroscopy. A Computer Program for Association Constant Determination

A computer program is presented for the computation of association constants for host/guest compounds based on experimental data obtained from the NMR spectra of samples with different host/guest ratios of known concentration.     

On genus and embeddings of torsion-free nilpotent groups of class two

Summary We study embeddings between torsion-free nilpotent groups having isomorphic localizations. Firstly, we show that for finitely generated torsion-free nilpotent groups of nilpotency class 2, the property of having isomorphicP-localizations (whereP denotes any set of primes) is equivalent to the existence of mutual embeddings of finite index not divisible by any prime inP. We then focus on a certain family Γ of nilpotent groups whose Mislin genera can be identified with quotient sets of ideal class groups in quadratic fields. We show that the multiplication of equivalence classes of groups in Γ induced by the ideal class group structure can be described by means of certain pull-back diagrams reflecting the existence of enough embeddings between members of each Mislin genus. In this sense, the family Γ resembles the family N₀ of infinite, finitely generated nilpotent groups with finite commutator subgroup. We also show that, in further analogy with N₀, two groups in Γ with isomorphic localizations at every prime have isomorphic localizations at every finite set of primes. We supply counterexamples showing that this is not true in general, neither for finitely generated torsion-free nilpotent groups of class 2 nor for torsion-free abelian groups of finite rank. Supported by DGICYT grant PB94-0725 This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag.     

Scattering pour l'équation de Schrödinger en présence d'un potentiel répulsif

We study scattering theory for linear Schrödinger equations, when the reference Hamiltonian is ?Δ?〈x〉^α, in $\text{R}{}^{\mathrm{n}}$, with 0<α?2. The notion of short range perturbative potential is much weaker than for the usual reference Hamiltonian ?Δ. We also consider the case where 〈x〉² is replaced by a general second order polynomial. To cite this article: J.-F. Bony et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Bond relaxation phenomenon and impurity modes frequencies in III–V compounds

In regard with very recent studies which evidence the bond relaxation phenomenon in III–V solid solutions, a new approach is proposed to determine theoretically the isoelectronic impurity modes frequencies. It is based on an embedded molecular unit model which accounts for the relaxation in the neighboring of the substituted atom and so avoids both the single-site and virtual crystal approximations. The results obtained for GaAs in some III–V compounds are compared with the experimental available data.     

Eigenanalysis on a bivariate covariance kernel

Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative distribution function is used. Some bounds for the trace of the kernel and some inequalities for a continuous random variable concerning a function and its derivative are obtained. We also obtain relations to diagonal expansions and canonical correlation analysis and, as a by-product, series of constants for some particular distributions.