α,α-Difluorophosphonohydroxamic Acid Derivatives among the Best Antibacterial Fosmidomycin Analogues

Three α,α-difluorophosphonate derivatives of fosmidomycin were synthesized from diethyl 1,1-difluorobut-3-enylphosphonate and were evaluated on Escherichia coli. Two of them are among the best 1-deoxy-d-xylulose 5-phosphate reductoisomerase inhibitors, with IC₅₀ in the nM range, much better than fosmidomycin, the reference compound. They also showed an enhanced antimicrobial activity against E. coli on Petri dishes in comparison with the corresponding phosphates and the non-fluorinated phosphonate.     

A Unifying Local Convergence Result for Newton's Method in Riemannian Manifolds

We consider the problem of finding a singularity of a differentiable vector field X defined on a complete Riemannian manifold. We prove a unified result for theexistence and local uniqueness of the solution, and for the local convergence of a Riemannian version of Newton's method. Our approach relies on Kantorovich's majorant principle: under suitable conditions, we construct an auxiliary scalar equation φ(r) = 0 which dominates the original equation X(p) = 0 in the sense that the Riemannian-Newton method for the latter inherits several features of the real Newton method applied to the former. The majorant φ is derived from an adequate radial parametrization of a Lipschitz-type continuity property of the covariant derivative of X, a technique inspired by the previous work of Zabrejko and Nguen on Newton's method in Banach spaces. We show how different specializations of the main result recover Riemannian versions of Kantorovich's theorem and Smale's α-theorem, and, at least partially, the Euclidean self-concordant theory of Nesterov and Nemirovskii. In the specific case of analytic vector fields, we improve recent developments inthis area by Dedieu et al. . Some Riemannian techniques used here were previously introduced by Ferreira and Svaiter in the context of Kantorovich's theorem for vector fields with Lipschitz continuous covariant derivatives.     

QCD, conformal invariance and the two Pomerons

Using the solution of the BFKL equation including the leading and subleading conformal spin components, we show how the conformal invariance underlying the leading expansion of perturbative QCD leads to elastic amplitudes described by two effective Pomeron singularities. One Pomeron is the well-known “hard” BFKL leading singularity, while the new one appears from a shift of the higher conformal spin BFKL singularities from subleading to leading position. This new effective singularity is compatible with the “soft” Pomeron and thus, together with the “hard” Pomeron, meets at large the “double Pomeron” solution which has recently been conjectured by Donnachie and Landshoff. Received: 8 February 1999 / Revised version: 8 March 1999 / Published online: 18 June 1999     

Some effective solvents for rapid and reliable characterization of phenylthiohydantoin-amino acids

Summary One-dimensional chromatography with internal standards permits reliable identification of the phenylthiohydantoins from all the common amino acids with the following TLC systems: silica gel — chloroform/n-butyl acetate (9010), di-isopropylether/ethanol (955), dichloromethane/ethanol/acetic acid (9082) ortrans-dichloroethylene/ethanol/acetic acid (88102); and cellulose with 25% formic acid — heptane/isobutanol/75% fromic acid (40309) or silica gel — chloroform/ ethanol/acetic acid/water (50470.52.5).Abbreviations: PTH=phenylthiohydantoin, TLC=thin-layer chromatography, HPTLC=high-performance TLC; other abbreviations: see end of text. Proportions in solvent mixtures are v/v except where otherwise indicated.     

Contribution of Kinematical and Thermal Full-field Measurements for Mechanical Properties Identification: Application to High Cycle Fatigue of Steels

The purpose of this work is to extend the use of unconventional tests and full field measurements (kinematical and thermal) to the identification of the effect of a wide plastic pre-strain range on the high cycle fatigue properties of a dual-phase steel. An unconventional specimen is designed. The geometry of this specimen permits a constant gradient of pre-strain to be obtained after a monotonic tensile test. Then, a self-heating test under cyclic loading is carried out on the pre-strained specimen. During this cyclic test, the thermal field is measured using an infrared camera. Finally, a suitable numerical strategy is proposed to identify a given thermal source model taking into account the influence of plastic pre-strain. The results show that, with the unconventional test and the procedure developed in this work, the influence of a plastic pre-strain range on fatigue properties can be identified by using only one specimen when, for a classical fatigue campaign, a great number of specimens is required.     

The gradient and heavy ball with friction dynamical systems: the quasiconvex case

We consider the gradient system $\dot x(t)+\nabla\phi(x(t))=0$ and the so-called heavy ball with friction dynamical system $\ddot x(t) +\lambda\dot x(t)+\nabla\phi(x(t))=0$ , as well as an implicit discrete (proximal) version of it, and study the asymptotic behavior of their solutions in the case of a smooth and quasiconvex objective function Φ. Minimization properties of trajectories are obtained under various additional assumptions. We finally show a minimizing property of the heavy ball method which is not shared by the gradient method: the genericity of the convergence of each trajectory, at least when Φ is a Morse function, towards local minimum of Φ.     

Saturation and BFKL dynamics in the HERA data at small-x

We show that the HERA data for the inclusive structure function F₂(x,Q²) for x10⁻² and 0.045Q²45 GeV² can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x₀ of x at which the saturation scale Q_s equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.     

Diffuse interface model for high speed cavitating underwater systems

High speed underwater systems involve many modelling and simulation difficulties related to shocks, expansion waves and evaporation fronts. Modern propulsion systems like underwater missiles also involve extra difficulties related to non-condensable high speed gas flows. Such flows involve many continuous and discontinuous waves or fronts and the difficulty is to model and compute correctly jump conditions across them, particularly in unsteady regime and in multi-dimensions. To this end a new theory has been built that considers the various transformation fronts as ‘diffuse interfaces’. Inside these diffuse interfaces relaxation effects are solved in order to reproduce the correct jump conditions. For example, an interface separating a compressible non-condensable gas and compressible water is solved as a multiphase mixture where stiff mechanical relaxation effects are solved in order to match the jump conditions of equal pressure and equal normal velocities. When an interface separates a metastable liquid and its vapor, the situation becomes more complex as jump conditions involve pressure, velocity, temperature and entropy jumps. However, the same type of multiphase mixture can be considered in the diffuse interface and stiff velocity, pressure, temperature and Gibbs free energy relaxation are used to reproduce the dynamics of such fronts and corresponding jump conditions. A general model, based on multiphase flow theory is thus built. It involves mixture energy and mixture momentum equations together with mass and volume fraction equations for each phase or constituent. For example, in high velocity flows around underwater missiles, three phases (or constituents) have to be considered: liquid, vapor and propulsion gas products. It results in a flow model with 8 partial differential equations. The model is strictly hyperbolic and involves waves speeds that vary under the degree of metastability. When none of the phase is metastable, the non-monotonic sound speed is recovered. When phase transition occurs, the sound speed decreases and phase transition fronts become expansion waves of the equilibrium system. The model is built on the basis of asymptotic analysis of a hyperbolic total non-equilibrium multiphase flow model, in the limit of stiff mechanical relaxation. Closure relations regarding heat and mass transfer are built under the examination of entropy production. The mixture equation of state (EOS) is based on energy conservation and mechanical equilibrium of the mixture. Pure phases EOS are used in the mixture EOS instead of cubic one in order to prevent loss of hyperbolicity in the spinodal zone of the phase diagram. The corresponding model is able to deal with metastable states without using Van der Waals representation.