Enantiomeric resolution of new aromatase inhibitors by liquid chromatography on cellulose chiral stationary phases

Analytical HPLC methods using derivatized cellulose chiral stationary phases were developed for the direct enantioseparation of substituted [1-(imidazo-1-yl)-1-phenylmethyl)]-benzothiazolinone and benzoxazolinone derivatives with one chiral center. Those analogues of fadrozole constitute new potent nonsteroidal inhibitors of aromatase (P450 arom). The separations were made using normal phase methodology with a mobile phase consisting of n-hexane-alcohol (ethanol, 1-propanol, or 2-propanol) in various proportions, and a silica-based cellulose tris-3,5-dimethylphenylcarbamate (Chiralcel OD-H), or tris-methylbenzoate (Chiralcel OJ). The effects of concentration of various aliphatic alcohols in the mobile phase were studied. A better separation was achieved on cellulose carbamate phase compared with the cellulose ester phase. The effects of structural features of the solutes along with the temperature of the column on the discrimination between the enantiomers were examined. Baseline separation (Rs > 1.5) was easily obtained in many cases.     

Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions

We survey the properties of two parameters introduced by C. Ding and the author for quantifying the balancedness of vectorial functions and of their derivatives. We give new results on the distribution of the values of the first parameter when applied to F + L, where F is a fixed function and L ranges over the set of linear functions: we show an upper bound on the nonlinearity of F by means of these values, we determine then the mean of these values and we show that their maximum is a nonlinearity parameter as well, we prove that the variance of these values is directly related to the second parameter. We briefly recall the known constructions of bent vectorial functions and introduce two new classes obtained with Gregor Leander. We show that bent functions can be used to build APN functions by concatenating the outputs of a bent (n, n/2)-function and of some other (n, n/2)-function. We obtain this way a general infinite class of quadratic APN functions. We show that this class contains the APN trinomials and hexanomials introduced in 2008 by L. Budaghyan and the author, and a class of APN functions introduced, in 2008 also, by Bracken et al.; this gives an explanation of the APNness of these functions and allows generalizing them. We also obtain this way the recently found Edel?CPott cubic function. We exhibit a large number of other sub-classes of APN functions. We eventually design with this same method classes of quadratic and non-quadratic differentially 4-uniform functions.     

Synthesis of enantiopure cis- and trans-2,3-disubstituted piperidines

The synthesis of enantiopure cis- and trans-2,3-disubstituted piperidines 4 is described. The key step of the synthesis involves the stereoselective reduction of chiral nonracemic lactams 2 by using BH3.Me2S. A rationalization of the stereoselectivity is presented.     

Lexicographic α-robustness: An alternative to min–max criteria

Robustness in Operations Research/Decision Aid is often associated with min–max and min–max regret criteria. This common approach to determine robust solutions consists in finding a solution which minimizes the maximal cost or regret. Nevertheless, these criteria are known to be too conservative. In this paper, we present and study a new robustness approach, called lexicographic α-robustness, which compensates for this major drawback and many others. Furthermore, we establish a link between lexicographic α-robustness and a third robustness approach called p-robustness.     

Padé–type rational and barycentric interpolation

In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin. Thus, the interpolants constructed in this way possess a Padé–type property at 0. Numerical examples show the interest of the procedure. The interpolation procedure can be easily modified to introduce a partial knowledge on the poles and the zeros of the function to approximated. A strategy for removing the spurious poles is explained. A formula for the error is proved in the real case. Applications are given.     

Bipotentials for Non-monotone Multivalued Operators: Fundamental Results and Applications

This is a survey of recent results about bipotentials representing multivalued operators. The notion of bipotential is based on an extension of Fenchel’s inequality, with several interesting applications related to non-associated constitutive laws in non-smooth mechanics, such as Coulomb frictional contact or non-associated Drücker-Prager model in plasticity.     

Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies

We derive symplectic integrators for a class of highly oscillatory Hamiltonian systems. Our approach is based upon a two-scale expansion of the solution to the Hamilton–Jacobi equation associated to the original dynamics. This Note presents an extension of the approach previously introduced in Le Bris and Legoll (2007, 2010) [10], [11] to the case where the fast frequencies of the system, instead of being constant, explicitly depend on the slow degrees of freedom.     

Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics

This paper is an introduction to the modelling of viscoelastic fluids,with an emphasis on micromacro(or multiscale) models.Some elements of mathematical and numerical analysis are provided.These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop Stress Tensor E?ects on Fluid Mechanics in January 2010.     

H2O2: a Ca2+ or Mg2+‐sensing function in statin passive diffusion

In a previous paper Guillaume's group demonstrated that magnesium (Mg²⁺ concentration range 0.00–2.60 mm ) increased the passive diffusion of statins and thus played a role in their potential toxicity. In order to confirm an increase in this passive diffusion by divalent salt cations, the role of calcium chloride (CaCl₂) on the statin–immobilized artificial membrane (IAM) association was studied. It was demonstrated that calcium supplementation (Ca²⁺ concentration range 0.00–3.25 mm ) increases the statin passive diffusion. In addition, it was shown that the Ca²⁺ effect on the statin–IAM association is higher than that of Mg²⁺. These results show that Ca²⁺ enhances the passive diffusion of drugs into biological membranes and thus their potential toxicity. Also, addition of H₂O₂ to the medium showed a hyperbolic response for the statin passive diffusion and this effect was enhanced for the highest Ca²⁺ or Mg²⁺ concentrations in the medium. H₂O₂ is likely to interact with the polar head groups of the IAM through dipole–dipole interactions. The conformational changes in H₂O₂–IAM result in a higher degree of exposure of hydrophobic areas, thus explaining why the binding of pravastatin, which showed the lowest logP value, was less affected by H₂O₂. This result shows the significant contribution of H₂O₂ and thus the oxidative stress on the statin passive diffusion. Much of the sensitivity derives from the action of Ca²⁺ or Mg²⁺, in turn supported the idea that H₂O₂ may serve a Ca²⁺ or Mg²⁺ sensing function in statin passive diffusion Copyright © 2015 John Wiley & Sons, Ltd.