Multiple dual-mode centrifugal partition chromatography, a semi-continuous development mode for routine laboratory-scale purifications

Nowadays, centrifugal partition chromatography (CPC) separations can be routinely achieved at the laboratory scale. The solvent system selection has been made easy, as generic sets of solvent systems are described in publications and books. This approach, however, generally reduces the scope of optimization strategies for two important parameters: selectivity and sample solubility. This can be very limiting for the preparative separation of structurally similar compounds. Multiple dual-mode (MDM) CPC has been developed to provide an easy-to-use alternative technique to circumvent this problem. A MDM separation consists of a succession of dual-mode runs (i.e. multiple inversion of stationary and mobile phase) that can only be achieved because both chromatographic phases are liquids. This original elution mode is thus a semi-continuous process with a classical sample injection and which only requires a single CPC column. Underlying mechanisms of MDM were studied using a model mixture of acenaphthylene and naphthalene. A mixture of two synthetic pairs of diastereomers was then successfully submitted to MDM CPC, in the framework of the synthesis of biologically active compounds.     

Distribution modulo 1 of a linear sequence associated to a multiplicative function evaluated at polynomial arguments

In two previous papers,the first named author jointly with Florian Luca and Henryk Iwaniec,have studied the distribution modulo 1 of sequences which have linear growth and are mean values of multiplicative functions on the set of all the integers.In this note,we give a first result concerning sequences with linear growth associated to the mean values of multiplicative functions on a set of polynomial values,proving the density modulo 1 of the sequencem[∑((m2+1))(m2+1)(m≤n)]n.This result is but an illustration of the theme which is currently being developed in the PhD thesis of the second named author.     

7373170279850

We conjecture that 7,373,170,279,850 is the largest integer which cannot be expressed as the sum of four nonnegative integral cubes.

     

Computation of the Distribution of the Maximum of Stationary Gaussian Processes

To test the presence of signal in a “signal plus noise” model, the maximum of the observation is a good statistic. To compute threshold or power, it is necessary to compute the distribution of this statistic under a stationary model. Unfortunately, no general theoretical solutions exist. The paper presents a numerical solution in the case of stationary Gaussian processes on the real line with differentiable sample paths. It is based on the so called “Record method” followed by quasi Monte Carlo integration. An explicit evaluation of the error, which is new is given. Our method applies also, of course, to random sequences and provides some lower bound of the tail for processes with non differentiable paths. Some examples are given at the end that concern both continuous and discrete time cases.     

Synthesis of s-triazolo[4,3-b]pyridazine C-nucleosides

A one step synthesis of s-triazolo[4,3-b]pyridazine using 3-chloro-6-hydrazinopyridazine and an appropriate thioformimidate is described. Applying this procedure to 5-O-benzoyl-1-benzylthio-1-formimidate-D-ribofuranose, 5′ benzoyl-6-chloro-3β-D-ribofuranosyl-s-triazolo[4,3-b]pyridazine was obtained. Substitutions of chlorine by nucleophilic reagents afforded some derivatives of a new series of C-nucleo-sides. Structural determination including anomeric configuration assignment is discussed based mainly on ¹H nmr spectroscopy.     

Numerical simulations of gas-particle flows with combustion

This work is devoted to the numerical modelling of a reactive gas-particle flow that arises in internal ballistic. The model, proposed by Gough [2], takes into account complex physical phenomena such as mass transfer, drag force or intra granular stress. A non-conservative finite volume approach adapted from [11] is applied in order to simulate the model. After an academic validation test case of the scheme, the combustion propagation ignited by a cylindrical perforated primer is then simulated and compared with experiments.