Synthesis and characterization of an MRI Gd‐based probe designed to target the translocator protein

DPA‐713 is the lead compound of a recently reported pyrazolo[1,5‐a]pyrimidineacetamide series, targeting the translocator protein (TSPO 18 kDa), and as such, this structure, as well as closely related derivatives, have been already successfully used as positron emission tomography radioligands. On the basis of the pharmacological core of this ligands series, a new magnetic resonance imaging probe, coded DPA‐C₆‐(Gd)DOTAMA was designed and successfully synthesized in six steps and 13% overall yield from DPA‐713. The Gd‐DOTA monoamide cage (DOTA = 1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetic acid) represents the magnetic resonance imaging reporter, which is spaced from the phenylpyrazolo[1,5‐a]pyrimidineacetamide moiety (DPA‐713 motif) by a six carbon‐atom chain. DPA‐C₆‐(Gd)DOTAMA relaxometric characterization showed the typical behavior of a small‐sized molecule (relaxivity value: 6.02 mM^?1 s^?1 at 20 MHz). The good hydrophilicity of the metal chelate makes DPA‐C₆‐(Gd)DOTAMA soluble in water, affecting thus its biodistribution with respect to the parent lipophilic DPA‐713 molecule. For this reason, it was deemed of interest to load the probe to a large carrier in order to increase its residence lifetime in blood. Whereas DPA‐C₆‐(Gd)DOTAMA binds to serum albumin with a low affinity constant, it can be entrapped into liposomes (both in the membrane and in the inner aqueous cavity). The stability of the supramolecular adduct formed by the Gd‐complex and liposomes was assessed by a competition test with albumin. Copyright © 2013 John Wiley & Sons, Ltd.     

Preparation of Chiral Amino Esters by Asymmetric Phase‐Transfer Catalyzed Alkylations of Schiff Bases in a Ball Mill

The asymmetric alkylation of Schiff bases under basic conditions in a ball mill was performed. The starting Schiff bases of glycine were prepared beforehand by milling protected glycine hydrochloride and benzophenone imine, in the absence of solvent. The Schiff base was then reacted with a halogenated derivative in a ball mill in the presence of KOH. By adding a chiral ammonium salt derived from cinchonidine, the reaction proceeded asymmetrically under phase‐transfer catalysis conditions, giving excellent yields and enantiomeric excesses up to 75 %. Because an equimolar amount of starting material was used, purification was greatly simplified.     

A thermostated coupled apparatus for the simultaneous determination of adsorption isotherms and differential enthalpies of adsorption at high pressure and high temperature

In order to assess and improve the quality of high pressure and temperature adsorption isotherms and differential enthalpies of adsorption on microporous and mesoporous materials, a specific thermostated device comprising a differential heat flow calorimeter coupled with a home-built manometric system has been built. The differential heat flow calorimeter is a Tian Calvet Setaram C80 model which can be operated isothermally, the manometric system is a stainless steel homemade apparatus. The thermostated coupled apparatus allows measurements for pressure up to 2.5?MPa and temperature from 303 to 423?K. Reliability and reproducibility were established by measuring adsorption isotherms on a benchmark sorbent (Filtrasorb F400). A detailed experimental study of the adsorption of pure carbon dioxide and methane has been made on activated carbons (Filtrasorb F400 and EcoSorb); a new procedure for determining the differential enthalpies of adsorption based on the stepwise method is also proposed. The error in the determination of the amount adsorbed is about 3.6%, and the error in the determination of the differential enthalpies of adsorption is 4%.     

Broadband excitation pulses for high‐field solid‐state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses (“hard pulses”) are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid‐state samples under magic‐angle‐spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting ¹³C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer. Copyright © 2012 John Wiley & Sons, Ltd.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions

In this paper, a new class of Runge–Kutta methods is introduced. Some basic properties of this subgroup of algebraically stable methods are presented and a complete parametric representation is given. Necessary and sufficient order conditions for lower order methods as well as sufficient order conditions for higher order methods are derived yielding a significantly reduced number of conditions when compared with general Runge–Kutta methods. Design examples conclude this paper.     

Amplitude des oscillations d'ondes solitaires généralisées

Various physical systems of dispersive waves admit solutions in the form of generalized solitary waves. Such waves result from the resonance between a long localized wave and short periodic oscillations. Many estimates (rigorous and numerical) have been given for the amplitude of the ripples in the tail of the generalized solitary wave when its central part has a sech² shape. This Note provides estimates (not yet rigorous) for the ripple amplitude when the central part is flat and wide. To cite this article: C. Fochesato, F. Dias, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Time-Ordering and a Generalized Magnus Expansion

Both the classical time-ordering and the Magnus expansion are well known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including, however, directly a non-trivial initial condition. As a by-product we recover a variant of the time-ordering operation, known as ${\mathsf{T}^\ast}$ -ordering. Eventually, placing our results in the general context of Rota–Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations.