A variational approach of the rank function

In the same spirit as the one of the paper (Hiriart-Urruty and Malick in J. Optim. Theory Appl. 153(3):551–577, 2012) on positive semidefinite matrices, we survey several useful properties of the rank function (of a matrix) and add some new ones. Since the so-called rank minimization problems are the subject of intense studies, we adopt the viewpoint of variational analysis, that is the one considering all the properties useful for optimizing, approximating or regularizing the rank function.     

A fluorescent assay for chloride transport; identification of a synthetic anionophore with improved activity

A fluorescent assay based on the chloride-sensitive probe, lucigenin, is developed for monitoring chloride transport into vesicles, and used to compare the effectiveness of three steroid-derived transporters.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.     

On defect groups for generalized blocks of the symmetric group

In a paper of 2003, Külshammer, Olsson and Robinson defined-blocks for the symmetric groups, where >1 is an arbitraryinteger. In this paper, we give a definition for the defectgroup of the principal -block. We then check that, in the Abeliancase, we have an analogue of one of Broué's conjectures.     

Framework functionalisation triggers metal complex binding

Post-synthetic derivatisation of a porous material produces a functionalized material that binds the metal complex V(O)acac2, in contrast to the unfunctionalized precursor, which is inactive for complex binding.     

Structure-activity relationships in cholapod anion carriers: enhanced transmembrane chloride transport through substituent tuning

Chloride transport by a series of steroid-based "cholapod" receptors/carriers was studied in vesicles. The principal method involved preincorporation of the cholapods in the vesicle membranes, and the use of lucigenin fluorescence quenching to detect inward-transported Cl-. The results showed a partial correlation between anion affinity and transport activity, in that changes at the steroidal 7 and 12 positions affected both properties in concert. However, changes at the steroidal 3-position yielded irregular effects. Among the new steroids investigated the bis-p-nitrophenylthiourea 3 showed unprecedented activity, giving measurable transport through membranes with a transporter/lipid ratio of 1:250 000 (an average of <2 transporter molecules per vesicle). Increasing transporter lipophilicity had no effect, and positively charged steroids had low activity. The p-nitrophenyl monourea 25 showed modest but significant activity. Measurements using a second method, requiring the addition of transporters to preformed vesicle suspensions, implied that transporter delivery was problematic in some cases. A series of measurements employing membranes of different thicknesses provided further evidence that the cholapods act as mobile anion carriers.     

A microfluidic device based on droplet storage for screening solubility diagrams

This work describes a new microfluidic device developed for the rapid screening of solubility diagrams. In several parallel channels, hundreds of nanolitre volume droplets of a given solution are first stored with a gradual variation in the solute concentration. Then, the application of a temperature gradient along these channels enables us to read directly and quantitatively phase diagrams, concentration vs. temperature. We show, using a solution of adipic acid, that we can measure ten points of the solubility curve in less than 1 hr and with only 250 microL of solution.