Mesomorphic bipyridine building blocks bearing an sp3 carbon and a hydroxy function

The synthesis of novel symmetrical liquid crystalline compounds based on 5-methyl-5-[2-(4-alkyloxyphenyl)-2-hydroxyethyl]-2,2-bipyridines is reported, together with some physical properties. Although the chelating head-groups are connected via a chiral sp³ carbon atom, all the materials are mesomorphic. Intermolecular hydrogen bonding between pyridino and hydroxy fragments in the mesophases is made apparent by FTIR spectroscopy.     

Tuning the Regioselective Functionalization of Trifluoromethylated Dienes via Lanthanum-Mediated Single C−F Bond Activation

The development of new fluorine-containing building blocks and their efficient synthetic access is currently a challenging research field. Herein, the highly regio- and stereoselective addition of a large range of aldehydes onto trifluoromethylated benzofulvenes was achieved using a simple La/I₂/DIBAL-Cl system via a selective C−F bond activation process. This versatile methodology provided homodienyl alcohols bearing a terminal CF₂-alkene with potential further applications, as shown by the dehydration to the first benzofulvenes carrying a difluorovinyl group. In addition, for certain electron-poor aldehydes, unprecedented ipso substitution of the CF₃ group in a diene was observed, which, according to DFT studies, is related to the presence of the large, Lewis-acidic lanthanum metal.     

Porphyrins and Polyoxometalate Scaffolds

Polyoxometalates (POMs) can act as unique reservoirs for multiple electron transfers. As POMs display only weak absorption in the visible spectrum, they can be associated with chromophores such as porphyrins and porphyrin antennae. In this Minireview, the research dedicated to the combination of porphyrins and polyoxometalates is put in context and the state of the art identifying the challenges addressed in the optimization of hybrid materials for applications is detailed.     

Practical Syntheses of Functionalized 1-Oxo-L,2,3,4-Tetrahydro-β-carboline-3-carboxylic Acid Esters

Three methods have been proposed for the preparation of functionalized 1-oxo-1,2,3,4-tetrahydro-β-carboline-3 carboxylates (3) from which the “acylazide formation-Curtius rearrangement-acid catalyzed ring closure” sequence starling from hemi-ester hemi-acids (8) seemed to be quite general.     

Malliavin and Dirichlet structures for independent random variables

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron–Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of $U$-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions.     

An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

Metamorphosis of images in reproducing kernel Hilbert spaces

Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the practical application of metamorphosis is a numerical method based on shooting from the initial momentum, as this would enable the use of statistical methods based on this momentum, as well as the estimation of templates from hyper-templates using morphing. In this paper we introduce a shooting method, in the particular case of morphing images that lie in a reproducing kernel Hilbert space (RKHS). We derive the relevant shooting equations from a Lagrangian frame of reference, present the details of the numerical approach, and illustrate the method through morphing of some simple images.