Recurrence formulas for Macdonald polynomials of type <Emphasis Type="Italic">A</Emphasis>

We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero component on the kth fundamental weight. We give the explicit decomposition of any Macdonald polynomial of type A in terms of this basis.     

Inversion of the Pieri formula for Macdonald polynomials

We give the explicit analytic development of Macdonald polynomials in terms of “modified complete” and elementary symmetric functions. These expansions are obtained by inverting the Pieri formula. Specialization yields similar developments for monomial, Jack and Hall-Littlewood symmetric functions.     

Les équations de Hua d'un domaine borné symétrique du type tube

Sans résumé     

Aqueous Electrochemical Reduction of Carbon Dioxide and Carbon Monoxide into Methanol with Cobalt Phthalocyanine

Conversion of CO₂ into valuable molecules is a field of intensive investigation with the aim of developing scalable technologies for making fuels using renewable energy sources. While electrochemical reduction into CO and formate are approaching industrial maturity, a current challenge is obtaining more reduced products like methanol. However, literature on the matter is scarce, and even more for the use of molecular catalysts. Here, we demonstrate that cobalt phthalocyanine, a well‐known catalyst for the electrochemical conversion of CO₂ to CO, can also catalyze the reaction from CO₂ or CO to methanol in aqueous electrolytes at ambient conditions of temperature and pressure. The studies identify formaldehyde as a key intermediate and an unexpected pH effect on selectivity. This paves the way for establishing a sequential process where CO₂ is first converted to CO which is subsequently used as a reactant to produce methanol. Under ideal conditions, the reaction shows a global Faradaic efficiency of 19.5 % and chemical selectivity of 7.5 %.     

Atomic decompositions for tensor products and polynomial spaces

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product , for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X.     

PLA nano- and microparticles for drug delivery: an overview of the methods of preparation

The controlled release of medicaments remains the most convenient way of drug delivery. Therefore, a wide variety of reports can be found in the open literature dealing with drug delivery systems. In particular, the use of nano- and microparticles devices has received special attention during the past two decades. PLA and its copolymers with GA and/or PEG appear as the preferred substrates to fabricate these devices. The methods of fabrication of these particles will be reviewed in this article, describing in detail the experimental variables associated with each one with regard to the influence of them on the performance of the particles as drug carriers. An analysis of the relationship between the method of preparation and the kind of drug to encapsulate is also included. Furthermore, certain issues involved in the addition of other monomeric substrates than lactic acid to the particles formulation as well as novel devices, other than nano- and microparticles, will be discussed in the present work considering the published literature available.     

Jack polynomials and free cumulants

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group.     

Two New Retigerane‐Type Sesterterpenoids from the Lichen Leprocaulon microscopicum

Two new sesterterpenes, 1 and 2 , have been isolated from the lichen Leprocaulon microscopicum. In addition to classic chromatographic methods, a liquid‐liquid chromatography technique, namely centrifugal partition chromatography (CPC) was applied for the purification of compound 2 . The structures were determined by analyses of mass spectrometry and 1D‐ and 2D‐NMR data. The relative configuration of the isolated compounds was assigned on the basis of 2D‐NOESY experiments. The two compounds possess a rare pentacyclic carbon skeleton typical for lichen metabolism, and quite unusual in the vegetal kingdom.