H?lder metric regularity of set-valued maps

This paper is devoted to metric regularity of set-valued maps from a complete metric space to a Banach space. In particular we extend a known characterization of the regularity modulus to maps defined on reflexive spaces. The higher order metric regularity, i.e. an extension of metric regularity to H?lder context, is also investigated using high order variations of set-valued maps and results of similar nature are obtained for conical metric regularity.     

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆(picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃](C₃H₅N₂)₃ ⋅ 3H₂O series (Ln=Ce–Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.     

Study of the O-glycidylation of natural phenolic compounds. The relationship between the phenolic structure and the reaction mechanism

The O-alkylation reaction by epichlorohydrin of some natural phenolic compounds such as 4-methylcatechol, gallic acid, protocatechuic acid, pyrogallol and resorcinol was investigated. Phenolic compounds reacted first with epichlorohydrin in the presence of benzyltriethylammonium chloride as phase transfer catalyst. Then, an aqueous solution of sodium hydroxide was added.It was demonstrated that the two competitive mechanisms involved in the O-alkylation reaction were highly dependent of the starting material. The O-alkylated products obtained in this reaction could be further used as bisphenol A substitutes in the synthesis of epoxy resins pre-polymers.     

The Radical Formula for Noncommutative Rings

Ukrainian Mathematical Journal - We determine some classes of left modules satisfying the radical formula in a noncommutative ring. We also show that, under a certain condition, a finitely...     

Purification of a 166mHo solution by successive high-performance liquid chromatography and gravitational chromatography for half-life determination

A methodology to purify a ^166mHo solution has been developed by a combination of activity and mass concentration measurements in order to further determine the ^166mHo half-life. The isobaric interference at m/q ? 166 requires Ho purification from non-natural Er with a high purification degree due to the large amount of Ho as opposed to Er. The Ho/Er separation was achieved using high-performance liquid chromatography on a semi-preparative column followed by purification on gravitational chromatography. The efficiency of the separation was evaluated after precise determination of the Er isotopic composition. The purification methodology enabled to separate Ho from Er.