Distributional versions of littlewood’s Tauberian theorem

We provide several general versions of Littlewood’s Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.     

Phase separation of carboxylic acids on graphite surface at submonolayer regime

Mixing behaviour of solid crystalline monolayers adsorbed onto graphite from different mixtures of undecanoic and dodecanoic acids at submonolayer coverage has been investigated. X-ray diffraction measurements have been collected from a variety of compositions as a function of temperature. An extensive phase separation is found for all the compositions – the scattering patterns characteristic of the pure material crystalline structures being preserved across the entire composition range. The temperature dependence of the monolayer melting points and their depression is also clearly indicative of separation of the two surface components, in clear contrast to that expected if the two carboxylic acids mixed ideally in the monolayer.     

Lanthanide tetrasulfophthalocyanines incorporated to SiO2 gels

The sandwich-type lanthanide phthalocyanines, HLn(Pc)₂, are macrocyclic molecules with important optical properties. New routes are proposed to successfully trap soluble substituted phthalocyanines in SiO₂ materials prepared by the sol-gel method. Specifically, the phthalocyanines studied in this work are lanthanide 2, 9, 16, 23–bistetrasulfophthalocyanines, HLn(TSPc)₂, where Ln = Sm, Eu, Dy and Ho, and they were trapped in silica networks. The design routes to trap and bind the macrocycles into the inorganic matrix pore systems are described here. These considerations show that interesting materials with potential applications in electronic, optics and catalysis can be obtained.     

N1,N1-Diethyl-N2-(2,3,4,6-tetra-O-acetyl-β-d-glucopyranosyl)acet­amidine

The solid-state conformation of the title compound, C₂₀H₃₂N₂O₉, has been determined at 150 K. The pyran­ose ring has a distorted chair conformation. Among the possible conformations of the C—N glycosidic bond, that of the E rotamer is observed and a short intramolecular C_methyl⋯O contact may partly stabilize this conformation. Crystal cohesion is stabilized by an extensive network of weak C—H⋯O hydrogen bonds and close contacts.     

How Many Water Molecules Does it Take to Dissociate HCl?

The potential energy surfaces of the HCl(H₂O)_n (n is the number of water molecules) clusters are systematically explored using density functional theory and high‐level ab initio computations. On the basis of electronic energies, the number of water molecules needed for HCl dissociation is four as reported by some experimental groups. However, this number is five owing to the inclusion of entropic factors. Wiberg bond indices are calculated and analyzed, and the results provide a quadratic correlation and classification of clusters according to the nondissociated, partially dissociated, and fully dissociated character of the H?Cl bond. Our computations show that if temperature is not controlled during the experiment, the values obtained for the dipole moment (or for any measurable property) are susceptible to change, providing a different picture of the number of water molecules needed for HCl dissociation in a nanoscopic droplet.     

Time series interpolation via global optimization of moments fitting

Most time series forecasting methods assume the series has no missing values. When missing values exist, interpolation methods, while filling in the blanks, may substantially modify the statistical pattern of the data, since critical features such as moments and autocorrelations are not necessarily preserved.     

Novel Applications of Raney Nickel/Isopropanol: Efficient System for the Reduction of Organic Compounds

Catalytic hydrogenation of various organic substrates with Raney nickel in isopropanol proceeds under mild conditions of temperature and pressure. Comparison with other catalysts systems evidenced the superiority of Raney nickel/isopropanol.