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.     

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.     

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.     

Smart polymeric membranes: pH-induced non-linear changes in pore size

A new kind of synthetic membrane was designed with the capacity to adjust the pore diameter in a wide range of sizes (from 0.8 to 22.3 microns) just by changing the pH of the aqueous medium where it is immersed; in this way it is possible to control externally the pore size of the membrane. A non-linear mathematical model, based on the overlap of the electrical double layers of charged particles, was developed to explain the oscillatory behavior of the pore size when the pH was varied. This model fits correctly this oscillatory behavior. Scanning electron microscope images were obtained in low-vacuum conditions to reduce, as much as possible, possible changes in the external conditions after the immersion in water.     

An extension of the integral test

We identify a class of functions for which an extension of the well known integral test holds, namely, the series is Cesàro summable if and only if the integral is. We also give the corresponding multidimensional results.

     

The microstructure of porous building materials: Study of a cement and lime mortar

Building materials such as cement mortars and concrets present a very broad distribution of pore sizes, from some tenths of angstroms to several micra. This distribution is very important in establishing their macroscopic properties, e.g., vapor adsorption and desorption and moisture transfer. It is, thus, important to develop procedures to analyze the microstructure of these materials in the full range of pore sizes. In the present work, two complementary methods are used for obtaining the pore sizes distribution of a cement and lime mortar, often used as a building coating material. Electron scanning microscopy is used for pore sizes greater than 1250 å, from a sequence of pictures taken with magnifications from 25x to 12500x, for highly polished surfaces. The heterogeneous spatial distribution of pores is discussed, related to the problem of the geometrical reconstitution of porous structure. For pore sizes smaller than 1250 å, adsorption isotherms obtained at 30 C are used. Molecular physical adsorption is supposed to be the dominant adsorption mechanism in a wide range of relative humidities and modeled using the De Boer and Zwikker theory. This is confirmed by a very high correlation coefficient equal to 0.994 for the present case, for values of RH smaller than 80%. Capillary condensation is supposed to become significant at the point where the adsorption curve deviates from the linear behavior as predicted by the De Boer and Zwikker theory, and the Broekhoff and De Boer theory is used for predicting the pore size distribution from the adsorption isotherm,starting from the deviation point andincreasing RH. The results show the pore size distribution between 200 å and 13m.