Letters to the editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chief, Chandler Davis.     

Existence for a degenerate diffusion problem with a nonlinear operator

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed as an example.      

Search of theH particle in antiproton-nuclear interactions

The proposal of hunting theH-particle taking advantage of antiproton annihilation at rest on³He is discussed. The obtained K^* beam should allow one to obtain a flux ofΞ ^? with momentum low enough to optimize the fusion probability (ΞN) to give anH. The experimental apparatus to detectH-events as the only missing mass of the fully reconstructed reaction¯p ³He →KKπ ⁺ H is the OBELIX Spectrometer at LEAR. A detailed Monte Carlo simulation of the overall acceptance of OBELIX for the above reaction is performed. The obtained final rate shows the feasibility of the experiment also in a not dedicated detector like OBELIX.     

Surface characterization of recycled tire rubber to be used in cement paste matrix

The surface modification of tire rubber after treatment with saturated NaOH aqueous solution was investigated by HATR infrared analysis, potentiometric titration, and contact angle measurements. Infrared analysis of the powdered treated rubber showed a decrease in absorption at 1540, 1450, and 1395 cm(-1). This decrease is attributed to the removal of zinc stearate, an additive present in tire formulations that often migrates and diffuses to the surface, resulting in poor adhesion between the rubber and other materials. The potentiometric titration of the suspension of powdered rubber in 0.1 M NaCl showed that more hydrochloric acid was consumed by the untreated rubber, most likely a result of the hyrdrolysis of the zinc stearate to the organic acid. Contact angles of flat tire pieces showed an homogeneity enhancement of the treated rubber surface. The decrease of the zinc stearate on the treated rubber surface explains the improvement in the adhesion of this material to the cement matrix, observed in a previous research. The promising results of this study are a starting point for future research on incorporating rubber particles into cementitious materials as a means of successfully utilizing the vast amounts of tire waste currently in landfills.     

Natural abundance 13C - 13C coupling constants observed via double quantum coherence. Structural elucidation by the one- and the two-dimensional NMR experiements of velloziolone,a new seco-diterpene.

With the help of Natural Abundance ¹³C - ¹³C Coupling Constants, observed via double quantum coherence, the structural determination of VELLOZIOLONE (1), a new diterpene, has been carried out.     

Structural determination of ruthenium-porphyrin complexes relevant to catalytic epoxidation of olefins

A reproducible synthesis of a competent epoxidation catalyst, [Ru(VI)(TPP)(O)2)] (TPP = tetraphenylporphyrin dianion), starting from [Ru(II)(TPP)(CO)L] (L = none or CH3OH), is described. The molecular structure of the complex was determined by using ab initio X-ray powder diffraction (XRPD) methods, and its solution behavior was in detail investigated by NMR techniques such as PGSE (pulsed field gradient spin-echo) measurements. [Ru(IV)(TPP)(OH)]2O, a reported byproduct in the synthesis of [Ru(VI)(TPP)(O)2], was synthesized in a pure form by oxidation of [Ru(II)(TPP)(CO)L] or by a coproportionation reaction of [Ru(VI)(TPP)(O)2] and [Ru(II)(TPP)(CO)L], and its molecular structure was then determined by XRPD analysis. [Ru(VI)(TPP)(O)2] can be reduced by dimethyl sulfoxide or by carbon monoxide to yield [Ru(II)(TPP)(S-DMSO)2] or [Ru(II)(TPP)(CO)(H2O)], respectively. These two species were characterized by conventional single-crystal X-ray diffraction analysis.     

Reactivity of methyl mandelate-Ti(IV)-enediolate: oxidative homocoupling versus aldol and direct Mannich-type syn-diastereoselective condensation

[reaction: see text] Methyl mandelate undergoes quantitative oxidative homocoupling on treatment with TiCl4/amine at room temperature. In the presence of ArCHO, quantitative syn-diastereoselective aldol condensation takes over the dimerization, whereas exclusive Mannich-type syn-diastereoselective reaction is observed in the presence of both ArCHO and PhNH2. The subsequent reactions of the title intermediate do not depend on how it is generated.     

A more convenient and general procedure for O-monobenzylation of diols via stannylenes: a critical reevaluation of the Bu2SnO method

A more consistent, straightforward, and economical protocol for generation of stannylene species and their reaction with BnBr leading to products of O-monobenzylation of diols has been set. It has shown to be specially indicated for substrates bearing vicinal trans 1,2-diol moieties on cyclohexane backbones, which are more resistant to these transformations. Such protocol has been successfully applied to myo-inositol derivatives and acyclic diols.     

Recovery of pyridine from aqueous solution by membrane pervaporation

Three different membranes, based on poly(dimethylsiloxane) (PDMS), cation-exchange material and poly(vinyl alcohol) (PVA) respectively, were tudied for the separation of pyridine-water mixtures by pervaporation. The PDMS membrane was preferentially permeable to pyridine and the other two were selective towards water. Three membranes showed different permeation performance, allowing the application of the technique to the separation of feeds of different composition. The temperature profile of the permeability suggests that it is possible to carry out the operation at an elevated temperature in order to achieve high productivity. A combination of the three types of membranes was designed for the production of anhydrous pyridine from dilute pyridine aqueous solution by pervaporation.