Ligand tethering by ion-exchange for the immobilization of homogeneous catalysts

A Rh phosphine complex, derived from the Wilkinson’s catalyst, has been immobilized by ion-exchange on the ammonium form of a Al-MCM-41 sample. Ammonium ions have been exchanged by cholamine ions, which act as an amine ligand, and then the Wilkinson’s catalyst has been immobilized by substitution of a phosphine ligand by the anchored amine. This is a novel immobilization procedure, as a ligand, instead of the whole complex, is tethered to the support by ion exchange. The obtained hybrid catalyst has been characterized by Elemental Analysis, DRIFTS and XPS. The quantitative exchange of ammonium by cholamine and coordination of Rh to amines has been observed. Most of the anchored Rh is considered to be coordinated to the ligand tethered to the support and a small proportion seems to be interacting with the protonated ligand or with the support surface. The catalyst has been tested in the hydrogenation of cyclohexene and in the hydroformylation of 1-octene. In the first case the catalyst is active and reusable, while a strong Rh leaching takes place in the second one.

Growing Neural Gas approach for obtaining homogeneous maps by restricting the insertion of new nodes

The Growing Neural Gas model is used widely in artificial neural networks. However, its application is limited in some contexts by the proliferation of nodes in dense areas of the input space. In this study, we introduce some modifications to address this problem by imposing three restrictions on the insertion of new nodes. Each restriction aims to maintain the homogeneous values of selected criteria. One criterion is related to the square error of classification and an alternative approach is proposed for avoiding additional computational costs. Three parameters are added that allow the regulation of the restriction criteria. The resulting algorithm allows models to be obtained that suit specific needs by specifying meaningful parameters.

Preparation of homogeneous CNT coatings in insulating capillary tubes by an innovative electrochemically-assisted method

Preparation of homogeneous CNT coatings in insulating silica capillary tubes is carried out by an innovative electrochemically-assisted method in which the driving force for the deposition is the change in pH inside the confined space between the inner electrode and the capillary walls. This method represents a great advancement in the development of CNT coatings following a simple, cost-effective methodology.

An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.