Metal-free oxidative self-coupling of aldehydes or alcohols to symmetric carboxylic anhydrides

A metal-free synthesis of symmetrical anhydrides has been developed starting from aldehydes, both aliphatic and aromatic or primary benzylic alcohols. The reaction occurs at room temperature and makes use of trichloroisocyanuric acid (TCCA) as an oxidant providing the desired carboxylic anhydrides in satisfactory yields.     

Influence of inert components on the formation of conducting channels in ion-exchange membranes

In this work, the results of investigation of the influence of inert binder and reinforcing fabric on structural organization and mechanism of current transfer in homogeneous and heterogeneous ion-exchange membranes are presented by theoretical analysis of parameters of the extended three-wire conductivity model. It was established that analogy in reorganization of the current paths takes place in the course of inclusion of the reinforcing fabric in perfluorinated membranes and addition of polyethylene and nylon 6 to ion-exchange resins during preparation of heterogeneous membranes. In comparison with perfluorinated membranes, the essential difference in conducting properties of heterogeneous membranes is the opportunity for the current transfer via the channel filled with equilibrium solution. The size of this channel decreases with increase in the volume fraction of the inert component inside the membrane.     

A solution to the Baer splitting problem

Let be a commutative domain. We prove that an -module is projective if and only if for any torsion module . This answers in the affirmative a question raised by Kaplansky in 1962.

     

Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Efficiency and sustainability assessment for a group of farmers in the Brazilian Amazon

The aim of this paper is to use DEA models to evaluate sustainability in agriculture. Several variables are taken into account and the resulting efficiency is measured by comparison. The performance of family farms is analysed here (variables: farmed area, work force, and production). As agricultural sustainability depends on the maintenance of systems of production for long periods of time, the models were run for the years of 1986 and 2002. Tiered DEA models were used to group farmers in sustainability categories. Non-parametric regression models were used to identify the factors affecting the efficiency measurements. All the results indicate that the majority of the farmers increased their efficiency along the time. These improvements may support the existence of sustainability.     

On Koornwinder classical orthogonal polynomials in two variables

In 1975, Tom Koornwinder studied examples of two variable analogues of the Jacobi polynomials in two variables. Those orthogonal polynomials are eigenfunctions of two commuting and algebraically independent partial differential operators. Some of these examples are well known classical orthogonal polynomials in two variables, such as orthogonal polynomials on the unit ball, on the simplex or the tensor product of Jacobi polynomials in one variable, but the remaining cases are not considered classical by other authors. The definition of classical orthogonal polynomials considered in this work provides a different perspective on the subject. We analyze in detail Koornwinder polynomials and using the Koornwinder tools, new examples of orthogonal polynomials in two variables are given.     

Spaces of idempotent measures of compact metric spaces

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.     

On differential properties for bivariate orthogonal polynomials

In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.