A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

A review of biochars’ potential role in the remediation, revegetation and restoration of contaminated soils

Biochars are biological residues combusted under low oxygen conditions, resulting in a porous, low density carbon rich material. Their large surface areas and cation exchange capacities, determined to a large extent by source materials and pyrolysis temperatures, enables enhanced sorption of both organic and inorganic contaminants to their surfaces, reducing pollutant mobility when amending contaminated soils. Liming effects or release of carbon into soil solution may increase arsenic mobility, whilst low capital but enhanced retention of plant nutrients can restrict revegetation on degraded soils amended only with biochars; the combination of composts, manures and other amendments with biochars could be their most effective deployment to soils requiring stabilisation by revegetation. Specific mechanisms of contaminant-biochar retention and release over time and the environmental impact of biochar amendments on soil organisms remain somewhat unclear but must be investigated to ensure that the management of environmental pollution coincides with ecological sustainability.

[Ga10S16(NC7H9)4]2-: a hybrid supertetrahedral nanocluster

The synthesis and characterisation of a hybrid supertetrahedral nanocluster, [Ga10S16(NC7H9)4]2−, in which the terminal S2− anions have been replaced by covalently bonded amine molecules, is described.