Fisher-Hartwig asymptotics refers to the large n form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the o...

The paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfi...

Optical sensing of palladium ions has attracted considerable attention due to their serious environmental and health problems. Water resources, soil, dust and natural ora have been contaminated by increased palladium emissions which are caused by a wide spectrum of applications such as the electrical and electronic industries, catalytic converters, dental appliances, fuel cells and jewellery. ...