Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Local radial Phragmén-Lindelöf estimates for plurisubharmonic functions on analytic varieties

We give a sufficient condition for a local radial Phragmén-Lindelöf principle on analytic varieties. This condition is expressed in terms of existence of hyperbolic directions.

     

Two-dimensional phase unwrapping using a minimum spanning treealgorithm

Phase unwrapping refers to the determination of phase from modulo 2pi data, some of which may not be reliable. In 2D, this is equivalent to confining the support of the phase function to one or more arbitrarily shaped regions. A phase unwrapping algorithm is presented which works for 2D data known only within a set of nonconnected regions with possibly nonconvex boundaries. The algorithm includes the following steps: segmentation to identify connectivity, phase unwrapping within each segment using a Taylor series expansion, phase unwrapping between disconnected segments along an optimum path, and filling of phase information voids. The optimum path for intersegment unwrapping is determined by a minimum spanning tree algorithm. Although the algorithm is applicable to any 2D data, the main application addressed is magnetic resonance imaging (MRI) where phase maps are useful.     

Comparative study of the specific heat of superconducting and non-superconducting YBa2Cu3O7−x

We have measured the specific heat, the electrical resistance and the magnetic susceptibility of YBa₂Cu₃O_7–x in a superconducting (sc) and in a non-superconducting (nsc) version. The latter was obtained by inducing a small loss of oxygen. In the sc sample we find a jump of the specific heat with C=3.6 J mole^–1 K^–1. Below the maximum nearT _c the specific heat of the sc version drops too fast for an electronic effect alone: there is a cross-over from excess to deficiency already at 0.9T _c . The specific heat of the nsc version shows a change of slope in the temperature range between 70 and 80 K, which indicates the existence of a second specific heat anomaly, which apparently exists independently of that due to the onset of superconductivity and explains at least partially the premature crossover.Alexander von Humboldt fellow. On leave in absence from Centro Atomico Bariloche—CNEA Argentina