Numerical evaluation of analytic functions by Cauchy's theorem

The use of the Cauchy theorem (instead of the Cauchy formula) in complex analysis together with numerical integration rules is proposed for the computation of analytic functions and their derivatives inside a closed contour from boundary data for the analytic function only. This approach permits a dramatical increase of the accuracy of the numerical results for points near the contour. Several theoretical results about this method are proved. Related numerical results are also displayed. The present method together with the trapezoidal quadrature rule on a circular contour is investigated from a theoretical point of view (including error bounds and corresponding asymptotic estimates), compared with the numerically competitive Lyness-Delves method and rederived by using the Theotokoglou results on the error term. Generalizations for the present method are suggested in brief.     

Adsorption and dissociation of O2 on Pt-Co and Pt-Fe alloys

Self-consistent periodic density functional theory calculations (GGA-PW91) have been performed to study the adsorption of O and O(2) and the dissociation of O(2) on the (111) facets of ordered Pt(3)Co and Pt(3)Fe alloys and on monolayer Pt skins covering these two alloys. Results are compared with those obtained on two Pt(111) surfaces, one at the equilibrium lattice constant and the other laterally compressed by 2% to match the strain in the Pt alloys. The absolute magnitudes of the binding energies of O and O(2) follow the same order in the two alloy systems: Pt skin < compressed Pt(111) < Pt(111) < Pt(3)Co(111) or Pt(3)Fe(111). The reduced activity of the compressed Pt(111) and Pt skins for oxygen can be rationalized as being due to the shifting of the d-band center increasingly away from the Fermi level. We propose that an alleviation of poisoning by O and enhanced rates for reactions involving O may be some of the reasons why Pt skins are more active for the oxygen reduction reaction in low-temperature fuel cells. Finally, a linear correlation between the transition-state and final-state energies of O(2) dissociation on monometallic and bimetallic surfaces is revealed, pointing to a simple way to screen for improved cathode catalysts.     

Extension Principles for Dual Multiwavelet Frames of $$L_2(\mathbb {R}^s)$$ constructed from Multirefinable Generators

In this work we prove that any pair of homogeneous dual multiwavelet frames of \(L_2(\mathbb {R}^s)\) constructed from a pair of refinable function vectors gives rise to a pair of nonhomogeneous dual multiwavelet frames and vice versa. We also prove that the Mixed Oblique Extension Principle characterizes dual multiwavelet frames. Our results extend recent characterizations of affine dual frames derived from scalar refinable functions obtained in [3].     

The collapse transition of poly(styrene-b-(N-isopropyl acrylamide)) diblock copolymers in aqueous solution and in thin films

The thermal behavior of a poly(styrene-b-N-isopropyl acrylamide) diblock copolymer was studied in aqueous solution as well as in thick and in thin films. The polymer was synthesized using reversible addition–fragmentation chain transfer. The critical micelle concentration in aqueous solution was determined using fluorescence correlation spectroscopy. The lower critical solution temperature (LCST) of micellar solutions was detected using microcalorimetry and turbidimetry at 31 °C. Using dynamic light scattering, the collapse of the micelles at the LCST as well as their clustering above was observed. These findings were corroborated with small-angle X-ray scattering. In thick films immersed in water, similar findings were made. In a thin film, however, the LCST is depressed and is found at 26–27 °C.