On the Exponential Convergence of Spline Approximation Methods for Wiener-Hopf Equations

This paper deals with the study of some new multidimensional operators of fractional calculus. These operators are considered in certain spaces of test and generalized functions. Some mapping properties and product rules are obtained.     

Second-kind integral formulations of the capacitance problem

The standard approach to calculating electrostatic forces and capacitances involves solving a surface integral equation of the first kind. However, discretizations of this problem lead to ill-conditioned linear systems and second-kind integral equations usually solve for the dipole density, which can not be directly related to electrostatic forces. This paper describes a second-kind equation for the monopole or charge density and investigates different discretization schemes for this integral formulation. Numerical experiments, using multipole accelerated matrix–vector multiplications, demonstrate the efficiency and accuracy of the new approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

High-performance single fundamental mode AlGaAs VCSELs with mode-selective mirror reflectivities

We present inverted surface relief vertical-cavity surface-emitting lasers (VCSELs) showing a side-mode suppression ratio above 30 dB up to maximum optical output powers of 6.3 mW and differential quantum efficiencies exceeding 90%. An evaluation of 160 relief devices on a sample incorporating graded layers yields 157 lasers with single-mode output powers of at least 2.9 mW, proving the high effectiveness of the technique despite the comparatively simple manufacture.     

A solid-liquid extraction approach to elucidate the chemical availability of metals in soil and sediment assuming Langmuir isotherm behaviour

In an earlier paper (Anal. Chim. Acta 514 (2004) 137) we claimed that the maximal extractability of a metal from soil or sediment for a user-defined extractant, i.e. the chemical availability in that particular extractant, may be biased as a result of inadequate volume to mass (V/m) ratios. Correcting for that artifact using an implementation of the simple linear isotherm model gave good results although we cautioned the general applicability. In this paper we will theoretically derive the limitations of that approach based on the more general assumption that sorption processes are described by a Langmuir isotherm.NIST reference material 8704 was extracted with 1 mol l⁻¹ NaOAc (adjusted to pH 5) to experimentally verify the applicability of the Langmuir isotherm approach and illustrate the deviations obtained for some metals using the linear isotherm approach. Of the seven metals measured (Cr, Co, Ni, Cu, Zn, Cd, and Ba) only for Cr and Cu severe discrepancies between both approaches were found, which could be traced back to non-linear isotherm behaviour. Moreover, the Langmuir isotherm approach showed that the above mentioned extractability artifact is even more serious than earlier assumed applying the linear isotherm approach.     

Manipulating 2D metal-organic networks via ligand control

High-resolution scanning tunneling microscopy has revealed how ligand control can be successfully employed to eliminate isomeric phases and defects in 2D coordination networks that are self-assembled at a surface support by replacing symmetric dicarboxylato linker ligands to dissymmetric carboxylpyridyl linker ligands.     

QM/MM modelling of oleamide hydrolysis in fatty acid amide hydrolase (FAAH) reveals a new mechanism of nucleophile activation

Fatty acid amide hydrolase (FAAH), a promising target for the treatment of several central and peripheral nervous system disorders, such as anxiety, pain and hypertension, has an unusual catalytic site, and its mechanism has been uncertain; hybrid quantum mechanics/molecular mechanics (QM/MM) calculations reveal a new mechanism of nucleophile activation (involving a Lys-Ser-Ser catalytic triad), with potentially crucial insights for the design of potent and selective inhibitors.     

Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon

We propose interferometric methods capable of measuring either the total angular momentum, or simultaneously measuring the spin and orbital angular momentum of single photons. This development enables the measurement of any angular momentum eigenstate of a single photon. The work allows the investigation of single-photon two-qubit entangled states and has implications for high density information transfer.     

Hierarchical assembly of two-dimensional homochiral nanocavity arrays

We demonstrate the rational design of nanoporous two-dimensional supramolecular structures by the hierarchical assembly of organic molecules and transition metal atoms at surfaces. Single-molecule level observations with scanning tunneling microscopy monitor the successive aufbau of structures with increasing complexity. From the primary components secondary mononuclear chiral complexes are formed, which represent antecedents for tertiary polynuclear metal-organic nanogrids. These nanogrids represent the constituents of the eventually evolving two-dimensional networks comprising homochiral nanocavity arrays. Our findings visualize the evolution of complex matter in an exemplary way: from per se achiral species via chiral intermediates to mesoscale dissymmetric structures.     

cis-Dihydroxylation and epoxidation of alkenes by [Mn(2)O(RCO(2))(2)(tmtacn)(2)]: tailoring the selectivity of a highly H(2)O(2)-efficient catalyst

The carboxylic acid promoted cis-dihydroxylation and epoxidation of alkenes catalyzed by [MnIV2O3(tmtacn)2]2+ 1 employing H2O2 as oxidant is described. The use of carboxylic acids at cocatalytic levels not only is effective in suppressing the inherent catalase activity of 1, but also enables the tuning of the catalyst's selectivity. Spectroscopic studies and X-ray analysis confirm that the control arises from the in situ formation of carboxylate-bridged dinuclear complexes, for example, 2 {[MnIII2O(CCl3CO2)2(tmtacn)2]2+} and 3 {[MnII2(OH)(CCl3CO2)2(tmtacn)2]+}, during catalysis. For the first time, the possibility to tune, through the carboxylate ligands employed, both the selectivity and activity of dinuclear Mn-based catalysts is demonstrated. To our knowledge, the system 1/2,6-dichlorobenzoic acid (up to 2000 turnover numbers for cis-cyclooctanediol) is the most active Os-free cis-dihydroxylation catalyst reported to date.