Special functions and systems in Hermitian Clifford analysis: Higher codimension

In this paper, we investigate a Cauchy–Kowalevski (CK) extension problem that arises naturally within the framework of Hermitian Clifford analysis, which concerns the study of Dirac‐like operators in several complex variables. The work presented here includes CK extensions of higher codimension and in particular the CK extension of the Gauss distribution in several complex variables. Copyright © 2013 John Wiley & Sons, Ltd.     

Tools for Malliavin Calculus in UMD Banach Spaces

In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called umd property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizations, a chain rule for Lipschitz functions, a sufficient condition for pathwise continuity and an Itô formula for non-adapted processes.     

Evaluation of Water-in-Crude-Oil Emulsion Stability Using Critical Electric Field: Effect of Emulsion Preparation Procedure and Crude Oil Properties

The critical electrical field has been used as a tool to probe water in crude emulsion stability to electrical fields in many previous studies. Given the increasing importance of this metric, this study investigates factors that are important to the reproducibility of the measurement and the effect of emulsion preparation variables on the critical electric field. It was observed that the emulsion preparation procedure has a strong effect on the measured critical electric field due to droplet size effects. Furthermore, the effect of crude oil properties on the critical electric field was investigated using emulsions from different oils but with the same average droplet diameter, where it was found that the measurement was dominated by crude oil viscosity.     

Liquid Chromatographic Determination of Cationic Surfactants in Environmental Samples using a Continuous Post-Column Ion-Pair Extraction Detector with a Sandwich Phase Separator

Abstract

A new detection technique is described for the quantitative analysis of cationic surfactants by HPLC via post-column ion-pair formation. A new sandwich type phase separator, as part of the extraction detector, was successfully introduced. The method was used to determine ditallowdimethylammonium chloride (DTDMAC) in various environmental samples. Detection limits of DTDMAC in river water were about 2 μg/1 (60 ng absolute; S/N = 5) and 10 ng/1 (260 pg absolute; S/N = 5), using methyl orange and 9,10-dimethoxyanthracene-2-sulphonate (DAS) as ion-pairing reagents, respectively. The environmental concentration of DTDMAC found on random samples from two Belgian rivers range from 30 to 40 μg/1. The reproducibility of the determination of DTDMAC in river water was 4.2% (RSD) (n = 20).     

The Class of Clifford-Fourier Transforms

Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical Fourier transform. This is applied to the so-called Clifford-Fourier transform (see Brackx et al., J. Fourier Anal. Appl. 11:669–681, 2005). The integral kernel of this transform is a particular solution of a system of PDEs in a Clifford algebra, but is, contrary to the classical Fourier transform, not the unique solution. Here we determine an entire class of solutions of this system of PDEs, under certain constraints. For each solution, series expressions in terms of Gegenbauer polynomials and Bessel functions are obtained. This allows to compute explicitly the eigenvalues of the associated integral transforms. In the even-dimensional case, this also yields the inverse transform for each of the solutions. Finally, several properties of the entire class of solutions are proven.     

Wetting of a self-assembled 1,4-benzenedimethanethiol monolayer on gold and silver: An adhesion force spectroscopy study

Using atomic force microscopy we investigated how local capillary phenomena are affected by the deposition of a self-assembled 1,4-benzenedimethanethiol (BDMT) layer on epitaxially grown Au(1 1 1) and Ag(1 1 1) films. Force-distance curves monitored at varying relative humidity show clear differences in the adhesion forces on the different samples, which can be explained in terms of a change in the wetting behavior due to the presence of the molecules. Moreover, we found that not only the chemical structure of the molecules but also their orientation strongly influences the strength of the capillary forces. A detailed analysis of the measurements shows that condensation of water vapor on Au(1 1 1) films is drastically enhanced due to the vertically aligned BDMT molecules, while on Ag(1 1 1) water condensation is reduced due to a parallel molecule orientation.     

Ruthenium complexes bearing bidentate Schiff base ligands as efficient catalysts for organic and polymer syntheses

A concise overview is given on mononuclear and dinuclear, bidentate Schiff base ruthenium complexes with different additional ligands and on their applications in various chemical transformations such as Kharasch addition, enol-ester synthesis, alkyne dimerization, olefin metathesis and atom transfer radical polymerization. These new ruthenium complexes, conveniently prepared from commonly available ruthenium compounds, are very stable, exhibit a good tolerance towards organic functionalities, air and moisture and display high activity and chemoselectivity in chemical transformations. Relevant features of coordination chemistry connected with the reaction mechanism and chemoselectivity are also fully described. Since the nature of Schiff bases can be changed in a variety of ways, appealing routes for designing and preparing novel ruthenium complexes can be foreseen in the future.     

The relationship between nanoscale architecture and function in photovoltaic multichromophoric arrays as visualized by Kelvin probe force microscopy

The physicochemical properties of organic (multi)component films for optoelectronic applications depend on both the mesoscopic and nanoscale architectures within the semiconducting material. Two main classes of semiconducting materials are commonly used: polymers and (liquid) crystals of small aromatic molecules. Whereas polymers (e.g., polyphenylenevinylenes and polythiophenes) are easy to process in solution in thin and uniform layers, small molecules can form highly defined (liquid) crystals featuring high charge mobilities. Herein, we combine the two material types by employing structurally well-defined polyisocyanopeptide polymers as scaffolds to precisely arrange thousands of electron-accepting molecules, namely, perylenebis(dicarboximides) (PDIs), in defined chromophoric wires with lengths of hundreds of nanometers. The polymer backbone enforces high control over the spatial location of PDI dyes, favoring both enhanced exciton and charge transfer. When blended with an electron-donor system such as regioregular poly(3-hexylthiophene), this polymeric PDI shows a relative improvement in charge generation and diffusion with respect to monomeric, aggregated PDI. In order to correlate this enhanced behavior with respect to the architecture, atomic force microscopy investigations on the mixtures were carried out. These studies revealed that the two polymers form interpenetrated bundles having a nanophase-segregated character and featuring a high density of contact points between the two different phases. In order to visualize the relationship between the architecture and the photovoltaic efficiency, Kelvin probe force microscopy measurements were carried out on submonolayer-thick films. This technique allowed for the first time the direct visualization of the photovoltaic activity occurring in such a nanoscale phase-segregated ultrathin film with true nanoscale spatial resolution, thus making possible a study of the correlation between function and architecture with nanoscale resolution.     

Light‐Driven Rotary Molecular Motors on Gold Nanoparticles

We report the synthesis of unidirectional light‐driven rotary molecular motors based on chiral overcrowded alkenes and their immobilisation on the surface of gold nanoparticles through two anchors. Using a combination of ¹H and ¹³C NMR, UV/Vis and CD spectroscopy, we show that these motors preserve their photochemical and thermal behaviour after they have been attached to gold nanoparticles. Furthermore, we describe the synthesis of ²H‐ and ¹³C‐labelled derivatives that were used to verify the unidirectionality of the rotary cycle of these motors both in solution and while grafted to gold nanoparticles. Taken together, these data support the conclusion that these motors maintain their unidirectional rotary cycle when grafted to the surface of small (ca. 2 nm) gold nanoparticles. Thus, continuous irradiation of the system under appropriate conditions leads to unidirectional rotation of the upper half of the molecules relative to the entire nanoparticle.