Weak properties of weighted convolution algebras

Suppose that is a weighted convolution algebra on with the weight normalized so that the corresponding space of measures is the dual space of the space of continuous functions. Suppose that is a continuous nonzero homomorphism, where is also a convolution algebra. If is norm dense in , we show that is (relatively) weak dense in , and we identify the norm closure of with the convergence set for a particular semigroup. When is weak continuous it is enough for to be weak dense in . We also give sufficient conditions and characterizations of weak continuity of . In addition, we show that, for all nonzero in , the sequence converges weak to 0. When is regulated, converges to 0 in norm.

     

Molecular Mixed‐Metal Manganese Oxido Cubanes as Precursors to Heterogeneous Oxygen Evolution Catalysts

Well‐defined mixed‐metal [CoMn₃O₄] and [NiMn₃O₄] cubane complexes were synthesized and used as precursors for heterogeneous oxygen evolution reaction (OER) electrocatalysts. The discrete clusters were dropcasted onto glassy carbon (GC) and indium tin oxide (ITO) electrodes, and the OER activities of the resulting films were evaluated. The catalytic surfaces were analyzed by various techniques to gain insight into the structure‐function relationships of the electrocatalysts’ heterometallic composition. Depending on preparation conditions, the Co‐Mn oxide was found to change metal composition during catalysis, while the Ni–Mn oxides maintained the NiMn₃ ratio. XAS studies provided structural insights indicating that the electrocatalysts are different from the molecular precursors, but that the original NiMn₃O₄ cubane‐like geometry was maintained in the absence of thermal treatment ( 2‐Ni ). In contrast, the thermally generated 3‐Ni develops an oxide‐like extended structure. Both 2‐Ni and 3‐Ni undergo structural changes upon electrolysis, but they do not convert into the same material. The observed structural motifs in these heterogeneous electrocatalysts are reminiscent of the biological oxygen‐evolving complex in Photosystem II, including the MMn₃O₄ cubane moiety. The reported studies demonstrate the use of discrete heterometallic oxide clusters as precursors for heterogeneous water oxidation catalysts of novel composition and the distinct behavior of two sets of mixed metal oxides.     

Palladium-catalysed cross-coupling as a key step in the synthesis of pyridyl-benzamides, -benzylamines and -sulfonamides

Novel N-, O- and S-substituted pyridyl-benzamides, -benzylamines and -sulfonamides were prepared by means of palladium-catalysed cross-coupling reactions. The synthetic approach, using Pd₂(dba)₃ as palladium source and rac-BINAP as supporting ligand, proved to be successful for CN, CO and CS cross-coupling reactions. One of the substrates underwent an unexpected nucleophilic aromatic substitution of fluorine, rather than the expected CN cross-coupling reaction.     

Switching the electrochemical impedance of low-density self-assembled monolayers

Because the active remodeling of biointerfaces is a paramount feature of nature, it is very likely that future, advanced biomaterials will be required to mimic at least certain aspects of the dynamic properties of natural interfaces. This need has fueled a quest for model surfaces that can undergo reversible switching upon application of external stimuli. Herein, we report the synthesis and characterization of a model system for studying reversibly switching surfaces based on low-density monolayers of mercaptohexadecanoic acid and mercaptoundecanoic acid. These monolayers were assembled on both gold and silver electrodes. When conducting electrochemical impedance spectroscopy under physiological conditions, these monolayers exhibit significant changes in their electrochemical barrier properties upon application of electrical DC potentials below +400 mV with respect to a standard calomel electrode. We further found the impedance switching to be reversible under physiological conditions. Moreover, the impedance can be fine-tuned by changing the magnitude of the applied electrical potential. Before and during impedance switching at pH 7.4 in aqueous buffer solutions, the low-density monolayers showed good stability according to grazing angle infrared spectroscopy data. We anticipate low-density monolayers to be potentially useful model surfaces when designing active biointerfaces for cell-based studies or rechargeable biosensors.     

Kinoform optics applied to X‐ray photon correlation spectroscopy

Moderate‐demagnification higher‐order silicon kinoform focusing lenses have been fabricated to facilitate small‐angle X‐ray photon correlation spectroscopy (XPCS) experiments. The geometric properties of such lenses, their focusing performance and their applicability for XPCS measurements are described. It is concluded that one‐dimensional vertical X‐ray focusing via silicon kinoform lenses significantly increases the usable coherent flux from third‐generation storage‐ring light sources for small‐angle XPCS experiments.     

Streak camera crosstalk reduction using a multiple delay optical fiber bundle

The streak camera is one of the fastest photodetection systems, while its capability of multiplexing is particularly attractive to many applications requiring parallel data acquisition. The degree of multiplexing in a streak camera is limited by the crosstalk between input channels. We developed a technique that introducing a fixed time delay between adjacent fiber channels in a customized two-dimensional to one-dimensional fiber array to significantly reduce crosstalk both at the sample plane and at the input of a streak camera. A prototype system has been developed that supports 100 input channels, and its performance in fluorescence microscopy is demonstrated.     

The human heart proteome: Two-dimensional maps using narrow-range immobilised pH gradients

The analysis of complex proteomes is undertaken using a variety of techniques and technologies such as 2-DE, surface-enhanced laser desorption ionisation, and various types of MS. In order to overcome the complexities of protein expression in discrete proteomes, sample fractionation has become an important aspect of proteomic experiments. The use of narrow-range IPGs (nrIPGs) is of special importance using the 2-DE proteomics workflow, since an enhanced visualisation of a given proteome is achieved through an improved physical separation and resolution of proteins. The work described in this paper presents a series of protein maps of the human heart left ventricle proteome that have been generated using nrIPGs for the first, IEF, dimension of 2-DE. A total of 374 gel spots were excised from seven different pH gradients, covering the range pH 3-10, giving rise to a total of 388 identifications from 110 unique proteins. Using Gene Ontologies (GOs), the identified proteins were found to be associated with 97 types of GO Process, 144 types of GO Function, and 54 types of GO Component. It is hoped that the maps presented in this paper will be of use to other researchers for reference purposes.