Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

Structuring reductive media containing protic ionic liquids and their application to the formation of metallic nanoparticles

Herein, we present a facile method for the formation of monodispersed metal nanoparticles (NPs) at room temperature from M^(III)Cl₃ (with M = Au, Ru, Mn, Fe or V) in different media based on N,N-dimethylformamide (DMF) or water solutions containing a protic ionic liquid (PIL), namely the octylammonium formate (denoted OAF) or the bis(2-ethyl-hexyl)ammonium formate (denoted BEHAF). These two PILs present different structures and redox-active structuring properties that influence their interactions with selected molecular compounds (DMF or water), as well as the shape and the size of formed metal NPs in these solutions. Herein, the physical properties, such as the thermal, transport and micellar properties, of investigated PIL solutions were firstly investigated in order to understand the relation between PILs structure and their properties in solutions with DMF or water. The formation of metal NPs in these solutions was then characterized by using UV–vis spectroscopy, transmission electron microscopy (TEM), scanning electron microscopy (SEM) and dynamic light scattering (DLS) measurements. From our investigations, it appears that the PILs structure and their aggregation pathways in selected solvents affect strongly the formation, growths, the shape and the size of metal NPs. In fact by using this approach, the shape-/size-controlled metal NPs can be generated under mild condition. This approach suggests also a wealth of potential for these designer nanomaterials within the biomedical, materials, and catalysis communities by using designer and safer media based on PILs.

Tunable gold nanoparticles shape and size in reductive and structuring media containing protic ionic liquids

Herein, a facile method was developed for preparing high concentration of monodispersed gold nanoparticles (NPs) at room temperature from gold(III) chloride by using different media based on N,N-dimethylformamide or water solutions containing a protic ionic liquid (PIL), namely, the octylammonium formate or the bis(2-ethyl-hexyl)ammonium formate, based on which both PILs were used as redox-active structuring media. The formation of gold NPs in these systems was then characterized using UV-visible spectroscopy, transmission electron microscopy, and dynamic light scattering. From these investigations, it appears that the structure and aggregation pathway of PILs in selected solvents affect strongly the formation, growth, the shape, and the size of gold NPs. In fact, by using this approach, the shape-/ size-controlled gold NPs (branched and spherical) can be generated under mild condition. This approach suggests also a wealth of potential for these designer nanomaterials within the biomedical, materials, and catalysis communities by using designer and safer media based on PILs.

Quantum yield measurements for the photocatalytic oxidation of Acid Orange 7 (AO7) and reduction of 2,6-dichloroindophenol (DCIP) on transparent TiO2 films of various thickness

This work comprises the photoactivity assessment of transparent sol–gel TiO2 coatings of various thickness using two test systems. The initial rates of both photocatalytic reactions, namely the oxidative bleaching of Acid Orange 7 (AO7) and the reductive bleaching of 2,6-dichlorindophenol (DCIP) increase linearly with increasing titania film thickness as well as with increasing absorbed light flux. The latter work revealed quantum yields (QY) of 0.19% and 92% for the AO7 and DCIP test system, respectively. The low QY for the AO7 oxidation is due to the combination of a slow irreversible reduction of oxygen and also for the oxidation of AO7, thus favouring the high efficiency for electron–hole recombination that is typical for aqueous organic pollutants. In contrast, the very high QY for the photocatalysed reduction of DCIP is due to the presence of a vast excess of glycerol which traps the photogenerated holes efficiently and so allow time for the slower reduction of dye to take place. Furthermore, the oxidation of glycerol results in the generation of highly reducing R-hydroxyalkyl radicals that are able to also reduce DCIP. As a consequence of this ‘current doubling’ effect, the observed QY (92%) is much higher than the apparent theoretical value of 50%.

Reductive photocatalysis and smart inks

Semiconductor-sensitised photocatalysis is a well-established and growing area of research, innovation and commercialisation; the latter being mostly limited to the use of TiO2 as the semiconductor. Most of the work on semiconductor photocatalytic systems uses oxygen as the electron acceptor and explores a wide range of electron donors; such systems can be considered to be examples of oxidative photocatalysis, OP. OP underpins most current examples of commercial self-cleaning materials, such as: glass, tiles, concrete, paint and fabrics. OP, and its myriad of applications, have been reviewed extensively over the years both in this journal and elsewhere. However, the ability of TiO2, and other semiconductor sensitisers, to promote reductive photocatalysis, RP, especially of dyes, is significant and, although less well-known, is of growing importance. In such systems, the source of the electrons is some easily oxidised species, such as glycerol. One recent, significant example of a RP process is with respect to photocatalyst activity indicator inks. paiis, which provide a measure of the activity of a photocatalytic film under test via the rate of change of colour of the dye in the ink coating due to irreversible RP. In contrast, by incorporating the semiconductor sensitiser in the ink, rather than outside it, it is possible to create an effective UV dosimeter, based on RP, which can be used as a sun-burn warning indicator. In the above examples the dye is reduced irreversibly, but when the photocatalyst in an ink is used to reversibly photoreduce a dye, a novel, colourimetric oxygen-sensitive indicator ink can be created, which has commercial potential in the food packaging industry. Finally, if no dye is present in the ink, and the semiconductor photocatalyst-loaded ink film coats an easily reduced substrate, such as a metal oxide film, then it can be used to reduce the latter and so, for example, clean up tarnished steel. The above are examples of smart inks, i.e. inks that are active and provide either dynamic information (such as UV dose or O2 level) or a useful function (such as tarnish removal), and all work via a RP process and are reviewed here

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Ionic liquids containing secondary hydroxyl-groups and a method for their preparation.

The invention provides ionic liqs., [R'1CH(OH)CH2]NR'nX (X = anion, R' = alkyl, alkenyl, alkynyl, cycloalkyl, alkylcarbonylalkyl, alkoxy, haloalkyl, haloalkoxy, alkenyloxy, alkynyloxy, cycloalkyloxy, aryl), having a secondary hydroxyl group, and an atom-efficient method for the prepn. of these ionic liqs., by epoxidn. of a protonated nitrogen- contg. org. base (which can optionally be prepd. in situ) in the presence of an anion suitable for supporting ionic liq. formation. Thus, reaction of 1-methylimidazole with HCl in EtOH ∼ 25° followed by treatment with propylene oxide gave 1-(2-hydroxypropyl)-3-methylimidazolium chloride. [on SciFinder(R)]

Targeting of photooxidative damage on single-stranded DNA representing the bcr-abl chimeric gene using oligonucleotide-conjugates containing [Ru(phen)3](2+)-like photosensitiser groups

Photooxidative damage was induced predominantly at a single guanine base in a target DNA by irradiation (lambda > 330 nm) in the presence of complementary oligodeoxynucleotide conjugates (ODN-5'-linker-[Ru(phen)3]2+) (phen = 1,10-phenanthroline). The target DNA represents the b2a2 variant of the chimeric bcr-abl gene implicated in the pathogenesis of chronic myeloid leukaemia, and the sequence of the 17mer ODN component of the conjugate (3' G G T A G T T A T T C C T T C T T 5') was complementary to the junction region of the sense strand sequence of this oncogene. Two different conjugates were prepared, both of them by reaction of the appropriate succinimide ester with 5'-hexylamino-derivatised 17mer ODN. In Ru-ODN-1 (7) the linker was -(CH2)6-NHCO-bpyMe (-bpyMe = 4'-[4-methyl-2,2'-bipyridyl]), whereas in Ru-ODN-2 (13) it was -(CH2)6-NHCO-(CH2)3-CONH-phen. Photoexcitation of either of the conjugates when hybridised with the 32P-5'-end-labelled target 34mer 5'T G A C C A T C A A T A A G G A A G A A G21 C C C T T C A G C G G C C 3' (ODN binding site underlined) led to an alkali-labile site predominantly (> 90%) at the G21 base, which is at the junction of double-stranded and single-stranded regions of the hybrid. Greater yields were found with Ru-ODN-1 (7) than with Ru ODN-2 (13). In contrast to this specific cleavage with Ru-ODN-1 (7) or Ru-ODN-2 (13), alkali-labile sites were generated at all guanines when the 34mer was photolysed in the presence of the free sensitiser [Ru(phen)3]2+. Since [Ru(phen)3]2+ was shown to react with 2'-deoxyguanosine to form the diastereomers of a spiroiminodihydantoin derivative (the product from 1O2 reaction), 1O2 might also be an oxidizing species in the case of Ru-ODN-1 (7) and Ru-ODN-2 (13). Therefore to determine the range of reaction, a series of 'variant' targets was prepared, in which G21 was replaced with a cytosine and a guanine substituted for a base further towards the 3'-end (e.g. Variant 3; 5'T G A C C A T C A A T A A G G A A G A A C C G23 C T T C A G C G G32 C C3'). While it was noted that efficient reaction took place at distances apparently remote from the photosensitiser (e.g at G32, but not G23 for Variant 3), this effect could be attributed to hairpinning of the single-stranded region of the target. These results are therefore consistent with the photooxidative damage being induced by a reaction close to the photosensitiser rather than by a diffusible species such as 1O2.

RMA with quantile normalization mixes biological signals between different sample groups in microarray data analysis

Quantile normalization (QN) is a technique for microarray data processing and is the default normalization method in the Robust Multi-array Average (RMA) procedure, which was primarily designed for analysing gene expression data from Affymetrix arrays. Given the abundance of Affymetrix microarrays and the popularity of the RMA method, it is crucially important that the normalization procedure is applied appropriately. In this study we carried out simulation experiments and also analysed real microarray data to investigate the suitability of RMA when it is applied to dataset with different groups of biological samples. From our experiments, we showed that RMA with QN does not preserve the biological signal included in each group, but rather it would mix the signals between the groups. We also showed that the Median Polish method in the summarization step of RMA has similar mixing effect. RMA is one of the most widely used methods in microarray data processing and has been applied to a vast volume of data in biomedical research. The problematic behaviour of this method suggests that previous studies employing RMA could have been misadvised or adversely affected. Therefore we think it is crucially important that the research community recognizes the issue and starts to address it. The two core elements of the RMA method, quantile normalization and Median Polish, both have the undesirable effects of mixing biological signals between different sample groups, which can be detrimental to drawing valid biological conclusions and to any subsequent analyses. Based on the evidence presented here and that in the literature, we recommend exercising caution when using RMA as a method of processing microarray gene expression data, particularly in situations where there are likely to be unknown subgroups of samples.