Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

Huddling in groups leads to daily energy savings in free-living African Four-Striped Grass Mice, Rhabdomys pumilio

1. Free-living animals make complex decisions associated with optimizing energy and nutrient intake. In environments where ambient temperatures fall below the thermoneutral zone, homeotherms must choose whether or not to forage, how long and what to forage for, and whether or not to perform activities that conserve energy.

The dichotomy in the DNA-binding behaviour of ruthenium(II) complexes bearing benzoxazole and benzothiazole groups

The substituted tris(bipyridine)ruthenium(II) complexes {[Ru(bpy)(2)(4,4'-bbob)](2+) and [Ru(bpy)(2)(5,5'-bbob)](2+) [where bpy = 2,2'-bipyridine and bbob = bis(benzoxazol-2-yl)-2,2'-bipyridine] have been prepared and compared to the previously studied complex [Ru(bpy)(2)(4,4'-bbtb)](2+) [where bbtb = bis(benzothiazol-2-yl)-2,2'-bipyridine]. From the UV/VIS titration studies, Delta-[Ru(bpy)(2)(4,4'bbob)](2+) displays a stronger association than the Lambda-isomer with calf-thymus DNA (ct-DNA). For [Ru(bpy)(2)(5,5'-bbob)](2+), there appears to be minimal interaction with ct-DNA. The results of fluorescence titration studies suggest that [Ru(bpy)(2)(4,4'-bbob)](2+) gives an increase in emission intensity with increasing ct-DNA concentrations, with an enantiopreference for the A isomer, confirmed by membrane dialysis studies. The fluorescent intercalation displacement studies revealed that [Ru(bpy)(2)(4,4'-bbob)](2+) and [Ru.(bpy)(2)(5,5'bbob)](2+) display a preference for more open DNA structures such as bulge and hairpin sequences. While Delta-[Ru(bpy)(2)(4,4'-bbtb)](2+) has shown the most significant affinity for all the oligonucleotides sequences screened in previous studies, it is the A isomer of the comparable benzoxazole ruthenium(II) complex (Delta-[Ru(bpy)(2)(4,4'-bbob)](2+)) that preferentially binds to DNA.

Authenticity and stakeholder planning in the segregated city

This paper is concerned with the production and reproduction of segregation in Northern Ireland and how territoriality has impacted on the Protestant community in Derry/Londonderry. The city was pivotal in the development of the most recent conflict, has a majority Catholic population, sits on a contested border and has attempted to respond to expressions of alienation that have emerged from the Protestant community. The research used multiple methods to understand the nature of alienation and exclusion using secondary data, a quantitative household survey, in-depth interviews and focus
groups. This empirical commitment was important in identifying and unpacking the claims of various stakeholders with an interest in the use and development of the area. It is argued here that a version of Collaborative Planning provides a loosely articulated conceptual and methodological framework for drawing Protestant communities into the wider planning framework for the city. The data, however, suggest that the nature of stakeholders is complex and contradictory, and discursive practice that seeks consensus has limits, especially in validating or legitimating the assertions of self-acclaimed stakeholders. The research shows that the Protestant community had declined and residualised but had little experience of direct conflict with the majority community. Moreover, the Protestant community is now more likely to use the city centre (a predominantly Catholic space) for consumption and work, and its demographic decline has stopped. These findings are important as policy responses and community relations programmes have failed to distinguish between measurable socioeconomic needs and claims concerning ethnic alienation based on emotion and manipulation. Such alienation has tended to bolster single identity communities who have little or no prospect and/or knowledge of the collaborative efforts required to deliver meaningful regeneration. More realistic strategies based on agonism focus attention on power relations and the authenticity of positions adopted by competing interests in land use management and change. The paper concludes by highlighting the need to acknowledge and value contestation but to challenge sectarian discourses represented as legitimate claims about community needs and priorities.

Imidazolium ionic liquid crystals with pendant mesogenic groups

Ionic liquid crystals were obtained by coupling one or two mesogenic units (cholesterol or cyanobiphenyl) to an imidazolium cation. Anions are bromide, bis(trifluoromethylsulfonyl)imide, and tetrakis(2-thenoyltrifluoroacetonato)europate(III). The mesomorphism of the compounds depends on the type and number of mesogenic units and on the type of anion. In general, the most stable mesophases are observed for the bis(trifluoromethylsulfonyl)imide salts. Most of the compounds containing cholesterol moieties show enantiotropic SmA* phases over a broad temperature range, and some of them are room temperature liquid crystals. Modeling of the small-angle X-ray scattering patterns revealed the molecular arrangement in these mesophases. On the contrary, most of the compounds containing cyanobiphenyl groups exhibit monotropic lamellar or nematic mesophases, depending on the number of mesogenic units. The imidazolium salts containing the tetrakis(2-thenoyltrifluoroacetonato)europate(III) anion show an intense red photoluminescence.

Using Focus Groups to Research Sensitive Issues: Insights from Group Interviews on Nursing in the Northern Ireland “Troubles”

In this article the authors discuss the usefulness of focus groups for researching sensitive issues using evidence from a study examining the experiences of nurses providing care in the context of the Northern Ireland Troubles. They conducted three group interviews with nurses during which they asked about the issues the nurses face(d) in providing nursing care amid enduring social division. Through a discursive analysis of within-group interaction, they demonstrate how participants employ a range of interpretive resources, the effect of which is to prioritize particular knowledge concerning the nature of nursing care. The identification of such patterned activity highlights the ethnographic value of focus groups to reveal social conventions guiding the production of accounts but also suggests that accounts cannot be divorced from the circumstances of their production. Consequently, the authors argue that focus groups should be considered most useful for illuminating locally sanctioned ways of talking about sensitive issues.

Pyrrolidinium Ionic Liquid Crystals with Pendant Mesogenic Groups

New ionic liquid crystals (including ionic metallomesogens) based oil the pyrrolidinium core are presented. N-Methylpyrrolidine was quaternized with different mesogenic groups connected to a flexible, omega-bromosubstituted alkyl spacer. The length of the flexible alkyl spacer between the cationic head group and the rigid mesogenic group was varied. The substituted pyrrolidinium cations were combined with bromide, bis(trifluoromethylsulfonyl)imide, tetrakis (2-thenoyltrifluoroacetonato)europate(III), and tetrabromouranyl anions. The influence of the type of mesogenic unit, the lengths of the flexible spacer and terminal alkyl chain, the size of the mesogenic group, and the type of anion oil the thermotropic mesomorphic behavior was investigated. Furthermore, the phase behavior was thoroughly compared with the previously reported mesomorphism of N-alkyl-N-methylpyrrolidinium salts. Low-ordered smectic A phases of the de Vries type, smectic C phases, higher-ordered smectic F/I phases, as well its crystal smectic phases (E and G, J, H, or K) were observed and investigated by polarizing optical microscopy, differential scanning calorimetry, and powder X-ray diffraction.