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.

A Novel Packet Marking Function for Real-Time Interactive MPEG-4 Video Applications in a Differentiated Services Network

The future convergence of voice, video and data applications on the Internet requires that next generation technology provides bandwidth and delay guarantees. Current technology trends are moving towards scalable aggregate-based systems where applications are grouped together and guarantees are provided at the aggregate level only. This solution alone is not enough for interactive video applications with sub-second delay bounds. This paper introduces a novel packet marking scheme that controls the end-to-end delay of an individual flow as it traverses a network enabled to supply aggregate- granularity Quality of Service (QoS). IPv6 Hop-by-Hop extension header fields are used to track the packet delay encountered at each network node and autonomous decisions are made on the best queuing strategy to employ. The results of network simulations are presented and it is shown that when the proposed mechanism is employed the requested delay bound is met with a 20% reduction in resource reservation and no packet loss in the network.

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.

Responses to interactive playback predict future pairing success in nightingales

Birdsong is a sexually selected trait that serves in territory defence and mate choice. Individual song traits can be affected by the body condition of the male and thus may reflect his quality. Such relations between male quality and general singing performance raise the question whether differences in male quality also affect response strategies used in dyadic interactions. To address this question, we studied the relation between pairing success of male common nightingales, Luscinia megarhynchos, and their responses to rivals posing different levels of threat. Using interactive playback, we exposed males prior to mating to either aggressively or moderately singing rivals (by song overlapping and song alternating, respectively). Males that remained unpaired throughout the season (bachelors) interrupted their singing significantly more often after being overlapped than after alternating playback, whereas subsequently mated males kept the number of singing interruptions more constant across playback treatment. This suggests that subsequently paired males are less discriminative than are bachelors when challenged by rivals varying in aggressiveness. Regardless of playback treatment, males that later became paired responded significantly more strongly than did bachelor males. Thus, an increase in singing after a vocal interaction prior to mating predicted future mating success. (c) 2006 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

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.

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.