The orbit space of the p-subgroup complex is contractible

We show that the quotient space of the p-subgroup complex of a finite group by the action of the group is contractible. This was conjectured by Webb. Received: June 28, 1996     

A Splitting Principle for Modular Group Representations

The author of this paper has shown previously how a complexrepresentation of a finite group can be split into a virtualsum of representations induced from one-dimensional representationsof subgroups in a natural way (sometimes known as explicit Brauerinduction). Here the modular case is treated, yielding an analogousresult at the level of Brauer characters in general, and inthe Green ring for trivial source modules. 2000 MathematicsSubject Classification 20C20 (primary); 55M35, 14F20 (secondary).     

Promoting student engagement with mathematics support

This article reports the findings of qualitative research undertakento seek to identify the key reasons why some students are notengaging with mathematics support provided by Loughborough University.The research involved a number of focus groups and ‘onthe spot’ interviews with ‘non-users’ fromacross the campus. Barriers identified include a lack of awarenessof the location of support and a fear of embarrassment. Furtherinterviews were conducted with regular users of the supportin an attempt to understand how some of these barriers to usagemight be overcome. The article will discuss actions that maybe taken to improve student engagement with mathematics supportand the issue of how student motivation may affect such action.     

A relative version of Webb’s theorem on the equivariant chain complex of a subgroup complex

We prove a relative version of the theorem of Webb that the augmented chain complex of the p-subgroup complex of a finite group, considered as a complex of modules for the group, is homotopy equivalent to a complex of projectives. This allows us to take into account the group of automorphisms of the group.     

Investigating the relationship between cell cycle stage and diosgenin-induced megakaryocytic differentiation of HEL cells using sedimentation field-flow fractionation

Differentiation therapy could be one strategy for stopping cancer cell proliferation. A plant steroid, diosgenin, is known to induce megakaryocytic differentiation in human erythroleukemia (HEL) cells. In recent studies, the use of sedimentation field-flow fractionation (SdFFF) allowed the preparation of subpopulations that may differ in regard to sensitivity to differentiation induction. The specific goal of this study was to determine the relationship between cell cycle stage and sensitivity to megakaryocytic differentiation induction of HEL cells. After first confirming the capacity of diosgenin to specifically select targets, hyperlayer SdFFF cell sorting was used to prepare fractions according to cell cycle position from crude HEL cells. The sensitivities of these fractions to diosgenin-induced differentiation were then tested. The coupling of SdFFF cell separation to imaging flow cytometry showed that G1-phase cells were more sensitive to differentiation induction than S/G2M-phase cells, confirming the relationship between cell status at the start of induction, the extent of the biological event, and the potential of SdFFF in cancer research.     

Intra- and intergroup vocal behavior in resident killer whales, Orcinus orca

Vocal communication within and between groups of individuals has been described extensively in birds and terrestrial mammals, however, little is known about how cetaceans utilize their sounds in their natural environment. Resident killer whales, Orcinus orca, live in highly stable matrilines and exhibit group-specific vocal dialects. Single call types cannot exclusively be associated with particular behaviors and calls are thought to function in group identification and intragroup communication. In the present study call usage of three closely related matrilines of the Northern resident community was compared in various intra- and intergroup contexts. In two out of the three matrilines significant changes in vocal behavior depending both on the presence and identity of accompanying whales were found. Most evidently, family-specific call subtypes, as well as aberrant and variable calls, were emitted at higher rates, whereas "low arousal" call types were used less in the presence of matrilines from different pods, subclans, or clans. Ways in which the observed changes may function both in intra- and intergroup communication.     

Modification of guanine residues in PNA-synthesis by PyBOP

The phosphonium-type coupling reagent PyBOP, when applied to the synthesis of peptide nucleic acid (PNA) oligomers, was found to form O⁴-phosphonium compounds of the nucleobase guanine which can be converted into C⁴-modified guanine-derived PNAs by nucleophiles.     

Corrigenda: Mackey Functors And Control of Fusion

In the introduction to [3] it is mistakenly claimed that Mislin'sproof uses Carlsson's proof of Segal's Burnside ring conjecture.In fact, Mislin uses instead the work of Carlsson, Miller andLannes on Sullivan's fixed-point conjecture, and work of Dwyerand Zabrodski [1]. There is, however, a proof by Snaith [2]that depends on a version of the Segal conjecture. 2000 MathematicsSubject Classification 20J06 (primary), 20C05 (secondary).     

Crystal and molecular structure of sodium paratungstate 26 hydrate

On standing, an acid solution of tungstate yields single crystals of the paratungstate salt Na₁₀[H₂W₁₂O₄₂]·26H₂O. The space group is P¯1, (No. 2),a=11.811(2),b=12.486(2),c=12.206(2) Å,=82.29(1),=115.12(1), =113.76(1)°,V=1485.6 ų,Z=1. The structure was solved by direct methods and refined toR=0.0397,R _w =0.0403 [w=( ² F)^–1]. The 12 WO₆ octahedra (shared edges and vertices) are distorted from regular geometry; one of the sodium ions exhibits disorder and there is extensive hydrogen bonding between the water molecules and the oxygens of the paratungstate anion.