Common transversals and complements in abelian groups

Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions

Casimir-Polder interaction between an atom and a small magnetodielectric sphere

On the basis of macroscopic quantum electrodynamics and point-scattering techniques, we derive a closed expression for the Casimir-Polder force between a ground-state atom and a small magnetodielectric sphere in an arbitrary environment. In order to allow for the presence of both bodies and media, local-field corrections are taken into account. Our results are compared with the known van der Waals force between two ground-state atoms. To continuously interpolate between the two extreme cases of a single atom and a macroscopic sphere, we also derive the force between an atom and a sphere of variable radius that is embedded in an Onsager local-field cavity. Numerical examples illustrate the theory.Comment: 9 pages, 4 figures, minor addition

Casimir force on amplifying bodies

Based on a unified approach to macroscopic QED that allows for the inclusion of amplification in a limited space and frequency range, we study the Casimir force as a Lorentz force on an arbitrary partially amplifying system of linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate that the force on a weakly polarisable/magnetisable amplifying object in the presence of a purely absorbing environment can be expressed as a sum over the Casimir--Polder forces on the excited atoms inside the body. As an example, the resonant force between a plate consisting of a dilute gas of excited atoms and a perfect mirror is calculated

Identification of the skeletal progenitor cells forming osteophytes in osteoarthritis.

OBJECTIVES: Osteophytes are highly prevalent in osteoarthritis (OA) and are associated with pain and functional disability. These pathological outgrowths of cartilage and bone typically form at the junction of articular cartilage, periosteum and synovium. The aim of this study was to identify the cells forming osteophytes in OA. METHODS: Fluorescent genetic cell-labelling and tracing mouse models were induced with tamoxifen to switch on reporter expression, as appropriate, followed by surgery to induce destabilisation of the medial meniscus. Contributions of fluorescently labelled cells to osteophytes after 2 or 8 weeks, and their molecular identity, were analysed by histology, immunofluorescence staining and RNA in situ hybridisation. Pdgfrα-H2BGFP mice and Pdgfrα-CreER mice crossed with multicolour Confetti reporter mice were used for identification and clonal tracing of mesenchymal progenitors. Mice carrying Col2-CreER, Nes-CreER, LepR-Cre, Grem1-CreER, Gdf5-Cre, Sox9-CreER or Prg4-CreER were crossed with tdTomato reporter mice to lineage-trace chondrocytes and stem/progenitor cell subpopulations. RESULTS: Articular chondrocytes, or skeletal stem cells identified by Nes, LepR or Grem1 expression, did not give rise to osteophytes. Instead, osteophytes derived from Pdgfrα-expressing stem/progenitor cells in periosteum and synovium that are descendants from the Gdf5-expressing embryonic joint interzone. Further, we show that Sox9-expressing progenitors in periosteum supplied hybrid skeletal cells to the early osteophyte, while Prg4-expressing progenitors from synovial lining contributed to cartilage capping the osteophyte, but not to bone. CONCLUSION: Our findings reveal distinct periosteal and synovial skeletal progenitors that cooperate to form osteophytes in OA. These cell populations could be targeted in disease modification for treatment of OA

Influence of shear stress and size on viability of endothelial cells exposed to gold nanoparticles

Screening nanoparticle toxicity directly on cell culture can be a fast and cheap technique. Nevertheless, to obtain results in accordance with those observed in live animals, the conditions in which cells are cultivated should resemble the one encountered in live systems. Microfluidic devices offer the possibility to satisfy this requirement, in particular with endothelial cell lines, because they are capable to reproduce the flowing media and shear stress experienced by these cell lines in vivo. In this work, we exploit a microfluidic device to observe how human umbilical vein endothelial cells (HUVEC) viability changes when subject to a continuous flow of culture medium, in which spherical citrate-stabilized gold nanoparticles of different sizes and at varying doses are investigated. For comparison, the same experiments are also run in multiwells where the cells do not experience the shear stress induced by the flowing medium. We discuss the results considering the influence of mode of exposure and nanoparticle size (24 and 13 nm). We observed that gold nanoparticles show a lower toxicity under flow conditions with respect to static and the HUVEC viability decreases as the nanoparticle surface area per unit volume increases, regardless of size

Real blocks with dihedral defect groups revisited

http://dx.doi.org/10.1017/S000497271200033

Restrictions of characters in p-solvable groups

Let G be a p-solvable group, P ≤ G a p-subgroup and χ ∈ Irr(G) such that χ(1)p ≥ |G : P |p. We prove that the restriction χP is a sum of characters induced from subgroups Q ≤ P such that χ(1)p = |G : Q|p. This generalizes previous results by Giannelli–Navarro and Giannelli–Sambale on the number of linear constituents of χP . Although this statement does not hold for arbitrary groups, we conjecture a weaker version which can be seen as an extension of Brauer–Nesbitt’s theorem on characters of p-defect zero. It also extends a conjecture of Wilde