Root data with group actions

Suppose $k$ is a field, $G$ is a connected reductive algebraic $k$-group, $T$ is a maximal $k$-torus in $G$, and $\Gamma$ is a finite group that acts on $(G,T)$. From the above, one obtains a root datum $\Psi$ on which $\text{Gal}(k)\times\Gamma$ acts. Provided that $\Gamma$ preserves a positive system in $\Psi$, not necessarily invariant under $\text{Gal}(k)$, we construct an inverse to this process. That is, given a root datum on which $\text{Gal}(k)\times\Gamma$ acts appropriately, we show how to construct a pair $(G,T)$, on which $\Gamma$ acts as above. Although the pair $(G,T)$ and the action of $\Gamma$ are canonical only up to an equivalence relation, we construct a particular pair for which $G$ is $k$-quasisplit and $\Gamma$ fixes a $\text{Gal}(k)$-stable pinning of $G$. Using these choices, we can define a notion of taking "$\Gamma$-fixed points" at the level of equivalence classes, and this process is compatible with a general "restriction" process for root data with $\Gamma$-action.Comment: v2: one word inserted, one citation inserted, one reference updated, one misspelling correcte

Type Iax Supernovae

Type Iax supernovae (SN Iax), also called SN 2002cx-like supernovae, are the largest class of peculiar white dwarf (thermonuclear) supernovae, with over fifty members known. SN Iax have lower ejecta velocity and lower luminosities, and these parameters span a much wider range, than normal type Ia supernovae (SN Ia). SN Iax are spectroscopically similar to some SN Ia near maximum light, but are unique among all supernovae in their late-time spectra, which never become fully nebular. SN Iax overwhelmingly occur in late-type host galaxies, implying a relatively young population. The SN Iax 2012Z is the only white dwarf supernova for which a pre-explosion progenitor system has been detected. A variety of models have been proposed, but one leading scenario has emerged: a type Iax supernova may be a pure-deflagration explosion of a carbon-oxygen (or hybrid carbon-oxygen-neon) white dwarf, triggered by helium accretion to the Chandrasekhar mass, that does not necessarily fully disrupt the star.Comment: Author version of a chapter in the 'Handbook of Supernovae', edited by A. Alsabti and P. Murdin, Springer. 31 pages, 6 figure

Permanent Superhumps in V1974 Cyg

We present results of 32 nights of CCD photometry of V1974 Cygni, from the years 1994 and 1995. We verify the presence of two distinct periodicities in the light curve: 0.0812585 day~1.95 hours and 0.0849767 d~2.04 hr. We establish that the shorter periodicity is the orbital period of the underlying binary system. The longer period oscillates with an average value of |dot(P)| ~ 3x10^(7)--typical to permanent superhumps. The two periods obey the linear relation between the orbital and superhump periods that holds among members of the SU Ursae Majoris class of dwarf novae. A third periodicity of 0.083204 d~2.00 hr appeared in 1994 but not in 1995. It may be related to the recently discovered anti-superhump phenomenon. These results suggest a linkage between the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence of an accretion disk and permanent superhumps in the system no later than 30 months after the nova outburst. From the precessing disk model of the superhump phenomenon we estimate that the mass ratio in the binary system is between 2.2 and 3.6. Combined with previous results this implies a white dwarf mass of 0.75-1.07 M sun.Comment: 11 pages, 10 eps. figures, Latex, accepted for publication in MNRA

A simultaneous generalization of independence and disjointness in boolean algebras

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.Comment: Sumbitted to Orde

A broadband metasurface Luneburg lens for microwave surface waves

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordA broadband planar microwave Luneburg lens made of a three-layer metasurface with hexagonal symmetry is presented. This metasurface supports a transverse-electric mode confined to the surface that presents very low dispersion and a stable mode index across a broad frequency band. This enables the lens to operate in the range of frequencies between 8 GHz and 19 GHz. The lens was manufactured using a lithographic technique with three 25 μm copper-coated Mylar sheets. The resulting device is only 75 μm thick, flexible, and light-weight.We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1). J.P.G. wishes to thank Flann Microwave Ltd (Bodmin, UK) for additional financial support of her studentshi

Theoretical basis and practical aspects of small specimen creep testing

Interest in and the application of small specimen creep test techniques are increasing. This is because it is only possible to obtain small samples of material in some situations, for example, the scoop samples that are removed from in-service components, the heat-affected zones that are created when welds are used to join components and the desire to produce only small amounts of material in alloy development programmes. It is therefore important to review and compare the theoretical basis and practical aspects of each of the small specimen creep testing methods, in order to clearly understand which of the methods is the best for any specific application. This article provides the theoretical basis for each commonly used test method

Hypnosis in the Criminal Case: Facts and Fallacies

Throughout the past century, criminal cases have been documented in which a party has sought to introduce into evidence information obtained through the process of hypnosis. The usefulness of the technique of hypnosis in various psychological the rapies has already been well established. The courts, however, have differed markedly in their decisions on the admissibility of hypnotic material into evidence. Consequently, no clear rationale or guidelines for admissibility have been established

Tolerance of Artemia to static and shock pressure loading

Hydrostatic and hydrodynamic pressure loading has been applied to unicellular organisms for a number of years due to interest from food technology and extremophile communities. There is also an emerging interest in the response of multicellular organisms to high pressure conditions. Artemia salina is one such organism. Previous experiments have shown a marked difference in the hatching rate of these organisms after exposure to different magnitudes of pressure, with hydrostatic tests showing hatching rates at pressures up to several GPa, compared to dynamic loading that resulted in comparatively low survival rates at lower pressure magnitudes. In order to begin to investigate the origin of this difference, the work presented here has focussed on the response of Artemia salina to (quasi) one-dimensional shock loading. Such experiments were carried out using the plate-impact technique in order to create a planar shock front. Artemia cysts were investigated in this manner along with freshly hatched larvae (nauplii). The nauplii and cysts were observed post-shock using optical microscopy to detect motility or hatching, respectively. Hatching rates of 18% were recorded at pressures reaching 1.5 GPa, as determined with the aid of numerical models. Subjecting Artemia to quasi-one-dimensional shock loading offers a way to more thoroughly explore the shock pressure ranges these organisms can survive

Detailed volumetric analysis of the hypothalamus in behavioral variant frontotemporal dementia

Abnormal eating behaviors are frequently reported in behavioral variant frontotemporal dementia (bvFTD). The hypothalamus is the regulatory center for feeding and satiety but its involvement in bvFTD has not been fully clarified, partly due to its difficult identification on MR images. We measured hypothalamic volume in 18 patients with bvFTD (including 9 MAPT and 6 C9orf72 mutation carriers) and 18 cognitively normal controls using a novel optimized multimodal segmentation protocol, combining 3D T1 and T2-weighted 3T MRIs (intrarater intraclass correlation coefficients ≥0.93). The whole hypothalamus was subsequently segmented into five subunits: the anterior (superior and inferior), tuberal (superior and inferior), and posterior regions. The presence of abnormal eating behavior was assessed with the revised version of the Cambridge Behavioural Inventory (CBI-R). The bvFTD group showed a 17 % lower hypothalamic volume compared with controls (p < 0.001): mean 783 (standard deviation 113) versus 944 (73) mm(3) (corrected for total intracranial volume). In the hypothalamic subunit analysis, the superior parts of the anterior and tuberal regions and the posterior region were significantly smaller in the bvFTD group compared with controls. There was a trend for a smaller hypothalamic volume, particularly in the superior tuberal region, in those with severe eating disturbance scores on the CBI-R. Differences were seen between the two genetic subgroups with significantly smaller volumes in the MAPT but not the C9orf72 group compared with controls. In summary, bvFTD patients had lower hypothalamic volumes compared with controls. Different genetic mutations may have a differential impact on the hypothalamus

In vivo measurement of surface pressures and retraction distances applied on abdominal organs during surgery

This study undertook the in vivo measurement of surface pressures applied by the fingers of the surgeon during typical representative retraction movements of key human abdominal organs during both open and hand-assisted laparoscopic surgery. Surface pressures were measured using a flexible thin-film pressure sensor for 35 typical liver retractions to access the gall bladder, 36 bowel retractions, 9 kidney retractions, 8 stomach retractions, and 5 spleen retractions across 12 patients undergoing open and laparoscopic abdominal surgery. The maximum and root mean square surface pressures were calculated for each organ retraction. The maximum surface pressures applied to these key abdominal organs are in the range 1 to 41 kPa, and the average maximum surface pressure for all organs and procedures was 14 ± 3 kPa. Surface pressure relaxation during the retraction hold period was observed. Generally, the surface pressures are higher, and the rate of surface pressure relaxation is lower, in the more confined hand-assisted laparoscopic procedures than in open surgery. Combined video footage and pressure sensor data for retraction of the liver in open surgery enabled correlation of organ retraction distance with surface pressure application. The data provide a platform to design strategies for the prevention of retraction injuries. They also form a basis for the design of next-generation organ retraction and space creation surgical devices with embedded sensors that can further quantify intraoperative retraction forces to reduce injury or trauma to organs and surrounding tissues