Tilting mutation of weakly symmetric algebras and stable equivalence

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a weakly symmetric algebra A, presented by a quiver with relations, we give a detailed description of the quiver and relations of the algebra obtained by mutating at a single loopless vertex of the quiver of A. In this form the mutation procedure appears similar to, although significantly more complicated than, the mutation procedure of Derksen, Weyman and Zelevinsky for quivers with potentials. By definition, weakly symmetric algebras connected by a sequence of tilting mutations are derived equivalent, and hence stably equivalent. The second aim of this article is to study these stable equivalences via a result of Okuyama describing the images of the simple modules. As an application we answer a question of Asashiba on the derived Picard groups of a class of self-injective algebras of finite representation type. We conclude by introducing a mutation procedure for maximal systems of orthogonal bricks in a triangulated category, which is motivated by the effect that a tilting mutation has on the set of simple modules in the stable category.Comment: Description and proof of mutated algebra made more rigorous (Prop. 3.1 and 4.2). Okuyama's Lemma incorporated: Theorem 4.1 is now Corollary 5.1, and proof is omitted. To appear in Algebras and Representation Theor

On Berenstein-Douglas-Seiberg Duality

I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed.Comment: 22 pages, LaTe

H3+ in Diffuse Interstellar Clouds: a Tracer for the Cosmic-Ray Ionization Rate

Using high resolution infrared spectroscopy we have surveyed twenty sightlines for H3+ absorption. H3+ is detected in eight diffuse cloud sightlines with column densities varying from 0.6x10^14 cm^-2 to 3.9x10^14 cm^-2. This brings to fourteen the total number of diffuse cloud sightlines where H3+ has been detected. These detections are mostly along sightlines concentrated in the Galactic plane, but well dispersed in Galactic longitude. The results imply that abundant H3+ is common in the diffuse interstellar medium. Because of the simple chemistry associated with H3+ production and destruction, these column density measurements can be used in concert with various other data to infer the primary cosmic-ray ionization rate, zeta_p. Values range from 0.5x10^-16 s^-1 to 3x10^-16 s^-1 with an average of 2x10^-16 s^-1. Where H3+ is not detected the upper limits on the ionization rate are consistent with this range. The average value of zeta_p is about an order of magnitude larger than both the canonical rate and rates previously reported by other groups using measurements of OH and HD. The discrepancy is most likely due to inaccurate measurements of rate constants and the omission of effects which were unknown when those studies were performed. We believe that the observed column density of H3+ is the most direct tracer for the cosmic-ray ionization rate due to its simple chemistry. Recent models of diffuse cloud chemistry require cosmic-ray ionization rates on the order of 10^-16 s^-1 to reproduce observed abundances of various atomic and molecular species, in rough accord with our observational findings.Comment: Accepted to ApJ, 35 pages, 5 figures, 5 table

Torsion pairs and simple-minded systems in triangulated categories

Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if its closure under extensions is all of T. We construct torsion pairs in T associated to any subset X of a simple-minded system S, and use these to define left and right mutations of S relative to X. When T has a Serre functor \nu, and S and X are invariant under \nu[1], we show that these mutations are again simple-minded systems. We are particularly interested in the case where T is the stable module category of a self-injective algebra \Lambda. In this case, our mutation procedure parallels that introduced by Koenig and Yang for simple-minded collections in the derived category of \Lambda. It follows that the mutation of the set of simple \Lambda-modules relative to X yields the images of the simple \Gamma-modules under a stable equivalence between \Gamma\ and \Lambda, where \Gamma\ is the tilting mutation of \Lambda\ relative to X.Comment: Minor corrections. To appear in Applied Categorical Structures. The final publication is available at springerlink.com: http://link.springer.com/article/10.1007%2Fs10485-014-9365-

Seasonal dependence of peroxy radical concentrations at a Northern hemisphere marine boundary layer site during summer and winter: evidence for radical activity in winter

Peroxy radicals (HO2+Σ RO2) were measured at the Weybourne Atmospheric Observatory (52° N, 1° E), Norfolk using a PEroxy Radical Chemical Amplifier (PERCA) during the winter and summer of 2002. The peroxy radical diurnal cycles showed a marked difference between the winter and summer campaigns with maximum concentrations of 12 pptv at midday in the summer and maximum concentrations as high as 30 pptv (10 min averages) in winter at night. The corresponding nighttime peroxy radical concentrations were not as high in summer (3 pptv). The peroxy radical concentration shows a distinct anti-correlation with increasing NOx during the daylight hours. At night, peroxy radicals increase with increasing NOx indicative of the role of NO3 chemistry. The average diurnal cycles for net ozone production, N(O3) show a large variability in ozone production, P(O3), and a large ozone loss, L(O3) in summer relative to winter. For a daylight average, net ozone production in summer was higher than winter (1.51±0.5 ppbv h−1 and 1.11±0.47 ppbv h−1, respectively). The variability in NO concentration has a much larger effect on N(O3) than the peroxy radical concentrations. Photostationary state (PSS) calculations show an NO2 lifetime of 5 min in summer and 21 minutes in the winter, implying that steady-state NO-NO2 ratios are not always attained during the winter months. The results show an active peroxy radical chemistry at night and that significant oxidant levels are sustained in winter. The net effect of this with respect to production of ozone in winter is unclear owing to the breakdown in the photostationary state

The atmospheric impacts of monoterpene ozonolysis on global stabilised Criegee intermediate budgets and SO2 oxidation : experiment, theory and modelling

The gas-phase reaction of alkenes with ozone is known to produce stabilised Criegee intermediates (SCIs). These biradical/zwitterionic species have the potential to act as atmospheric oxidants for trace pollutants such as SO₂, enhancing the formation of sulfate aerosol with impacts on air quality and health, radiative transfer and climate. However, the importance of this chemistry is uncertain as a consequence of limited understanding of the abundance and atmospheric fate of SCIs. In this work we apply experimental, theoretical and numerical modelling methods to quantify the atmospheric impacts, abundance and fate of the structurally diverse SCIs derived from the ozonolysis of monoterpenes, the second most abundant group of unsaturated hydrocarbons in the atmosphere. We have investigated the removal of SO₂ by SCIs formed from the ozonolysis of three atmospherically important monoterpenes (<i>α</i>-pinene, <i>β</i>-pinene and limonene) in the presence of varying amounts of water vapour in large-scale simulation chamber experiments that are representative of boundary layer conditions. The SO₂ removal displays a clear dependence on water vapour concentration, but this dependence is not linear across the range of [H₂O] explored. At low [H₂O] a strong dependence of SO₂ removal on [H₂O] is observed, while at higher [H₂O] this dependence becomes much weaker. This is interpreted as being caused by the production of a variety of structurally (and hence chemically) different SCIs in each of the systems studied, which displayed different rates of reaction with water and of unimolecular rearrangement or decomposition. The determined rate constants, <i>k</i>(SCI+H₂O), for those SCIs that react primarily with H₂O range from 4 to 310  ×  10⁻¹⁵ cm³ s⁻¹. For those SCIs that predominantly react unimolecularly, determined rates range from 130 to 240 s⁻¹. These values are in line with previous results for the (analogous) stereo-specific SCI system of <i>syn</i>-/<i>anti</i>-CH₃CHOO. The experimental results are interpreted through theoretical studies of the SCI unimolecular reactions and bimolecular reactions with H₂O, characterised for <i>α</i>-pinene and <i>β</i>-pinene at the M06-2X/aug-cc-pVTZ level of theory. The theoretically derived rates agree with the experimental results within the uncertainties. A global modelling study, applying the experimental results within the GEOS-Chem chemical transport model, suggests that &gt; 97 % of the total monoterpene-derived global SCI burden is comprised of SCIs with a structure that determines that they react slowly with water and that their atmospheric fate is dominated by unimolecular reactions. Seasonally averaged boundary layer concentrations of monoterpene-derived SCIs reach up to 1.4  ×  10⁴ cm⁻³ in regions of elevated monoterpene emissions in the tropics. Reactions of monoterpene-derived SCIs with SO₂ account for &lt; 1 % globally but may account for up to 60 % of the gas-phase SO₂ removal over areas of tropical forests, with significant localised impacts on the formation of sulfate aerosol and hence the lifetime and distribution of SO₂

On Morita and derived equivalences for cohomological Mackey algebras

By results of the second author, a source algebra equivalence between two p-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological Mackey functors. The main result of this paper proves a partial converse: an equivalence (resp. Rickard equivalence) between the categories of cohomological Mackey functors of two blocks of finite groups induces a permeable Morita (resp. derived) equivalence between the two block algebras

The LWA1 Radio Telescope

LWA1 is a new radio telescope operating in the frequency range 10-88 MHz, located in central New Mexico. The telescope consists of 258 pairs of dipole-type antennas whose outputs are individually digitized and formed into beams. Simultaneously, signals from all dipoles can be recorded using one of the instrument's "all dipoles" modes, facilitating all-sky imaging. Notable features of the instrument include high intrinsic sensitivity (about 6 kJy zenith system equivalent flux density), large instantaneous bandwidth (up to 78 MHz), and 4 independently-steerable beams utilizing digital "true time delay" beamforming. This paper summarizes the design of LWA1 and its performance as determined in commissioning experiments. We describe the method currently in use for array calibration, and report on measurements of sensitivity and beamwidth.Comment: 9 pages, 14 figures, accepted by IEEE Trans. Antennas & Propagation. Various minor changes from previous versio