Quiver grassmannians, quiver varieties and the preprojective algebra

Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In the current paper, we study these objects in detail. We show that the quiver grassmannians corresponding to submodules of certain injective modules are homeomorphic to the lagrangian quiver varieties of Nakajima which have been well studied in the context of geometric representation theory. We then refine this result by finding quiver grassmannians which are homeomorphic to the Demazure quiver varieties introduced by the first author, and others which are homeomorphic to the graded/cyclic quiver varieties defined by Nakajima. The Demazure quiver grassmannians allow us to describe injective objects in the category of locally nilpotent modules of the preprojective algebra. We conclude by relating our construction to a similar one of Lusztig using projectives in place of injectives.Comment: 30 pages. v2: minor corrections and notation changes, some proofs simplified. v3: Some statements and their proofs corrected. This version incorporates an erratum to the published version. See Appendix B for detail

Automatic comparison of global children’s and adult songs supports a sensorimotor hypothesis for the origin of musical scales

Music throughout the world varies greatly, yet some musical features like scale structure display striking crosscultural similarities. Are there musical laws or biological constraints that underlie this diversity? The “vocal mistuning” hypothesis proposes that cross-cultural regularities in musical scales arise from imprecision in vocal tuning, while the integer-ratio hypothesis proposes that they arise from perceptual principles based on psychoacoustic consonance. In order to test these hypotheses, we conducted automatic comparative analysis of 100 children’s and adult songs from throughout the world. We found that children’s songs tend to have narrower melodic range, fewer scale degrees, and less precise intonation than adult songs, consistent with motor limitations due to their earlier developmental stage. On the other hand, adult and children’s songs share some common tuning intervals at small-integer ratios, particularly the perfect 5th (~3:2 ratio). These results suggest that some widespread aspects of musical scales may be caused by motor constraints, but also suggest that perceptual preferences for simple integer ratios might contribute to cross-cultural regularities in scale structure. We propose a “sensorimotor hypothesis” to unify these competing theories

Clinic consultations with children and parents on the dietary management of cystic fibrosis

The aim of this paper is to examine clinic consultations on the dietary management of cystic fibrosis with particular consideration to the role of children.  The role of parents is also examined to determine how their involvement impacts on the role of children during consultations. The data are drawn from interviews with 32 Irish school aged children with cystic fibrosis and their parents, and participant observations during clinic consultations with a sub-group of 21 children. Data were analysed concurrently with data collection using a method of constant comparison, which involved comparing and contrasting incidents in the data to develop themes. Theoretical sampling was used to further explore and develop emergent themes. Discourse analysis was applied to clinic conversations. Children were seen to have little active involvement during consultations leaving them marginalised as conversations were directed at parents primarily and their accounts were privileged over those of children. A surveillance approach to consultations  involving interrogative style questioning and generally closed conversations  was seen to contribute to the marginalised position of children. In addition, dietary advice limited children s involvement because it was of little relevance to children s understandings of being healthy and to the dietary implications of these. The findings highlight a need to acknowledge children as active participants in their dietary care. Implications for developing a child-centred approach to dietary consultations are discussed including implications for working with children towards improved health outcomes of managing CF diet.  

The ambiguity of God : a post-colonial inquiry into the politics of theistic formulation in South Africa

Bibliography: leaves 115-131.This thesis sets out to locate a post-apartheid perspective within what might be described as postcolonial Religious Studies, drawing on the genealogical method of Michel Foucault. Roughly stated, I understand the methodology to represent a shift away from preoccupation with the actual truth or otherwise of an idea, towards concern with the agitation - the discord, the discrepancies - that characterizes the appearance of an idea. Within the parameters, paradigms and possibilities imposed by this method, I inquire into the politics of theistic formulation in South Africa prior to the Union of South Africa (1910). Part One of the thesis discusses the politics of the advent of the Christian God in Southern Africa. In the three chapters that comprise this section, I situate colonial beliefs about God within colonialism as a discursive genre; in particular, evidence is provided of the deployment of religious (and in particular theistic) sensibility as a strategic category in the Othering discourse by which European expansion into Southern Africa was promulgated. Chapter Two opens by observing that colonial constructions of Otherness served not only to "erase" (Spivak) autochthonic identity, but also to eulogize and assert the colonial Self. Contextualizing my argument in the debate about the ambiguous effects of colonial missionary activities, I examine the mythically imbued, Othering discourse of Robert Moffat as a particularly conspicuous instance of the missionary qua colonial Self. Chapter Three gathers the concerns of Part One around the problem of theistic formulation in a colonial context, by discussing John Colenso's discovery of a theistic sensibility indigenous to autochthonic Africans as an example of a transgression of the Christian discourse that colonialism made function as truth. Part Two makes use of the categories established in Part One, and applies them to Afrikanerdom: its Othering in British colonial discourse; its religiously imbued, mythic history; and its beliefs in God. Having brought to theistic formulation a Foucauldian suspicion of systems of truth, my argument turns in Part Three to bring a particular theology, theologia crucis, alongside Foucault: accepting that the "dogmatic finitization" (Wolfhart Pannenberg) of Christian belief is inherently susceptible to the play of power, I observe that theistic formulation cast in terms of the cross - the "Crucified God" (Jurgen Moltmann) - holds a subversive potential in which may lie possibilities for an alternative to "truth"

Flash ionization of the partially ionized wind of the progenitor of SN 1987A

The H II region created by the progenitor of SN 1987A was further heated and ionized by the supernova flash. Prior to the flash, the temperature of the gas was 4000 - 5000 K, and helium was neutral, while the post-flash temperature was only slightly less than 10^5 K, with the gas being ionized to helium-like ionization stages of C, N and O. We have followed the slow post-flash cooling and recombination of the gas, as well as its line emission, and find that the strongest lines are N V 1240 and O VI 1034. Both these lines are good probes for the density of the gas, and suitable instruments to detect the lines are STIS on HST and FUSE, respectively. Other lines which may be detectable are N IV] 1486 and [O III] 5007, though they are expected to be substantially weaker. The relative strength of the oxygen lines is found to be a good tracer of the color temperature of the supernova flash. From previous observations, we put limits on the hydrogen density, n_H, of the H II region. The early N V 1240 flux measured by IUE gives an upper limit which is n_H ~ 180 \eta^{-0.40} cm^{-3}, where \eta is the filling factor of the gas. The recently reported emission in [O III] 5007 at 2500 days requires n_H = (160\pm12) \eta^{-0.19} cm^{-3}, for a supernova burst similar to that in the 500full1 model of Ensman & Burrows (1992). For the more energetic 500full2 burst the density is n_H = (215\pm15) \eta^{-0.19} cm^{-3}. These values are much higher than in models of the X-ray emission from the supernova (n_H ~ 75 cm^{-3}), and it seems plausible that the observed [O III] emission is produced primarily elsewhere than in the H II region. We also discuss the type of progenitor consistent with the H II region. In particular, it seems unlikely that its spectral type was much earlier than B2 Ia.Comment: LaTeX, 23 pages including 4 figures. To appear in ApJ (Main Journal

2021-2022 John Oliveira String Competition - Winner\u27s Recital

https://spiral.lynn.edu/conservatory_john-oliveira/1008/thumbnail.jp

Ethyl and isopropyl 4-ferrocenylbenzoate.

The title compounds, [Fe(C5H5)(C14H13O2)] and [Fe(C5H5)- (C15H15O2)], respectively, contain the ferrocenyl 5(C5H4) and phenylene ±C6H4± rings in a nearly coplanar arrangement, with interplanar angles of 6.88 (12) and 10.5 (2), respectively. Molecules of the ethyl ester form dimers through 5(C5H5)CÐ H O C hydrogen bonds, with graph set R22 (20), and, together with Csp3ÐH (C5H5) interactions, generate a one-dimensional column (irregular ladder). Molecules of the isopropyl ester aggregate through 5(C5H5)CÐH (C6H4) interactions

Variational Ansatz for PT-Symmetric Quantum Mechanics

A variational calculation of the energy levels of a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 - (ix)^N with N positive and x complex is presented. Excellent agreement is obtained for the ground state and low lying excited state energy levels and wave functions. We use an energy functional with a three parameter class of PT-symmetric trial wave functions in obtaining our results.Comment: 9 pages -- one postscript figur