A class of quadratic deformations of Lie superalgebras

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.Comment: 26pp, LaTeX. Original title: "Finite dimensional quadratic Lie superalgebras"; abstract re-worded; text clarified; 3 references added; rearrangement of minor appendices into text; new subsection 4.

TRIAD - Preliminary design of an operational earth resources survey system. 1969 summer faculty fellowship program in engineering systems design

TRIAD, preliminary design of operational earth resources survey syste

TRIAD - Preliminary design of an operational earth resources survey system Final report

Design of operational earth resources survey syste

Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model

We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely-degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur

Using parent metaphors for learning about the neonatal care experience: an interpretive perspective

© 2019 The Author(s). The final, definitive version of this paper has been published in Journal of Child Health Care by Sage Publications Ltd. All rights reserved. It is available at: https://doi.org/10.1177/1367493519875853.This study focuses on how metaphors are used by parents who have had a premature baby to describe their neonatal care experience and how these can contribute to empathic learning of health professionals. In health, metaphors are commonly used to communicate and explain difficult topics. When patients tell their story, metaphor can be a means of expression from which we can learn about their experience of illness or hospitalisation. Limited research exits on how metaphor can improve our understanding of parent’s emotional experience in neonatal care and subsequently inform education in this field. Employing narrative inquiry within an interpretive, constructivist paradigm, 20 narrative interviews with 23 parents of premature babies were analysed using a process of metaphor identification. Findings revealed common metaphors used to describe experience. Metaphor clusters used by parents in order of frequency were journeying, altered reality, darkness, breaking, connections, fighting, salvation and being on the edge. Parents widely used compelling and emotive metaphors to describe and express both difficult and challenging times as well as progression forward. Metaphors serve as a powerful way for health professionals to learn about the emotional experiences of parents and potentially enhance their empathic understanding.Peer reviewe

The rate of brain abnormalities on in utero MRI studies in fetuses with normal ultrasound examinations of the brain and calculation of indicators of diagnostic performance

AIM To estimate the rate of unexpected brain abnormalities detected by in utero magnetic resonance imaging (iuMRI) in fetuses without abnormalities at ultrasonography (USS). MATERIALS AND METHODS A prospective cohort study of pregnant women whose fetus had no structural brain (or body) abnormalities recognised on antenatal ultrasonography. Women were recruited from 12 centres across the UK and underwent iuMRI at 18 gestational weeks or more in the [blinded for review]. The imaging studies were reviewed by an experienced neuroradiologist. The positive and negative predictive values of both USS and iuMRI have been calculated by combining the results of this study with the results from the main [blinded for review] study. RESULTS One hundred and ninety-eight pregnant women were recruited and underwent iuMRI of 205 fetuses. Brain abnormalities were shown on iuMRI in two fetuses that were not recognised on USS (one case of a focal cortical abnormality and one case of mild ventriculomegaly). The negative predictive value for USS was 99.5% and 100% for iuMRI. CONCLUSIONS To the authors' knowledge, this is the first study comparing USS and iuMRI in low-risk pregnancies. USS has a comparatively high rule-out for fetal brain abnormalities and should remain the screening tool of choice