Quasi-Lie structure of twisted derivations of Laurent polynomials

Hartwig, Larsson and the second author in [J. Algebra, 2005] defined a bracket on sigma-derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain some structural results on sigma-derivations on Laurent polynomials in one variable.Comment: 20 page

Understanding recovery in the context of lived experience of personality disorders: a collaborative, qualitative research study

Background Concepts of recovery increasingly inform the development and delivery of mental health services internationally. In the UK recent policy advocates the application of recovery concepts to the treatment of personality disorders. However diagnosis and understanding of personality disorders remains contested, challenging any assumption that mainstream recovery thinking can be directly translated into personality disorders services. Methods In a qualitative interview-based study understandings of recovery were explored in extended, in-depth interviews with six people purposively sampled from a specialist personality disorders’ service in the UK. An interpretive, collaborative approach to research was adopted in which university-, clinical- and service user (consumer) researchers were jointly involved in carrying out interviews and analysing interview data. Results Findings suggested that recovery cannot be conceptualised separately from an understanding of the lived experience of personality disorders. This experience was characterised by a complexity of ambiguous, interrelating and conflicting feelings, thoughts and actions as individuals tried to cope with tensions between internally and externally experienced worlds. Our analysis was suggestive of a process of recovering or, for some, discovering a sense of self that can safely coexist in both worlds. Conclusions We conclude that key facilitators of recovery – positive personal relationships and wider social interaction – are also where the core vulnerabilities of individuals with lived experience of personaility disorders can lie. There is a role for personality disorders services in providing a safe space in which to develop positive relationships. Through discursive practice within the research team understandings of recovery were co-produced that responded to the lived experience of personality disorders and were of applied relevance to practitioners

Catenarity in quantum nilpotent algebras

In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any two given prime ideals $P \subsetneq Q$ have the same length. This is achieved by proving that the prime spectra of these algebras have normal separation, and then establishing the mild homological conditions necessary to apply a result of Lenagan and the first author. The work also recovers the Tauvel height formula for quantum nilpotent algebras, a result that was first obtained by Lenagan and the authors through a different approach.Comment: 11 page

Atomic radiation of a recombining nitrogen plasma

International audienceShock layer radiation from atomic lines can represent the main source of radiation in the afterbody region of a space capsule during Earth entry. Studying the kinetics of excited states of atomic nitrogen is therefore important to correctly predict its corresponding radiation. The CentraleSupelec plasma torch facility provides a stable equilibrium plasma and can be used to study plasma kinetics and radiation in a controlled environment. Previous experiments were performed to supply measurements of excited states of molecular nitrogen in a nonequilibrium recombining flow. We extend these measurements to atomic lines to get measurement of excited states of atomic nitrogen. We performed optical emission spectroscopy from VUV to NIR and obtain measurements of atomic nitrogen states above 10eV. The VUV region allow access to low energy states of nitrogen. A departure from Boltzmann distribution is observed for the high excited states and their densities tend to be equal to the Saha-Boltzmann distribution. This was previously predicted and is experimentally observed in this paper. These results may be used to validate kinetic codes