The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools

A Tentative Modeling Study of the Effect of Wall Reactions on Oxidation Phenomena

This paper gives details of a tentative modeling study that investigates the inhibiting effect of internal reactor walls treated with acid..

A Memetic Analysis of a Phrase by Beethoven: Calvinian Perspectives on Similarity and Lexicon-Abstraction

This article discusses some general issues arising from the study of similarity in music, both human-conducted and computer-aided, and then progresses to a consideration of similarity relationships between patterns in a phrase by Beethoven, from the first movement of the Piano Sonata in A flat major op. 110 (1821), and various potential memetic precursors. This analysis is followed by a consideration of how the kinds of similarity identified in the Beethoven phrase might be understood in psychological/conceptual and then neurobiological terms, the latter by means of William Calvin’s Hexagonal Cloning Theory. This theory offers a mechanism for the operation of David Cope’s concept of the lexicon, conceived here as a museme allele-class. I conclude by attempting to correlate and map the various spaces within which memetic replication occurs

Influences on academics' approaches to development: voices from below

The purpose of this qualitative case study research was to explore faculty-based academics’ views on what influences their behaviours and attitudes towards their development. Informed by critical realist ontology, the data collection was carried out through narrative interviews with academics in two contrasting English Universities. Findings, or areas for reflection, have emerged about the constraints and enablements academics perceive in respect of their professional development. In particular, themes such as the significance of professional status; misaligned initiatives and priorities; the influence of supportive networks; and emergent personal, individual concerns have surfaced. The conclusion is drawn that the significance of agency raises the importance of responding to the ‘voices from below’

Memetic Perspectives on the Evolution of Tonal Systems

Cohn (1996) and Taruskin (1985) consider the increasing prominence during the nineteenth century of harmonic progressions derived from the hexatonic and octatonic pitch collections respectively. This development is clearly evident in music of the third quarter of the century onwards and is a consequence of forces towards non-diatonic organization latent in earlier music. This article conceptualizes such forces as memetic — drawing a distinction between memetic processes in music itself and those in the realm of music theory — and interprets the gradualistic evolution of tonal systems as one of their most significant consequences. After outlining hypotheses for the mechanisms driving such evolution, it identifies a number of ‘musemes’ implicated in hexatonic and octatonic organization in a passage from Mahler’s Symphony no. 10. Pople’s (2002) Tonalities music-analysis software is used to explore the tonal organization of the passage, which is considered in relation to the musemes hypothesized to generate and underpin it

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Poor maternal nutrition programmes a pro-atherosclerotic phenotype in ApoE-/- mice.

Numerous animal studies have consistently shown that early life exposure to LP (low-protein) diet programmes risk factors for CVD (cardiovascular disease) such as dyslipidaemia, high BP (blood pressure) and cardiac dysfunction in the offspring. However, studies on the effect of maternal under-nutrition on offspring development of atherosclerosis are scarce. Applying our LP model to the ApoE(-/-) atherosclerosis-prone mouse model, we investigated the development of atherosclerotic lesions in the aortic root of 6-month-old offspring. In addition, markers of plaque progression including SMA (smooth muscle actin) and Mac3 (macrophage marker 3) were studied. Pregnant dams were fed on a control (20% protein) or on an isocaloric LP diet (8% protein) throughout pregnancy and lactation. After weaning, male offspring were maintained on 20% normal laboratory chow. At 6 months of age, LP offspring showed a significantly greater plaque area (P<0.05) with increased cholesterol clefts and significantly higher indices of DNA damage compared with controls (P<0.05). The expression of HMG-CoA reductase (3-hydroxy-3-methyl-glutaryl-CoA reductase) (P<0.05) and LDL (low-density lipoprotein) receptor in the liver of LP offspring were increased. Furthermore, LP offspring had higher LDL-cholesterol levels (P<0.05) and a trend towards elevated insulin. There were no differences in other lipid measurements and fasting glucose between groups. These observations suggest that early exposure to an LP diet accelerates the development and increases the progression of atherosclerotic lesions in young adult offspring. Future studies are needed to elucidate the specific mechanisms linking in utero exposure to a diet low in protein to the development of atherosclerosis.This work was supported by the British Heart Foundation [grant numbers FS/09/029/27902, FS/09/050], the Biotechnology and Biological Sciences Research Council and the Cambridge Commonwealth Trust

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces