The role of schools in fostering pupil resilience

This study investigated the role of specialist provisions for pupils with social, emotional and behaviour difficulties (SEBD) in fostering resilience. The role schools play in resilience development was considered by measuring the association between the length of time a student had been in school with the strength of their resilience measured by a standardised test of resilience. Furthermore, possible ways in which resilience might develop in school were explored by looking at the possible mediating variables of having a sense of connection to school and having a significant peer relationship in school. The role of trait emotional intelligence (TEI) was also explored in this model by adding individual TEI as a moderating factor. Thirty-eight pupils from two SEBD schools took part in completing self-report questionnaires with the researcher. The length of time pupils spent in specialist schools was found to be predictive of both resilience resources and vulnerability, however none of the proposed variables explained this association. Exploratory analysis found TEI alone to be the most significant predictor of resilience outcomes. The theoretical implications are considered. The difficulties in measuring resilience as a construct are discussed, as well as the importance of completing research with this population, despite the challenges

Characterising small solutions in delay differential equations through numerical approximations

This paper discusses how the existence of small solutions for delay differential equations can be predicted from the behaviour of the spectrum of the finite dimensional approximations.Manchester Centre for Computational Mathematic

Closed-Flux Solutions to the Constraints for Plane Gravity Waves

The metric for plane gravitational waves is quantized within the Hamiltonian framework, using a Dirac constraint quantization and the self-dual field variables proposed by Ashtekar. The z axis (direction of travel of the waves) is taken to be the entire real line rather than the torus (manifold coordinatized by (z,t) is RxR rather than $S_1$ x R). Solutions to the constraints proposed in a previous paper involve open-ended flux lines running along the entire z axis, rather than closed loops of flux; consequently, these solutions are annihilated by the Gauss constraint at interior points of the z axis, but not at the two boundary points. The solutions studied in the present paper are based on closed flux loops and satisfy the Gauss constraint for all z.Comment: 18 pages; LaTe

A review of school approaches to increasing pupil resilience

The purpose of this review is to evaluate the literature on whole school approaches to increasing resilience in pupils. This is pertinent with the increase in children and young people’s mental health needs creating extra pressure on schools to foster young people’s ability to withstand stress and adversity. Whilst previous reviews have considered the ways in which schools support their pupils, the extent to which resilience has been reliably measured has varied. Recently, several validated resilience measures have been developed which allows for potentially more robust research to take place. This systematic review therefore summarises and critiques the literature exploring whole school approaches to resilience development only where a validated measure has been used. Eleven studies were reviewed and demonstrate that there is a trend between school factors and pupil resilience. The importance of supportive relationships with both peers and staff in school is highlighted in several studies as well as the positive effect of including a robust health promoting school’s agenda situated within local communities. However, the number of limitations identified within the current literature suggests that this review is not able to offer clear recommendations to schools. This review will, however, be helpful to schools, local authorities and the government in allowing them to take more of a critical stance in understanding resilience within a school context

The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior

The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.Comment: 14 pages, 8 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Application

Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Application

The Screen representation of spin networks. Images of 6j symbols and semiclassical features

This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a function of two variables - a natural choice due to their origin as elements of a square orthogonal matrix - and illustrated by use of a projection on a square "screen" introduced recently. On these screens, shown are images which provide a systematic classification of features previously introduced to represent the caustic and ridge curves (which delimit the boundaries between oscillatory and evanescent behaviour according to the asymptotic analysis of semiclassical approaches). Particular relevance is given to the surprising role of the intriguing symmetries discovered long ago by Regge and recently revisited; from their use, together with other newly discovered properties and in conjunction with the traditional combinatorial ones, a picture emerges of the amplitudes and phases of these discrete wavefunctions, of interest in wide areas as building blocks of basic and applied quantum mechanics.Comment: 16 pages, 13 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

The construct validity of the Schutte Emotional Intelligence Scale in light of psychological type theory : a study among Anglican clergy

This study explores the construct validity of the Schutte Emotional Intelligence Scale in the light of psychological type theory that hypothesises a bias in item content to favour extraverts over introverts, sensing types over intuitive types, feeling types over thinking types, and perceiving types over judging types. Data provided by 364 Anglican clergy serving in the Church in Wales, who completed the Schutte Emotional Intelligence Scale alongside the Francis Psychological Type Scales, confirm higher scores among extraverts (compared with introverts), intuitive types (compared with sensing types), and feeling types (compared with thinking types), but found no significant difference between judging types and perceiving types. These data are interpreted to nuance the kind of emotional intelligence accessed by the Schutte Emotional Intelligence Scale and to encourage future scale development that may conceptualise emotional intelligence in ways more independent of psychological type preferences

The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional perspective provides the most natural extension to exhibit the role of these discrete functions as matrix elements that appear at the very foundation of the modern theory of classical discrete orthogonal polynomials. Here we present 2D and 1D recursion relations that are useful for the direct computation of the orthonormal 6j, which we name U. We present a convention for the order of the arguments of the 6j that is based on their classical and Regge symmetries, and a detailed investigation of new geometrical aspects of the 6j symbols. Specifically we compare the geometric recursion analysis of Schulten and Gordon with the methods of this paper. The 1D recursion relation, written as a matrix diagonalization problem, permits an interpretation as a discrete Schr\"odinger-like equations and an asymptotic analysis illustrates semiclassical and classical limits in terms of Hamiltonian evolution.Comment: 14 pages,9 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio