Absolute continuity and spectral concentration for slowly decaying potentials

We consider the spectral function $\rho(\mu)$ $(\mu \geq 0)$ for the Sturm-Liouville equation $y^{''}+(\lambda-q)y =0$ on $[0,\infty)$ with the boundary condition $y(0)=0$ and where $q$ has slow decay $O(x^{-\alpha})$ $(a>0)$ as $x\to \infty$. We develop our previous methods of locating spectral concentration for $q$ with rapid exponential decay (JCAM 81 (1997) 333-348) to deal with the new theoretical and computational complexities which arise for slow decay

Extensions of a New Algorithm for the Numerical Solution of Linear Differential Systems on an Infinite Interval

This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper examines the situation when the matrix that appears in the Levinson expansion has a double eigenvalue. Application is made to a fourth-order ODE with known special function solution

Boys and girls come out to play: Gender differences in children\u27s play patterns

This paper presents findings from The Irish Neighbourhood Play Study; a national, cross-border research project which recorded children’s play patterns in Ireland during 2012. The study incorporated 1688 families across 240 communities. This study recorded the play patterns of children in Ireland aged birth-14 years. The findings of the study are discussed here in the context of gendered patterns. Particular emphasis is placed on the skill differences developed through various play choices. These differences are explored within the context of established literature on the learning strengths of boys and girls. Established bodies of literature on children’s learning across gender lines has long been engaged in the debate about whether these differences are biological or socially constructed. This paper offers a parallel question; Are gender differences within learning, constructed through play choices within childhood? ©IATED (2017). Reproduced in Research Online with permission

The age of imagination: imagining play and invention: implications for creative development

This paper presents findings from The Irish Neighbourhood Play Study; a national, cross-border research project which recorded children’s play patterns in Ireland during 2012. The study incorporated 1688 families across 240 communities. Data was established on the play choices of children aged from birth to 14 years. Multiple differentials were explored including socio-economic and geographical environments. This paper focuses on the findings within imaginary play patterns for the full cohort. As such, it presents the play patterns for imaginary play in children aged birth-14 years. The findings are discussed in the context of developmental patterns with particular emphasis on the relationship between imaginary play and the development of creativity. Creativity is a key concept within contemporary education. Its central nexus is problem solving in the face of uncertainty. Within a rapidly changing world, it is a key skill requirement for today’s children as they grow towards efficacy within instability. The relationship between the development of creativity and children’s engagement with imaginary play practices are explored in this paper. ©IATED (2017). Reproduced in Research Online with permission

Children\u27s choices: the technology choices that children make within their free time. Influences and implications

The Irish Neighbourhood Play Research Project included almost 1700 families and 240 communities throughout Ireland. Using parental surveys and naturalistic observation, data was secured on how children in modern Ireland aged 0-14 are spending their free time. An all-island approach was taken incorporating cities, towns and rural areas across a variety of socio-economic groupings. Interesting findings arose from the data relating to the choices that children are making within their free time. This paper focuses on the choices they are making within technology use. Data on the children’s technological engagement will be presented and discussed through a child development lens. The positive and negative implications for both learning and development are raised. This generation of children will be the first to emerge into adulthood without ever experiencing a world without technology. For them, it will always have been central to their existence. What does this mean for the next generation of humanity? ©IATED (2016). Permission granted by IATED for inclusion in ResearchOnline@N

The influences of opportunity. Differences in children\u27s play choices across diverse communities in Ireland

This paper presents findings from The Irish Neighbourhood Play Project; a research study initiated by IT Sligo and Early Childhood Ireland in 2012. The focus of this paper is on the data section which highlights children’s play choices and opportunities across socio-economic communities. The study incorporated almost 1800 families across 240 communities. Data was collected within disadvantaged communities, middle class communities and affluent communities. Where and what children are playing was investigated. The choices children and families make within play have a direct effect on the developing brain of the young child (Acar & Torquati, 2015). This, in turn, affects school performance and engagement. Choices however, are often framed by opportunities; opportunities are framed by government policy and investment in community facilities as well as socio-cultural norms. The data from this project shows that children across socio-economic divides are engaging in dramatically different play, experiences and activities. Key differences also emerged in relation to how children in diverse communities are engaging with technology. The differences across multiple themes are startling and offer insights into the breadth of childhood experience across the Island of Ireland. ©IATED (2017). Reproduced in Research Online with permission