Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

Managing the risk of parenting

The aim of parents is to enable their children to become autonomous individuals capable of participating fully in the culture in which they live (Korbin 1997). Furthermore, the quality of parenting is reflected in an adult’s ability to recognize and adequately meet a child’s needs in a developmentally and emotionally appropriate manner (Donald & Jureidini 2004).Within contemporary society however, parents are faced with the tensions of providing boundaries whilst affording children rights. This in itself brings risks and a common thread that runs through approaches to parenting is the attempt to define a threshold of acceptable parenting. Above the threshold and a parent is good enough and below is not good enough. This paper will consider what the minimum requirements are and explore different dimensions of parenting. The concept of good enough parenting will be revisited in relation to risks that parents have to take, within the context of contemporary policy related to improving outcomes for children as enshrined in the Every Child Matters: Change for Children Agendas (Department for Education and skills 2003). The current dominance of a risk management approach to safeguarding children will be addressed within the context of a ‘risk society’ and the importance of the safety and well-being of the child will be examined It will be suggested that we need to achieve a better balance of ensuring the safety of the child, meeting the child's developmental needs, and supporting family functioning if we are to help parents manage the risks.