An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

The 90-degree problem of scattering theory revisited: dynamical turbulence effects versus nonlinear effects

The 90° problem of cosmic-ray transport theory is revisited in this paper. By using standard forms of the wave spectrum in the solar wind, the pitch-angle Fokker–Planck coefficient and the parallel mean free path are computed for different resonance functions. A critical comparison is made of the strength of 90° scattering due to plasmawave effects, dynamical turbulence effects and nonlinear effects. It is demonstrated that, only for low-energy cosmic particles, dynamical effects are usually dominant. The novel results presented here are essential for an effective comparison of heliospheric observations for the parallel mean free path with the theoretical model results.

The conjugacy problem for two-by-two matrices over polynomial rings

We give an effective solution of the conjugacy problem for two-by-two matrices over the polynomial ring in one variable over a finite field.

System oriented neural networks - Problem formulation, methodology and application

A novel methodology is proposed for the development of neural network models for complex engineering systems exhibiting nonlinearity. This method performs neural network modeling by first establishing some fundamental nonlinear functions from a priori engineering knowledge, which are then constructed and coded into appropriate chromosome representations. Given a suitable fitness function, using evolutionary approaches such as genetic algorithms, a population of chromosomes evolves for a certain number of generations to finally produce a neural network model best fitting the system data. The objective is to improve the transparency of the neural networks, i.e. to produce physically meaningful

Child abuse as a complex and wicked problem: Reflecting on policy developments in the United Kingdom in working with children and families with multiple problems

In spite of significant public concern, professional efforts and financial expenditure, there has been a perceived lack of progress in reducing the incidence of child abuse, and in improving the outcomes for children in both the short and longer term. In this article the authors reflect on recent policy developments in the United Kingdom relating to children and families experiencing multiple adversities, and argue that the current conceptualisation of child abuse is flawed. In adopting a rational technical approach to the management of child abuse, there is a tendency to focus on shorter term outcomes for the child, such as immediate safety, that primarily reflect the outputs of the child protection system. However, by viewing child abuse as a wicked problem, that is complex and less amenable to being solved, then child welfare professionals can be supported to focus on achieving longer term outcomes for children that are more likely to meet their needs. The authors argue for an earlier identification of and intervention with children who are experiencing multiple adversity, such as those living with parents misusing substances and exposed to intimate partner violence.