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.

Spatially resolved diagnostics on a micro atmospheric pressure plasma jet

Despite enormous potential for technological applications, fundamentals of stable non-equilibrium micro-plasmas at ambient pressure are still only partly understood. Micro-plasma jets are one sub-group of these plasma sources. For an understanding it is particularly important to analyse transport phenomena of energy and particles within and between the core and effluent of the discharge. The complexity of the problem requires the combination and correlation of various highly sophisticated diagnostics yielding different information with an extremely high temporal and spatial resolution. A specially designed rf microscale atmospheric pressure plasma jet (µ-APPJ) provides excellent access for optical diagnostics to the discharge volume and the effluent region. This allows detailed investigations of the discharge dynamics and energy transport mechanisms from the discharge to the effluent. Here we present examples for diagnostics applicable to different regions and combine the results. The diagnostics applied are optical emission spectroscopy (OES) in the visible and ultraviolet and two-photon absorption laser-induced fluorescence spectroscopy. By the latter spatially resolved absolutely calibrated density maps of atomic oxygen have been determined for the effluent. OES yields an insight into energy transport mechanisms from the core into the effluent. The first results of spatially and phase-resolved OES measurements of the discharge dynamics of the core are presented.

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.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

A Hybrid Evolutionary Approach to the Nurse Rostering Problem

Nurse rostering is a difficult search problem with many constraints. In the literature, a number of approaches have been investigated including penalty function methods to tackle these constraints within genetic algorithm frameworks. In this paper, we investigate an extension of a previously proposed stochastic ranking method, which has demonstrated superior performance to other constraint handling techniques when tested against a set of constrained optimisation benchmark problems. An initial experiment on nurse rostering problems demonstrates that the stochastic ranking method is better in finding feasible solutions but fails to obtain good results with regard to the objective function. To improve the performance of the algorithm, we hybridise it with a recently proposed simulated annealing hyper-heuristic within a local search and genetic algorithm framework. The hybrid algorithm shows significant improvement over both the genetic algorithm with stochastic ranking and the simulated annealing hyper-heuristic alone. The hybrid algorithm also considerably outperforms the methods in the literature which have the previously best known results.