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.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

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

A randomized controlled trial of tea tree oil (5%) body wash versus standard body wash to prevent colonization with methicillin-resistant Staphylococcus aureus (MRSA) in critically ill adults: research protocol

Background
Over the past ten years MRSA has become endemic in hospitals and is associated with increased healthcare costs. Critically ill patients are most at risk, in part because of the number of invasive therapies that they require in the intensive care unit (ICU). Washing with 5% tea tree oil (TTO) has been shown to be effective in removing MRSA on the skin. However, to date, no trials have evaluated the potential of TTO body wash to prevent MRSA colonization or infection. In addition, detecting MRSA by usual culture methods is slow. A faster method using a PCR assay has been developed in the laboratory, but requires evaluation in a large number of patients.

Methods/Design
This study protocol describes the design of a multicentre, phase II/III prospective open-label randomized controlled clinical trial to evaluate whether a concentration of 5% TTO is effective in preventing MRSA colonization in comparison with a standard body wash (Johnsons Baby Softwash) in the ICU. In addition we will evaluate the cost-effectiveness of TTO body wash and assess the effectiveness of the PCR assay in detecting MRSA in critically ill patients. On admission to intensive care, swabs from the nose and groin will be taken to screen for MRSA as per current practice. Patients will be randomly assigned to be washed with the standard body wash or TTO body wash. On discharge from the unit, swabs will be taken again to identify whether there is a difference in MRSA colonization between the two groups.

Discussion
If TTO body wash is found to be effective, widespread implementation of such a simple colonization prevention tool has the potential to impact on patient outcomes, healthcare resource use and patient confidence both nationally and internationally.

Trial Registration
[ISRCTN65190967]