Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

Towards an Operational Model for Prevention and Treatment of Asthma Attacks

Asthma is one of the major chronic diseases in many countries. At present there is no cure for asthma, but medical advances can help to reduce the chances of attacks of the condition. Efficient care for asthma involves complexity, uncertainty, variability and the use of scarce resources, and these are the same conditions that indicate a possible use for the modelling approach of operational research. This paper is concerned with a pilot model that was developed through joint work by medical professionals and operational researchers. The development of the model is explained and illustrative results indicate the potential value of the modelling approach for the care of asthma in the community.     

Mass spectral analysis and imaging of tissue by ToF-SIMS—The role of buckminsterfullerene, C60, primary ions

Recent developments in desorption/ionisation mass spectrometry techniques have made their application to biological analysis a realistic and successful proposition. Developments in primary ion source technology, mainly through the advent of polyatomic ion beams, have meant that the technique of secondary ion mass spectrometry (SIMS) can now access the depths of information required to allow biological imaging to be a viable option.Here the role of the primary ion C₆₀⁺ is assessed with regard to molecular imaging of lipids and pharmaceuticals within tissue sections. High secondary ion yields and low surface damage accumulation are demonstrated on both model and real biological samples, indicating the high secondary ion efficiency afforded to the analyst by this primary ion when compared to other cluster ion beams used in imaging. The newly developed 40 keV C₆₀⁺ ion source allows the beam to be focused such that high resolution imaging is demonstrated on a tissue sample, and the greater yields allow the molecular signal from the drug raclopride to be imaged within tissue section following in vivo dosing.The localisation shown for this drug alludes to issues regarding the chemical environment affecting the ionisation probability of the molecule; the importance of this effect is demonstrated with model systems and the possibility of using laser post-ionisation as a method for reducing this consequence of bio-sample complexity is demonstrated and discussed.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.