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.     

Isomorphism of the Baumslag-Solitar groups

Necessary and sufficient conditions for the isomorphism of two groups, each defined by a single relation of the type a^–1b^ma=bⁿ, are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1684–1686, December, 1991.     

Algebraic composition operators

The focus of this paper is on the following problem. Given a linear space F of complex-valued functions on a set X and a polynomial p(z), is there an algebraic composition operator on F whose characteristic polynomial equals p(z)? We show that the supply of all the polynomials p(z) for which the answer to this question is affirmative depends heavily on the structure of the space F.     

OXIDATION OF ASCORBIC ACID AS AN INDICATOR OF PHOTOOXIDATIVE STRESS IN THE EYE

When whole retinal pigmented epithelium (RPE) cells isolated from bovine eyes are incubated with 14C-labeled ascorbic acid and exposed to a visible laser, the ascorbic acid is oxidized to dehydro-L-ascorbic acid (DHA). The amount of ascorbic acid which is oxidized is proportional to the radiant exposure of the sample (i.e. the total amount of radiation per unit area delivered over the exposure time). Blue light is more effective than red light in driving the reaction. The amount of label appearing in the DHA fraction is increased if unlabeled DHA is present in the reaction mixture, indicating that some redox cycling of ascorbate is occurring in the RPE cells. The ascorbic acid oxidizing activity does not depend on intact cells, is not inactivated by heating the cells to 80 degrees C, and appears to reside mainly in the subcellular fraction which contains melanin pigment granules. The ascorbic acid oxidation may be caused by free radicals formed when melanin is illuminated with light. This reaction appears to be a useful method for quantifying the production of free radicals during photooxidative stress.     

A cavity with reduced mode conversion for gyrotrons

Mode conversion at discontinuities of an ordinary gyrotron cavity is examined. It is shown how the production of unwanted spurious modes can be reduced substantially by introducing smooth transition regions between the individual parts of the cavity. The cavity of the 140 GHz KfK gyrotron operating in the TE_10,4 mode is used as an example. Cavity and adjacent tapered output waveguide are optimized as a single unit.     

High temperature stability of maghemite in partially oxidized basalt lava

Mössbauer spectroscopy of basalt lava samples, exhibiting reversible thermal magnetization (J_S-T) curves with Curie temperatures of about 580°C, has revealed considerable amounts of maghemite (γ-Fe₂O₃) in many samples. In view of the expected instability, of maghemite at temperatures above 350°C, this reversibility is rather surprising. Here we report Mössbauer studies on heated lava samples, showing high content of maghemite. The samples were kept at 600°C in oxidizing, reducing, and inactive atmospheres, respectively, for different lengths of time, and then analyzed with Mössbauer spectroscopy at room temperature. The Mössbauer spectra showed that maghemite is stable in the oxidizing atmosphere for at least several hours. In the inactive atmosphere a considerable amount of maghemite still exists after two hours heating. In the reducing atmosphere maghemite had transformed to magnetite after only 30 minutes.     

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.