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S. Alexander

Publications and source records attributed to S. Alexander.

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Total curvature and simple pursuit on domains of curvature bounded above

We show how circumradius and asymptotic behavior of curves in CAT(0) and CAT(K) spaces(K>0) are controlled by growth rates of total curvature. We apply our results to pursuit and evasion games of capture type with simple pursuit motion, generalizing results that are known for convex Euclidean domains, and obtaining results that are new for convex Euclidean domains and hold on playing fields vastly more general than these.

math.MG

The Light Quanta Modulated Physiological Response of Brassica Juncea Seedlings Subjected to Ni(II) Stress

This work is a study of the inter-relationship between parameters that principally affect metal up-take in the plant. The relationships between the concentration of metal in the growth medium, Cs, the concentration of metal absorbed by the plant, Cp, and the total biomass achieved, M, all of which are factors relevant to the efficiency of phytoremediation of the plant, have been investigated via the macro-physiological response of Brassica juncea seedlings to Ni(II) stress. The factorial growth experiments treated the Ni(II) concentration in the agar gel and the diurnal light quanta (DLQ) as independently variable parameters. Observations included the evidence of light enhancement of Ni toxicity at the root as well as at the whole plant level, the shoot mass index as a possible indicator of shoot metal sequestration in B. juncea, the logarithmic variation of Cp with Cs and the power-law dependence of M on Cp. The sum total of these observations indicate that for the metal accumulator B. juncea with regard to its capacity to accumulate Ni, the overall metabolic nature of the plant is important; neither rapid biomass increase nor a high metal concentration capability favor the removal of high metal mass from the medium, but rather the plant with the moderate photosynthetically driven biomass growth and moderate metal concentrations demonstrated the ability to remove the maximum mass of metal from the medium. The implications of these observations in the context of the perceived need in phytoremediation engineering to maximize Cp and M simultaneously in the same plant, are discussed.

q-bio.OT

Brane Gases in the Early Universe

Over the past decade it has become clear that fundamental strings are not the only fundamental degrees of freedom in string theory. D-branes are also part of the spectrum of fundamental states. In this paper we explore some possible effects of D-branes on early Universe string cosmology, starting with two key assumptions: firstly that the initial state of the Universe corresponded to a dense, hot gas in which all degrees of freedom were in thermal equilibrium, and secondly that the topology of the background space admits one-cycles. We argue by t-duality that in this context the cosmological singularities are not present. We derive the equation of state of the brane gases and apply the results to suggest that, in an expanding background, the winding modes of fundamental strings will play the most important role at late times. In particular, we argue that the string winding modes will only allow four space-time dimensions to become large. The presence of brane winding modes with $p > 1$ may lead to a hierarchy in the sizes of the extra dimensions.

hep-th