Abstract. We consider numerical methods for a "quasi-boundary value" regularization of the backward parabolic problem given bywhere A is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value u(T ) by adding αu(0), where α is a small parameter. We show how this leads very naturally to a reformulation of the problem as a second-kind Fredholm integral equation, which can be very easily approximated using methods previously developed by Ames and Epperson. Error estimates and examples are provided. We also compare the regularization used here with that from Ames and Epperson.

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The highlighted article in this issue (Ashani and Pistinner, "Estimation of the Upper Limit of Human Butyrylcholinesterase Dose Required for Protection against Organophosphates toxicity: A Mathematically Based Toxicokinetic Model") is an innovative approach to modeling the amount of protective enzyme, human butyrylcholinesterase, that could be administered to humans to protect them from the lethal effects of organophosphate nerve agents. The threat of nerve agent exposures at lethal level regrettably remains a threat to military as well civilian populations, and the authors of this article have used their previous experimental data along with new in vitro data to devise and calibrate a mathematical model that could have practical utility in the prophylaxis of military personnel against chemical warfare agents.

The microbial contribution to soil organic matter (SOM) has recently been shown to be much larger than previously thought and thus its role in carbon sequestration may also be underestimated. In this study we employ (13)C ((13)CO₂) to assess the potential CO₂ sequestration capacity of soil chemoautotrophic bacteria and combine nuclear magnetic resonance (NMR) with stable isotope probing (SIP), techniques that independently make use of the isotopic enrichment of soil microbial biomass. In this way molecular information generated from NMR is linked with identification of microbes responsible for carbon capture. A mathematical model is developed to determine real-time CO₂ flux so that net sequestration can be calculated. Twenty-eight groups of bacteria showing close homologies with existing species were identified. Surprisingly, Ralstonia eutropha was the dominant group. Through NMR we observed the formation of lipids, carbohydrates, and proteins produced directly from CO₂ utilized by microbial biomass. The component of SOM directly associated with CO₂ capture was calculated at 2.86 mg C (89.21 mg kg(-1)) after 48 h. This approach can differentiate between SOM derived through microbial uptake of CO₂ and other SOM constituents and represents a first step in tracking the fate and dynamics of microbial biomass in soil.

CO 2 enrichment a b s t r a c t Sequestration of CO 2 via biological sinks is a matter of great scientific importance due to the potential lowering of atmospheric CO 2 . In this study, a custom built incubation chamber was used to cultivate a soil microbial community to instigate chemoautotrophy of a temperate soil. Real-time atmospheric CO 2 concentrations were monitored and estimations of total CO 2 uptake were made. After careful background flux corrections, 4.52 AE 0.05 g CO 2 kg À1 dry soil was sequestered from the chamber atmosphere over 40 h. Using isotopically labelled 13 CO 2 and GCMSeIRMS, labelled fatty acids were identified after only a short incubation, hence confirming CO 2 sequestration for soil. The results of this in vivo study provide the ground work for future studies intending to mimic the in situ environment by providing a reliable method for investigating CO 2 uptake by soil microorganisms.