Hydrogen and oxygen isotopic fractionation relative to medium water for two different carbohydrate metabolic pathways leading to cellulose synthesis were measured. This was accomplished by analysing stable hydrogen and oxygen isotope ratios of water and cellulose for seedlings. The seedlings had been germinated and heterotrophically grown in closed vessels from species having starch (Triticum aestivum L. and Hordeum vulgare L.) and lipids {Ricinus communis L. and Arachis hypogaea L.) as the primary substrate. Isotopic fractionation factors occurring during enzyme-mediated exchange of carbon-bound hydrogen with water or the addition of carbon-bound hydrogens from water during the synthesis of cellulose from either starch or lipids were similar (ranging from + 144 to + 166%o). About 34% and 67% of carbon-bound hydrogens were derived from water during the synthesis of cellulose from starch and lipid, respectively. Thus, the greater deuterium enrichment in cellulose from oil seed species associated with gluconeogenesis was caused by a greater proportion of water-derived carbon-bound hydrogens and not because of differences in fractionation factors. The proportion of carbon-bound hydrogens derived from water during these metabolic pathways was similar to that of oxygen derived from water. These results may explain the variability in D/H ratios of cellulose nitrate from terrestrial and aquatic plants.
The mean deltaD value of petiole water of Pterocarpus indicus Willd (deltaD = -9.0 +/- 2.5 per thousand, n = 3) was not significantly different from the mean value of stem water (-8.3 +/- 2.8 per thousand, n = 3). deltaD values of main vein water ranged from -11.1 to + 12.0 per thousand (n = 14) and increased along the main vein from petiole to the tip of leaves. Mesophyll water was highly enriched in deuterium (mean deltaD = +32.0 +/- 2.0 per thousand, n = 19) when compared with stem, petiole, and vein water. deltaD values of mesophyll water for different areas of the lamina, however, were not homogenous and could differ by as much as 20 per thousand.
We consider a constrained optimization problem over a discrete set where noise-corrupted observations of the objective and constraints are available. The problem is challenging because the feasibility of a solution cannot be known for certain, due to the noisy measurements of the constraints. To tackle this issue, we propose a new method that converts constrained optimization into the unconstrained optimization problem of finding a saddle point of the Lagrangian. The method applies stochastic approximation to the Lagrangian in search of the saddle point. The proposed method is shown to converge, under suitable conditions, to the optimal solution almost surely (a.s.) as the number of iterations grows. We present the effectiveness of the proposed method numerically in two settings: (1) inventory control in a periodic review system, and (2) staffing in a call center.
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