We propose a projection algorithm for solving split feasibility problems involving paramonotone equilibria and convex optimization. The proposed algorithm can be considered as a combination of the projection ones for equilibrium and convex optimization problems. We apply the algorithm for finding an equilibrium point with minimal environmental cost for a model in electricity production. Numerical results for the model are reported.

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Eugenol oxidase (EUGO), a member of the vanillyl alcohol oxidase family, catalyzes the oxidative reaction of vanillyl alcohol to vanillin. This compound is responsible for the vanilla aroma and is widely used as a flavoring agent in food, cosmetics, and pharmaceuticals. Previously, EUGO was cloned and expressed in E. coli TOP10, and purified by anion-exchange chromatography with Q-Sepharose resin but the purification factor was low. To improve the efficiency of the EUGO purification, in this study, we cloned eugo gene into pET-28a vector and expressed it in E. coli Tunetta. The SDS-PAGE analysis of protein extracts obtained from E. coli expressing EUGO under different induction conditions showed that EUGO was expressed mostly in the soluble fraction at 6 hours after induction with 0.1 mM IPTG at 25oC. EUGO was purified by immobilized−metal affinity chromatography with Ni2+-NTA agarose and the in vitro enzymatic activity was characterized. The specific activity of purified EUGO was nearly 4-fold higher than that of the crude enzyme sample. In particular, the enzyme preparation produced by the purification method based on Ni-NTA affinity in this study was 2,5-fold more pure than that produced by Q-sepharose purification method described previously.