Regularity conditions and Farkas-type results for systems with fractional functions

This paper deals with some new versions of Farkas-type results for a system involving cone convex constraint, a geometrical constraint as well as a fractional function. We first introduce some new notions of regularity conditions in terms of the epigraphs of the conjugate functions. By using these regularity conditions, we obtain some new Farkas-type results for this system using an approach based on the theory of conjugate duality for convex or DC optimization problems. Moreover, we also show that some recently obtained results in the literature can be rediscovered as special cases of our main results

Enhanced anaerobic co-digestion of fat, oil, and grease by calcium addition: Boost of biomethane production and microbial community shift

This work focused on the application of calcium (0.1-1% w/v) to overcome the inhibition caused by the high loadings (2% v/v) of fat, oil, and grease (FOG) in the context of biomethane production, organic removal, and microbial community shift. Addition of 0.5% calcium showed maximum biomethane production (6-fold increase); biomethane production decreased following the addition of calcium (> 0.5%). The highest organic removal rates were 83 and 89% upon the addition of 0.3 and 0.5% calcium, respectively. Addition of calcium facilitated the growth of bacteria of phylum Firmicutes from the Clostridium, Syntrophomonas, and Sedimentibacter genera. The population of members from the genus Methanosaeta increased after the addition of 0.5% calcium, which is one of the factors responsible for high biomethane production. This study demonstrated that addition of calcium is an attractive strategy to avoid the inhibition of the growth of anaerobic microflora due to the presence of high FOG concentrations