Four-dimensional homogeneous critical metrics for quadratic curvature functionals

We determine all homogeneous metrics which are critical for some quadratic curvature functional in dimension four

Examples of signature (2,2) manifolds with commuting curvature operators

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A

Cheese whey: a cost-effective alternative for hyaluronic acid production by Streptococcus zooepidemicus

This study focuses on the optimization of cheese whey formulated media for the production of hyaluronic acid HA by Streptococcus zooepidemicus. Culture media containing whey (W; 2.1 g/L) or whey hydrolysate (WH; 2.4 g/L) gave the highest HA productions. Both W and WH produced high yields on protein consumed, suggesting cheese whey is a good nitrogen source for S. zooepidemicus production of HA. Polysaccharide concentrations of 4.0 g/L and 3.2 g/L were produced in W and WH in a further scale-up to 5 L bioreactors, confirming the suitability of the low-cost nitrogen source. Cheese whey culture media provided high molecular weight (> 3000 kDa) HA products. This study revealed replacing the commercial peptone by the low-cost alternative could reduce HA production costs by up to a 70%compared to synthetic media.Isabel Rodriguez was funded by a postdoctoral contract from the Xunta de Galicia, Spain (Plan I2C, 2012). This research was financially supported by projects: MAT 2010-21509-C03-01 (Ministerio de Economia y Competitividad, Spain) and FP7 Project BiValBi. Biotechnologies to Valorise the regional food Biodiversity in Latin America (PIRSES-GA-2013-611493). The authors want to thank Benigno Pereira, the manager of Queizuar S.L. (A Coruna, Spain) for providing the cheese whey utilised to conduct this research. We also wish to thank Ana Duran and Margarita Nogueira (IIM-CSIC) for their excellent technical assistance