An approach to non simply laced cluster algebras

Let $\Delta$ be an oriented valued graph equipped with a group of admissible automorphisms satisfying a certain stability condition. We prove that the (coefficient-free) cluster algebra $\mathcal A(\Delta/G)$ associated to the valued quotient graph $\Delta/G$ is a subalgebra of the quotient $\pi(\mathcal A(\Delta))$ of the cluster algebra associated to $\Delta$ by the action of $G$. When $\Delta$ is a Dynkin diagram, we prove that $\mathcal A(\Delta/G)$ and $\pi(\mathcal A(\Delta))$ coincide. As an example of application, we prove that affine valued graphs are mutation-finite, giving an alternative proof to a result of Seven.Comment: 36 pages. Minor correction

Are physical performance and injury risk in a professional soccer team in match-play affected over a prolonged period of fixture congestion?

In this study, the effects of a prolonged period of fixture congestion (8 successive official matches in 26-days) on physical performance and injury risk and severity in a professional soccer team were investigated. Computerised motion-analysis was used to analyse the overall distance covered and that run at light- (0.0-11.0 km•h-1); low- (11.1-14.0 km•h-1); moderate- (14.1-19.7 km•h-1) and high-intensities (≥19.8 km•h-1) for the team as a whole. Distances were measured in metres per minute. Information on match injuries was recorded prospectively. The overall distance covered varied across successive matches (p<0.001) as more distance was run in games 4 and 7 compared to 2 and 3 respectively (126.6±12.3 m•min-1 and 125.0±13.2 m•min-1 vs. 116.0±8.0 m•min-1 and 115.5±11.0 m•min-1). Distance run in light-intensity exercise also varied (p<0.001) as more distance was covered in game 4 versus 1, 2, 3, 5 and 6 (75.5±3.8 m•min-1 vs. 70.6±2.4 m•min-1, 71.8±3.4 m•min-1, 69.3±2.6 m•min-1, 71.5±3.1 m•min-1, and 70.3±2.8 m•min-1) and in game 8 versus game 3 (73.1±3.8 vs. 69.3±2.6 m•min-1) respectively. When comparing match halves, there were no differences across games in overall or high-intensity distance covered and performance in these measures was similar for matches played before, during and after this period. Globally, no difference over the 8 games combined was observed between the reference team and opponents in any of the performance measures whereas the overall distance covered and that in low- (both p<0.001) and high-intensity running (p=0.040) differed in individual games. The incidence of match injury during the congested fixture period was similar to rates reported outside this period but the mean layoff duration of injuries was substantially shorter during the former (p<0.05). In summary, while the overall distance run and that covered at lower intensities varied across games, high-intensity running performance and injury risk were generally unaffected during a prolonged period of fixture congestion. These results might be linked to squad rotation and post-match recovery strategies in place at the present club

High purity H2 by sorption-enhanced chemical looping reforming of waste cooking oil in a packed bed reactor.

High purity hydrogen (>95%) was produced at 600 degrees C and 1 atm by steam reforming of waste cooking oil at a molar steam to carbon ratio of 4 using chemical looping, a process that features redox cycles of a Ni catalyst with the in-situ carbonation/calcination of a CO(2) sorbent (dolomite) in a packed bed reactor under alternated feedstreams of fuel-steam and air. The fuel and steam conversion were higher with the sorbent present than without it. Initially, the dolomite carbonation was very efficient (100%), and 98% purity hydrogen was produced, but the carbonation decreased to around 56% with a purity of 95% respectively in the following cycles. Reduction of the nickel catalyst occurred alongside steam reforming, water gas shift and carbonation, with H(2) produced continuously under fuel-steam feeds. Catalyst and CO(2)-sorbent regeneration was observed, and long periods of autothermal operation within each cycle were demonstrated