A sum-product theorem in function fields

Let $A$ be a finite subset of \ffield, the field of Laurent series in $1/t$ over a finite field $\mathbb{F}_q$. We show that for any $\epsilon>0$ there exists a constant $C$ dependent only on $\epsilon$ and $q$ such that $\max\{|A+A|,|AA|\}\geq C |A|^{6/5-\epsilon}$. In particular such a result is obtained for the rational function field $\mathbb{F}_q(t)$. Identical results are also obtained for finite subsets of the $p$-adic field $\mathbb{Q}_p$ for any prime $p$.Comment: Simplification of argument and note that methods also work for the p-adic

Improved bounds on the set A(A+1)

For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\in A}. We establish new estimates on the size of A(A+1) in the case where F is either a finite field of prime order, or the real line. In the finite field case we show that A(A+1) is of cardinality at least C|A|^{57/56-o(1)} for some absolute constant C, so long as |A| < p^{1/2}. In the real case we show that the cardinality is at least C|A|^{24/19-o(1)}. These improve on the previously best-known exponents of 106/105-o(1) and 5/4 respectively

Impacts of elevated atmospheric ozone on peatland below-ground DOC characteristics

Rising concentrations of tropospheric ozone are having detrimental impacts on the growth of crop and forest species and some studies have reported inhibition of the allocation of carbon below ground. The effects of ozone on peatland ecosystems have received relatively little attention, despite their importance within the global carbon cycle. During this study, cores from a Welsh minerotrophic fen and ombrotrophic bog were exposed to four ambient/ elevated ozone concentration regimes representing current and predicted 2050 profiles. A large and significant reduction in the concentration of porewater dissolved organic carbon (DOC) was recorded in the fen cores exposed to the elevated ozone concentrations (up to −55%), with a concurrent shift to a higher molecularweight of the remaining soil carbon. No effects of ozone on DOC concentrations or characteristics were recorded for the bog cores. The data suggest higher ozone sensitivity of plants growing in the fen-type peatland, that the impacts on the vegetation may affect soil carbon characteristics through a reduction in root exudates and that theremay have been a shift in the source of substrate DOC for microbial consumption from vegetation exudates to native soil carbon. Theremay also have been a direct effect of ozone molecules reacting with soil organic matter after being transported into the soil through the aerenchyma tissue of the overlying vegetation. These qualitative changes in the soil carbon in response to elevated ozone may have important implications for carbon cycling in peatland ecosystems, and therefore climate change

The greenhouse gas (GHG) emissions associated with aquatic carbon removal during drinking water treatment

Peatlands and other terrestrial ecosystems export large amounts of dissolved organic carbon (DOC) to freshwater ecosystems. In catchments used for supplying drinking water, water treatment works (WTWs) can remove large quantities of this organic matter, and can therefore play a unique modifying role in DOC processing and associated greenhouse gas (GHG) emissions within the fluvial system. During this study we quantified the GHG emissions due to processes associated with carbon (C) removal during water treatment at four contrasting WTWs in the UK. Our results demonstrate that the removal of DOC from raw water supplies via coagulation, leading to the formation of sludge, usually makes it less susceptible to short-term oxidation when compared to DOC remaining in the fluvial system. Although this could be considered a means of reducing CO2 emissions from waterborne carbon, the current practise of land spreading of sludge is unlikely to represent a long-term C sink and therefore water treatment probably only delays the rate at which fluvial C re-enters the atmosphere. Furthermore, we estimate that indirect CO2 missions resulting from electricity use during water treatment, together with the use of chemicals and CO2 degassing from the water during treatment, far outweigh any potential CO2 reductions associated with DOC removal. Thus, the post-treatment handling of sludge has the potential to mitigate, but not to negate, GHG emissions associated with water treatment processes

Animating Indian production culture: an interview with animation filmmaker and educator Ram Mohan

Recent studies in global creative industries have helped reveal how media practitioners conceive professional identities and generate communities around cultural production. Nowhere is this more apparent than in the evolving space of Indian cinema, where the first century of filmmakers have not only devised vibrant industries but played key roles in conceiving national identity. Indian Animation, often misunderstood as a recent arrival, has roots early in this joint project of national development and entertainment. Filmmaker, educator and ‘father of Indian animation’ Ram Mohan has been active at every stage, and continues to contribute to a new Indian culture of animation filmmaking. In this interview Ram Mohan traces the rise of animation within Indian filmmaking across his long and varied career