Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces

We formulate the necessary conditions for the maximal super-integrability of a certain family of classical potentials defined in the constant curvature two-dimensional spaces. We give examples of homogeneous potentials of degree -2 on $E^2$ as well as their equivalents on $S^2$ and $H^2$ for which these necessary conditions are also sufficient. We show explicit forms of the additional first integrals which always can be chosen polynomial with respect to the momenta and which can be of an arbitrary high degree with respect to the momenta

Roots of the affine Cremona group

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.Comment: 4 page

Strongly residual coordinates over A[x]

For a domain A of characteristic zero, a polynomial f over A[x] is called a strongly residual coordinate if f becomes a coordinate (over A) upon going modulo x, and f becomes a coordinate upon inverting x. We study the question of when a strongly residual coordinate is a coordinate, a question closely related to the Dolgachev-Weisfeiler conjecture. It is known that all strongly residual coordinates are coordinates for n=2 . We show that a large class of strongly residual coordinates that are generated by elementaries upon inverting x are in fact coordinates for arbitrary n, with a stronger result in the n=3 case. As an application, we show that all Venereau-type polynomials are 1-stable coordinates.Comment: 15 pages. Some minor clarifications and notational improvements from the first versio

Eureka and beyond: mining's impact on African urbanisation

This collection brings separate literatures on mining and urbanisation together at a time when both artisanal and large-scale mining are expanding in many African economies. While much has been written about contestation over land and mineral rights, the impact of mining on settlement, notably its catalytic and fluctuating effects on migration and urban growth, has been largely ignored. African nation-states’ urbanisation trends have shown considerable variation over the past half century. The current surge in ‘new’ mining countries and the slow-down in ‘old’ mining countries are generating some remarkable settlement patterns and welfare outcomes. Presently, the African continent is a laboratory of national mining experiences. This special issue on African mining and urbanisation encompasses a wide cross-section of country case studies: beginning with the historical experiences of mining in Southern Africa (South Africa, Zambia, Zimbabwe), followed by more recent mineralizing trends in comparatively new mineral-producing countries (Tanzania) and an established West African gold producer (Ghana), before turning to the influence of conflict minerals (Angola, the Democratic Republic of Congo and Sierra Leone)

Making sense of policy choices: understanding the roles of value predispositions, mass media, and cognitive processing in public attitudes toward nanotechnology

Using a nationally representative telephone survey of 1,015 adults in the United States, this study examines how value predispositions, communication variables, and perceptions of risks and benefits are associated with public support for federal funding of nanotechnology. Our findings show that highly religious individuals were less supportive of funding of nanotech than less religious individuals, whereas individuals who held a high deference for scientific authority were more supportive of funding of the emerging technology than those low in deference. Mass media use and elaborative processing of scientific news were positively associated with public support for funding, whereas factual scientific knowledge had no significant association with policy choices. The findings suggest that thinking about and reflecting upon scientific news promote better understanding of the scientific world and may provide a more sophisticated cognitive structure for the public to form opinions about nanotech than factual scientific knowledge. Finally, heuristic cues including trust in scientists and perceived risks and benefits of nanotech were found to be associated with public support for nanotech funding. We conclude with policy implications that will be useful for policymakers and science communication practitioners

Targeted emission reductions from global super-polluting power plant units

There are more than 30,000 biomass- and fossil-fuel-burning power plants now operating worldwide, reflecting a tremendously diverse infrastructure, which ranges in capacity from less than a megawatt to more than a gigawatt. In 2010, 68.7% of electricity generated globally came from these power plants, compared with 64.2% in 1990. Although the electricity generated by this infrastructure is vital to economic activity worldwide, it also produces more CO2 and air pollutant emissions than infrastructure from any other industrial sector. Here, we assess fuel- and region-specific opportunities for reducing undesirable air pollutant emissions using a newly developed emission dataset at the level of individual generating units. For example, we find that retiring or installing emission control technologies on units representing 0.8% of the global coal-fired power plant capacity could reduce levels of PM2.5 emissions by 7.7–14.2%. In India and China, retiring coal-fired plants representing 1.8% and 0.8% of total capacity can reduce total PM2.5 emissions from coal-fired plants by 13.2% and 16.0%, respectively. Our results therefore suggest that policies targeting a relatively small number of ‘super-polluting’ units could substantially reduce pollutant emissions and thus the related impacts on both human health and global climate