Torsion points on elliptic curves over number fields of small degree

We determine the set $S(d)$ of possible prime orders of $K$-rational points on elliptic curves over number fields $K$ of degree $d$, for $d = 4,5$ and $6$

UK governance after Brexit: yet more variable and even more disjointed

Michael Kenny and Jack Sheldon write that, although May's government has been prepared to make various concessions in its dealings with the devolved governments, tricky intergovernmental negotiations relating to Brexit are in line. How these will be managed will be one of the most difficult aspects of the Brexit process

New Records for \u3ci\u3eEuhrychiopsis Lecontei\u3c/i\u3e (Coleoptera: Curculionidae) and Their Densities in Wisconsin Lakes

The native aquatic weevil, Euhrychiopsis lecontei is currently being researched as a potential biological control for the exotic aquatic macrophyte Eurasian watermilfoil (Myriophyllum spicatum), yet little is known about its specific distribution in North America. In this study, E. lecontei was collected in 25 of 27 lakes surveyed for the weevil in Wisconsin, greatly increasing the known distribution of the species in this state. E. lecontei densities evaluated in 14 Wisconsin lakes ranged from \u3c0.01 to 1.91 weevils per apical stem of milfoil. These new records indicate that E. lecontei is widespread throughout Wisconsin and is associated with natural declines of M. spicatum in some lakes. Additional sampling for E. lecontei and research on its ecology and life history are needed to understand the role of this organism in aquatic ecosystems

Euhrychiopsis lecontei distribution, abundance, and experimental augmentations for Eurasian watermilfoil control in Wisconsin lakes

The specialist aquatic herbivore Euhrychiopsis lecontei (Dietz) is currently being researched as a potential biological control agent for Eurasian watermilfoil (Myriophyllum spicatum L.). Our research in Wisconsin focused on 1) determining milfoil weevil distribution across lakes, 2) assessing limnological characteristics associated with their abundance, and 3) evaluating milfoil weevil augmentation as a practical management tool for controlling Eurasian watermilfoil

Temporal and spatial changes in milfoil distribution and biomass associated with weevils in Fish Lake, WI

During the course of an eight year monitoring effort, the Wisconsin Department of Natural Resources documented a significant decline in milfoil biomass and distribution in Fish Lake, Wisconsin. Average milfoil biomass declined by 40- 50% from 374-524 g dw m -2 during 1991-93 to 265 g dw m -2 during both 1994 and 1995. Milfoil recovered fully in 1996- 98 to 446- 564 g dw m -2 . The size of the milfoil bed, as discerned from aerial photographs, shrank from a maximum coverage of 40 ha in 1991 to less than 20 ha during 1995. During the “crash” of 1994-95, milfoil plants exhibited typical signs of weevil-induced damage, including darkened, brittle, hollowed-out growing tips, and the arching and collapse of stems associated with loss of buoyancy. Monitoring of weevils and stem damage during 1995-98 showed highest densities and heaviest damage occurred near shore and subsequently fanned out into deeper water from core infestation sites each spring. The extent of milfoil stem damage was positively correlated with weevil densities (monthly sampling). However, weevil densities and stem damage were lower during 1995 (when milfoil biomass was in decline) than during 1996-98 (when milfoil biomass was fully recovered)

How can Boris Johnson keep the UK together?

Michael Kenny and Jack Sheldon discuss how Boris Johnson should approach intergovernmental matters in relation to Scotland and Northern Ireland