Phases of the excitonic condensate in two-layer graphene

Two graphene monolayers that are oppositely charged and placed close to each other are considered. Taking into account valley and spin degeneracy of electrons we analyze the symmetry of the excitonic insulator states in such a system and build a phase diagram that takes into account the effect of the symmetry breaking due to the external in-plane magnetic field and the carrier density imbalance between the layers.Comment: 12 pages, 6 figures, 1 tabl

Maximal Abelian Subgroups of the Isometry and Conformal Groups of Euclidean and Minkowski Spaces

The maximal Abelian subalgebras of the Euclidean e(p,0) and pseudoeuclidean e(p,1)Lie algebras are classified into conjugacy classes under the action of the corresponding Lie groups E(p,0) and E(p,1), and also under the conformal groups O(p+1,1) and O(p+1,2), respectively. The results are presented in terms of decomposition theorems. For e(p,0) orthogonally indecomposable MASAs exist only for p=1 and p=2. For e(p,1), on the other hand, orthogonally indecomposable MASAs exist for all values of p. The results are used to construct new coordinate systems in which wave equations and Hamilton-Jacobi equations allow the separation of variables.Comment: 31 pages, Latex (+ latexsym

Специальные факторы в ограничениях неприводимых модулей специальной линейной и симплектической групп на подсистемные подгруппы с двумя простыми компонентами

The restrictions of irreducible modules of special linear and symplectic groups in an odd characteristic p with p-large highest weights to a subsystem subgroup H of maximal rank with two simple components H1 and H2 are considered. The lower estimate for the number of composition factors for such restrictions, which are p-large for the subgroup H1 and are not too small for H2, is found. The lower estimates of the number of Jordan blocks of maximal size for the images of certain unipotent elements in the corresponding representations of such groups are determined. Рассматриваются ограничения неприводимых модулей специальной линейной и симплектической групп в нечетной характеристике p с большими относительно p старшими весами на подсистемную подгруппу H максимального ранга с двумя простыми компонентами H1 и H2. Найдена нижняя оценка числа композиционных факторов таких ограничений, которые являются p-большими для подгруппы H1 и не слишком малы для H2. На этой основе получены нижние оценки для числа блоков Жордана максимальной размерности у образов определенных унипотентных элементов в соответствующих представлениях рассматриваемых групп.

Estimating expansion of the range of oak processionary moth ( Thaumetopoea processionea ) in the UK from 2006 to 2019

Funder: Department for Environment, Food and Rural Affairs, UK GovernmentAbstract: The expansion of oak processionary moth (OPM) in South‐East England continues despite ongoing efforts to control the pest since its introduction in 2006. Using locations of OPM larval nests, supplied by the Forestry Commission and recorded as part of ongoing surveillance and control measures from 2006 onwards, we show that the expansion of the range of OPM in South‐East England up to 2019 was biphasic with a higher rate of expansion from 2015 onwards. The maximum rate of OPM range expansion in the United Kingdom from 2006 to 2014 was estimated as 1.66 km/year (95% CI = [1.22, 2.09]), whereas the 2015–2019 expansion rate was estimated as 6.17 km/year (95% CI = [5.49, 6.84]). This corresponds to an estimated species range distribution area of 7077 km2 in 2019. To explain the faster expansion of OPM range from 2015 onwards, we discuss potential reasons that include: natural capability of species of both short‐ and long‐distance dispersal; external factors such as environmental heterogeneity; a reduction of active control

Matrix Groups

VIII, 252 tr.; 23 cm