Quantum supergroups V. Braid group action

We construct a braid group action on quantum covering groups. We further use this action to construct a PBW basis for the positive half in finite type which is pairwise-orthogonal under the inner product. This braid group action is induced by operators on the integrable modules; however, these operators satisfy spin braid relations.Comment: v1. 31 pages v2. minor revisions, updated references, to appear in CM

Darboux transformations for differential operators on the superline

We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of order one. Similar statement holds for operators on the ordinary line

A Review of Time Relaxation Methods

The time relaxation model has proven to be effective in regularization of Navier–Stokes Equations. This article reviews several published works discussing the development and implementations of time relaxation and time relaxation models (TRMs), and how such techniques are used to improve the accuracy and stability of fluid flow problems with higher Reynolds numbers. Several analyses and computational settings of TRMs are surveyed, along with parameter sensitivity studies and hybrid implementations of time relaxation operators with different regularization techniques

Genetic diversity and structure of calanoid copepods: Molecular evolutionary patterns in coastal estuaries (Acartia tonsa) and the open ocean (Calanus spp)

Calanoid copepods are an important part of marine and estuarine ecosystems. However, it has been difficult to study their life histories, population structure, and evolution because they share a conserved morphology that complicates species identification. A primary focus of this study was the genetic and physiological variation of the calanoid copepod Acartia tonsa from four estuaries along the East Coast of the USA (Great Bay, NH, Buzzards Bay, MA, Narragansett Bay, RI, and Beaufort Inlet, NC). Based on DNA sequence variation for the mitochondrial cytochrome oxidase I (mtCOI) gene, significant population structure was observed between all pairs of estuarine populations (phi ST \u3e 0.9, p \u3c 0.0001), except for those of two neighboring estuaries, Buzzards Bay and Narragansett Bay. Based on amplified fragment length polymorphism (AFLP) markers, significant population structure was observed between Buzzards Bay and Narragansett Bay (thetaB = 0.042, 95% CI: 0.024--0.065). Individuals from the four estuarine populations were shown to interbreed with each other in reciprocal crosses in laboratory cultures. Crosses between individuals from Great Bay, NH and the other populations failed to produce fertile offspring. Thus, according to both the biological and evolutionary species concepts, the Great Bay, NH population of A. tonsa should be considered to be a different species from the Buzzards Bay, MA; Narragansett Bay, RI; and Beaufort Inlet, NC populations. Comparisons of physiological responses to high and low temperatures of Great Bay and Beaufort Inlet populations yielded evidence of significantly different responses to temperature extremes. Attempts to induce females to lay diapause egg by exposing them to low temperatures and short photoperiods produced only quiescent eggs. It was concluded that the currently identified group of A. tonsa contains at least two cryptic species that are genetically diverse, potentially evolutionarily and taxonomically distinct, and morphologically identical. The second focus of this study was a parallel analysis of nine species of Calanus based on DNA sequence variation of mtCOI. There was significant genetic divergence between all species, which was used to reconstruct the phylogenetic relationship among the species. The molecular phylogeny was in good agreement with hypotheses of evolutionary relationships based on morphological characters. The DNA sequences were also used to develop a PCR-based molecular protocol to rapidly identify four of the species of Calanus with very similar morphologies and overlapping geographic ranges. Considered together, the results of these studies showed that the conserved morphology of the calanoid copepods harbor a large amount of genetic diversity, which can be used to identify species and reconstruct their evolutionary relationships. These studies have also indicated that the true diversity of calanoid copepods is yet to be discovered