The mixed problem in Lipschitz domains with general decompositions of the boundary

This paper continues the study of the mixed problem for the Laplacian. We consider a bounded Lipschitz domain $\Omega\subset \reals^n$, $n\geq2$, with boundary that is decomposed as $\partial\Omega=D\cup N$, $D$ and $N$ disjoint. We let $\Lambda$ denote the boundary of $D$ (relative to $\partial\Omega$) and impose conditions on the dimension and shape of $\Lambda$ and the sets $N$ and $D$. Under these geometric criteria, we show that there exists $p_0>1$ depending on the domain $\Omega$ such that for $p$ in the interval $(1,p_0)$, the mixed problem with Neumann data in the space $L^p(N)$ and Dirichlet data in the Sobolev space $W^ {1,p}(D)$ has a unique solution with the non-tangential maximal function of the gradient of the solution in $L^p(\partial\Omega)$. We also obtain results for $p=1$ when the Dirichlet and Neumann data comes from Hardy spaces, and a result when the boundary data comes from weighted Sobolev spaces.Comment: 36 page

The Drosophila genome nexus: a population genomic resource of 623 Drosophila melanogaster genomes, including 197 from a single ancestral range population.

Hundreds of wild-derived Drosophila melanogaster genomes have been published, but rigorous comparisons across data sets are precluded by differences in alignment methodology. The most common approach to reference-based genome assembly is a single round of alignment followed by quality filtering and variant detection. We evaluated variations and extensions of this approach and settled on an assembly strategy that utilizes two alignment programs and incorporates both substitutions and short indels to construct an updated reference for a second round of mapping prior to final variant detection. Utilizing this approach, we reassembled published D. melanogaster population genomic data sets and added unpublished genomes from several sub-Saharan populations. Most notably, we present aligned data from phase 3 of the Drosophila Population Genomics Project (DPGP3), which provides 197 genomes from a single ancestral range population of D. melanogaster (from Zambia). The large sample size, high genetic diversity, and potentially simpler demographic history of the DPGP3 sample will make this a highly valuable resource for fundamental population genetic research. The complete set of assemblies described here, termed the Drosophila Genome Nexus, presently comprises 623 consistently aligned genomes and is publicly available in multiple formats with supporting documentation and bioinformatic tools. This resource will greatly facilitate population genomic analysis in this model species by reducing the methodological differences between data sets

Technical Performance Reduces during the Extra-Time Period of Professional Soccer Match-Play

Despite the importance of extra-time in determining progression in specific soccer tournament matches, few studies have profiled the demands of 120-minutes of soccer match-play. With a specific focus on the extra-time period, and using a within-match approach, we examined the influence of prolonged durations of professional soccer match-play on markers of technical (i.e., skilled) performance. In 18 matches involving professional European teams played between 2010 and 2014, this retrospective study quantified the technical actions observed during eight 15-minute epochs (E1: 00:00–14:59 min, E2: 15:00-29:59 min, E3: 30:00-44:59 min, E4: 45:00-59:59 min, E5: 60:00-74:59 min, E6: 75:00-89:59 min, E7: 90:00-104:59 min, E8: 105:00-119:59 min). Analysis of players who completed the demands of the full 120 min of match-play revealed that the cumulative number of successful passes observed during E8 (61±23) was lower than E1-4 (E1: 88±23, P=0.001; E2: 77±21, P=0.005; E3: 79±18, P=0.001; E4: 80±21, P=0.001) and E7 (73±20, P=0.002). Similarly, the total number of passes made in E8 (71±25) was reduced when compared to E1 (102±22, P=0.001), E3 (91±19, P=0.002), E4 (93±22, P≤0.0005) and E7 (84±20, P=0.001). The cumulative number of successful dribbles reduced in E8 (9±4) when compared to E1 (14±4, P=0.001) and E3 (12±4, P≤0.0005) and the total time the ball was in play was less in E8 (504±61 s) compared to E1 (598±70 s, P≤0.0005). These results demonstrate that match-specific factors reduced particular indices of technical performance in the second half of extra-time. Interventions that seek to maintain skilled performance throughout extra-time warrant further investigation

Conservation of a crystallographic interface suggests a role for β-sheet augmentation in influenza virus NS1 multifunctionality

The structure of a monomeric effector domain from influenza A virus NS1 is presented from diffraction data extending to 1.8 Å resolution. Comparison of this and other NS1 effector-domain structures shows conformational changes at a strand–strand packing interface, hinting at a role for β-strand augmentation in NS1 function

Observations of Mesospheric Temperature Variability Over the Andes

Observations of mesospheric OH(6,2) rotational temperatures by the Utah State University Mesospheric Temperature Mapper (MTM) located at the Andes Lidar Observatory, Cerro Pachon, Chile (30.3°S, 70.7°S) reveal a large range of nightly variations induced by atmospheric gravity waves and tides, as well as strong seasonal oscillations. This study investigates MTM temperature variability over the past 3.5 years comprising over 800 nights of high-quality data and compares the results with ground-based spectrometric measurements from nearby El Leoncito Observatory, Argentina, Maui-MALT, Hawaii MTM measurements (2001-2005) and coincident mesospheric temperature measurement by SABER on the NASA TIMED satellite

Prospects for local co-governance

British local authorities and their partners are increasingly developing new ways of working together with local communities. The nature of this co-working, however, is complex, multi-faceted and little understood. This article argues for greater clarity of thinking on the topic, by analysing this co-working as a form of political co-governance, and drawing attention in particular to issues of scale and democracy. Using evidence from a study of 43 local authority areas, 16 authorities are identified where co-governance is practised, following three main types of approach: service-influencing, service-delivering and parish council developing. It is concluded that strengthening political co-governance is essential for a healthy democracy

Heat and fluid flow in a scraped-surface heat exchanger containing a fluid with temperature-dependent viscosity

Scraped-surface heat exchangers (SSHEs) are extensively used in a wide variety of industrial settings where the continuous processing of fluids and fluid-like materials is involved. The steady non-isothermal flow of a Newtonian fluid with temperature-dependent viscosity in a narrow-gap SSHE when a constant temperature difference is imposed across the gap between the rotor and the stator is investigated. The mathematical model is formulated and the exact analytical solutions for the heat and fluid flow of a fluid with a general dependence of viscosity on temperature for a general blade shape are obtained. These solutions are then presented for the specific case of an exponential dependence of viscosity on temperature. Asymptotic methods are employed to investigate the behaviour of the solutions in several special limiting geometries and in the limits of weak and strong thermoviscosity. In particular, in the limit of strong thermoviscosity (i.e., strong heating or cooling and/or strong dependence of viscosity on temperature) the transverse and axial velocities become uniform in the bulk of the flow with boundary layers forming either just below the blade and just below the stationary upper wall or just above the blade and just above the moving lower wall. Results are presented for the most realistic case of a linear blade which illustrate the effect of varying the thermoviscosity of the fluid and the geometry of the SSHE on the flow

Revision of Madagascar's Dwarf Lemurs (Cheirogaleidae:Cheirogaleus): Designation of Species, Candidate Species Status and Geographic Boundaries Based on Molecular and Morphological Data

The genus Cheirogaleus, the dwarf lemurs, is a radiation of strepsirrhine primates endemic to the island of Madagascar. The dwarf lemurs are taxonomically grouped in the family Cheirogaleidae (Infraorder: Lemuriformes) along with the genera Microcebus, Mirza, Allocebus, and Phaner. The taxonomic history of the genus Cheirogaleus has been controversial since its inception due to a paucity of evidence in support of some proposed species. In this study, we addressed this issue by expanding the geographic breadth of samples by 91 individuals and built upon existing mitochondrial (cytb and COII) and nuclear (FIBA and vWF) DNA datasets to better resolve the phylogeny of Cheirogaleus. The mitochondrial gene fragments D-loop and PAST as well as the CFTR-PAIRB nuclear loci were also sequenced. In agreement with previous genetic studies, numerous deep divergences were resolved in the C. major, C. minor and C. medius lineages. Four of these lineages were segregated as new species, seven were identified as confirmed candidate species, and four were designated as unconfirmed candidate species based on comparative mitochondrial DNA sequence data gleaned from the literature or this study. Additionally, C. thomasi was resurrected. Given the widespread distribution of the genus Cheirogaleus throughout Madagascar, the methodology employed in this study combined all available lines of evidence to standardize investigative procedures in a genus with limited access to type material and a lack of comprehensive sampling across its total distribution. Our results highlighted lineages that likely represent new species and identified localities that may harbor an as-yet undescribed cryptic species diversity pending further field and laboratory work.We are most grateful to the Ahmanson Foundation, the Theodore F. and Claire M. Hubbard Family Foundation, the Primate Action Fund / Conservation International, the Margot Marsh Biodiversity Foundation, and the National Geographic Society, for financial assistance