Positive values of inhomogeneous quinary quadratic forms of type (4,1)

Here it is proved that if Q(x, y, z, t, u) is a real indefinite quinary quadratic form of type (4,1) and determinant D, then given any real numbers x0, y0, z0, t0, u0 there exist integers x, y, z, t, u such that 0 < Q(x+x0, y+y0, z+z0, t+t0, u+u0)<|D|1/3

Positive values of inhomogeneous 5-ary quadratic forms of type (3, 2)

Let Q(x, y, z, t, u) be a real indefinite 5-ary quadratic form of type (3,2) and determinant D(> 0). Then given any real numbers x0, y0, z0, t0, u0 there exist integers x, y, z, t, u such that 0 < Q(x+x0,y+y0,z+z0,t+t0,u+u0)≤(16D)1/5. All the critical forms are also determined

Effect of rib roughness pitch on thermal and thermo-hydraulic performance of a solar air heater roughened artificially with arc rib having gap

This experimental study on a solar air heater having absorber plate roughened artificially by providing roughness in the form of arc ribs having gap was carried out in the Department of Mechanical Engineering, Punjab Agricultural University, Ludhiana, India to study the effect of relative roughness pitch on thermal and thermohydraulic performance as well as to compare the performance of arc rib with gap roughened solar air heater with that of continuous arc rib roughened solar air heater. The roughness geometry parameters included relative roughness height of 0.043, angle of attack of 30 degree, relative gap position of 0.80, gap-width equal to the width of the rib and five values of relative roughness pitch ranging from 4 to 12 for flow Reynolds number range of 2000 to 16,000. The Nusselt number and friction factor were found to be more for relative roughness pitch value of 10 as compared to other values of relative roughness pitch. Thermo-hydraulic performance of solar air heaters roughened by arc with gap and continuous arc roughness geometries were found to be 1.91 times and 1.78 times respectively as compared to that of solar air heater having smooth absorber plate due to generation of turbulence in laminar sublayer region. However, improvement in thermo-hydraulic performance of solar air heater roughened by arc with gap geometry over continuous arc rib roughened solar air heater was attributed to generation of a region of turbulence on downstream side of the gap

Using a composite flow law to model deformation in the NEEM deep ice core, Greenland — Part 2: The role of grain size and premelting on ice deformation at high homologous temperature

The ice microstructure in the lower part of the North Greenland Eemian Ice Drilling (NEEM) ice core consists of relatively fine-grained ice with a single maximum crystallographic preferred orientation (CPO) alternated by much coarser-grained ice with a partial (great circle) girdle or multi-maxima CPO. In this study, the grain-size-sensitive (GSS) composite flow law of Goldsby and Kohlstedt (2001) was used to study the effects of grain size and premelting (liquid-like layer along the grain boundaries) on strain rate in the lower part of the NEEM ice core. The results show that the strain rates predicted in the fine-grained layers are about an order of magnitude higher than in the much coarser-grained layers. The dominant deformation mechanisms, based on the flow relation of Goldsby and Kohlstedt (2001), between the layers is also different, with basal slip rate limited by grain boundary sliding (GBS-limited creep) being the dominant deformation mechanism in the finer-grained layers, while GBS-limited creep and dislocation creep (basal slip rate limited by non-basal slip) contribute both roughly equally to bulk strain in the coarse-grained layers. Due to the large difference in microstructure between finer-grained ice and the coarse-grained ice at premelting temperatures (T>262 K), it is expected that the fine-grained layers deform at high strain rates, while the coarse-grained layers are relatively stagnant. The difference in microstructure, and consequently in viscosity, between impurity-rich and low-impurity ice can have important consequences for ice dynamics close to the bedrock

Positive Values of Non-homogeneous Indefinite Quadratic Forms of Type (2, 4)

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Hafnium isotopic variations in East Atlantic intraplate volcanism

The broad belt of intraplate volcanism in the East Atlantic between 25° and 37° N is proposed to have formed by two adjacent hotspot tracks (the Madeira and Canary tracks) that possess systematically different isotopic signatures reflecting different mantle source compositions. To test this model, Hf isotope ratios from volcanic rocks from all individual islands and all major seamounts are presented in this study. In comparison with published Nd isotope variations (6 εNd units), 176Hf/177Hf ratios span a much larger range (14 εHf units). Samples from the proposed Madeira hotspot track have the most radiogenic Hf isotopic compositions (176Hf/177Hfm up to 0.283335), extending across the entire field for central Atlantic MORB. They form a relatively narrow, elongated trend on the Nd vs. Hf isotope diagram (stretching over >10 εHf units) between a depleted N-MORB-like endmember and a moderately enriched composition located on, or slightly below, the Nd–Hf mantle array, which overlaps the proposed "C" mantle component of Hanan and Graham (1996). In contrast, all samples from the Canary hotspot track plot below the mantle array (176Hf/177Hfm = 0.282943–0.283067) and form a much denser cluster with less compositional variation (~4 εHf units). The cluster falls between (1) a low Hf isotope HIMUlike endmember, (2) a more depleted composition, and (3) the moderately enriched end of the Madeira trend. The new Hf isotope data confirm the general geochemical distinction of the Canary and Madeira domains in the East Atlantic. Both domains, however, seem to share a common, moderately enriched endmember that has "C"-like isotope compositions and is believed to represent subducted, =1 Ga

No evidence for tephra in Greenland from the historic eruption of Vesuvius in 79 CE: implications for geochronology and paleoclimatology

Volcanic fallout in polar ice sheets provide important opportunities to date and correlate ice-core records as well as to investigate the environmental impacts of eruptions. Only the geochemical characterization of volcanic ash (tephra) embedded in the ice strata can confirm the source of the eruption, however, and is a requisite if historical eruption ages are to be used as valid chronological checks on annual ice layer counting. Here we report the investigation of ash particles in a Greenland ice core that are associated with a volcanic sulfuric acid layer previously attributed to the 79 CE eruption of Vesuvius. Major and trace element composition of the particles indicates that the tephra does not derive from Vesuvius but most likely originates from an unidentified eruption in the Aleutian arc. Using ash dispersal modelling, we find that only an eruption large enough to include stratospheric injection is likely to account for the sizeable (24–85 μm) ash particles observed in the Greenland ice at this time. Despite its likely explosivity, this event does not appear to have triggered significant climate perturbations, unlike some other large extra-tropical eruptions. In light of a recent re-evaluation of the Greenland ice-core chronologies, our findings further challenge the previous assignation of this volcanic event to 79 CE. We highlight the need for the revised Common Era ice-core chronology to be formally accepted by the wider ice-core and climate modelling communities in order to ensure robust age linkages to precisely dated historical and paleoclimate proxy records

A Framework on the Emergence and Effectiveness of Global Health Networks

Since 1990 mortality and morbidity decline has been more extensive for some conditions prevalent in low- and middle-income countries than for others. One reason may be differences in the effectiveness of global health networks, which have proliferated in recent years. Some may be more capable than others in attracting attention to a condition, in generating funding, in developing interventions and in convincing national governments to adopt policies. This article introduces a supplement on the emergence and effectiveness of global health networks. The supplement examines networks concerned with six global health problems: tuberculosis (TB), pneumonia, tobacco use, alcohol harm, maternal mortality and newborn deaths. This article presents a conceptual framework delineating factors that may shape why networks crystallize more easily surrounding some issues than others, and once formed, why some are better able than others to shape policy and public health outcomes. All supplement papers draw on this framework. The framework consists of 10 factors in three categories: (1) features of the networks and actors that comprise them, including leadership, governance arrangements, network composition and framing strategies; (2) conditions in the global policy environment, including potential allies and opponents, funding availability and global expectations concerning which issues should be prioritized; (3) and characteristics of the issue, including severity, tractability and affected groups. The article also explains the design of the project, which is grounded in comparison of networks surrounding three matched issues: TB and pneumonia, tobacco use and alcohol harm, and maternal and newborn survival. Despite similar burden and issue characteristics, there has been considerably greater policy traction for the first in each pair. The supplement articles aim to explain the role of networks in shaping these differences, and collectively represent the first comparative effort to understand the emergence and effectiveness of global health networks