The monic integer transfinite diameter

We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter t_M(I) is defined as the infimum of all such supremums. We show that if I has length 1 then t_M(I) = 1/2. We make three general conjectures relating to the value of t_M(I) for intervals I of length less that 4. We also conjecture a value for t_M([0, b]) where 0 < b < 1. We give some partial results, as well as computational evidence, to support these conjectures. We define two functions that measure properties of the lengths of intervals I with t_M(I) on either side of t. Upper and lower bounds are given for these functions. We also consider the problem of determining t_M(I) when I is a Farey interval. We prove that a conjecture of Borwein, Pinner and Pritsker concerning this value is true for an infinite family of Farey intervals.Comment: 32 pages, 5 figure

On univoque Pisot numbers

We study Pisot numbers $\beta \in (1, 2)$ which are univoque, i.e., such that there exists only one representation of 1 as $1 = \sum_{n \geq 1} s_n\beta^{-n}$, with $s_n \in \{0, 1\}$. We prove in particular that there exists a smallest univoque Pisot number, which has degree 14. Furthermore we give the smallest limit point of the set of univoque Pisot numbers.Comment: Accepted by Mathematics of COmputatio

Hydrogeological control on spatial patterns of groundwater seepage in peatlands

Groundwater seepage to surface water is an important process to peatland ecosystems; however, the processes controlling seepage zone distribution and magnitude are not well understood. This lack of process-based understanding makes degraded peatland ecosystems difficult to restore and problematic for resource managers developing a sustainable design. Degraded peatlands, particularly abandoned cranberry farms, often have drainage ditches, applied surface sand, and decreased stream sinuosity to artificially lower the water table and support agriculture. These modifications disconnect the surface and groundwater continuum, which decreases thermal buffering of surface water significantly. The combination of a decreased influx of thermally buffered groundwater, a naturally low surface gradient, minimal canopy, and strong solar input causes surface water temperature extremes that degrade ecosystem health. Through strategically incorporating the natural processes to restore groundwater discharge to restored surface streams, surface water temperature extremes will be buffered promoting a healthy, resilient wetland ecosystem. Therefore, it is critical to understand the spatial hydrogeologic constraints that induce groundwater seepage. Here we examine the spatial relationship between surficial groundwater seepage and the subsurface hydrogeologic structure within a mineraltrophic peatland environment. We use multiple field methods to develop a process-based conceptual model of the ground water seepage development at the site; these methods include geophysical, thermal, and isotopic techniques. The results indicate that there are two distinct forms of groundwater discharge to the peatland platform: diffuse lower-flux marginal seepage and discrete higher-flux interior seepage. Both types of groundwater discharge develop through interactions with subsurface peatland basin structure, specifically when the basin slope is perpendicular to the regional groundwater gradient. These observations also allow insight into the formation of the groundwater discharge through time. The strong correlation between the subsurface basin structure and surficial groundwater expression will allow resource managers to more efficiently locate groundwater seepage on large, complex sites, and develop comprehensive management and restoration strategies for these critical ecosystems

A comparison of manual handling risks in different domestic waste collection systems using three separate evaluation methods

One of the greatest challenges for Local Authorities (LAs) is to operate sustainable systems of work. The most significant causes of physical absence is attributed to that of musculoskeletal disorders (MSDs). The study’s aim was to compare the reliability of the manual handling element of the Health and Safety Executives (HSEs) risk comparator tool for different domestic waste collection methods with self-reported pain via body-mapping and MSD ill health absence rates. Participatory body-mapping exercises were carried out in five authorities with one authority resurveyed, six months after the move from 35-50 litre containers to a wheeled bin recycling service. The lowest levels of self-reported pain were for services designed with 240l wheeled bins excluding glass; the highest levels were for services that included 100l of garden waste sacks and recycling boxes. Industry data supports previous laboratory studies showing wheeled bins to be associated with less MSD outcomes than boxes, baskets and sacks. Triangulation of data established a statistically significant correlation of 0.85 (Pearson) between average pain count (APC) and the mean MSD absence rates, with a strong correlation of 0.77 (Spearman) between APC and risk rating. The correlation is moderate, 0.49, (Spearman) between MSD absence and risk rating, reflecting possible intervening variables and a low participation rate by LAs. The contribution of this study is to improve the design of sustainable waste collection strategies to minimise MSD associated absence. In the absence of reliable absence data, body mapping should be used as a proxy method of assessing MSD risk

Analysis of the Copenhagen Accord pledges and its global climatic impacts‚ a snapshot of dissonant ambitions

This analysis of the Copenhagen Accord evaluates emission reduction pledges by individual countries against the Accord's climate-related objectives. Probabilistic estimates of the climatic consequences for a set of resulting multi-gas scenarios over the 21st century are calculated with a reduced complexity climate model, yielding global temperature increase and atmospheric CO2 and CO2-equivalent concentrations. Provisions for banked surplus emission allowances and credits from land use, land-use change and forestry are assessed and are shown to have the potential to lead to significant deterioration of the ambition levels implied by the pledges in 2020. This analysis demonstrates that the Copenhagen Accord and the pledges made under it represent a set of dissonant ambitions. The ambition level of the current pledges for 2020 and the lack of commonly agreed goals for 2050 place in peril the Accord's own ambition: to limit global warming to below 2 °C, and even more so for 1.5 °C, which is referenced in the Accord in association with potentially strengthening the long-term temperature goal in 2015. Due to the limited level of ambition by 2020, the ability to limit emissions afterwards to pathways consistent with either the 2 or 1.5 °C goal is likely to become less feasibl

Amino acids precursors in lunar finds

The consistent pattern is discussed of amino acids found in lunar dust from Apollo missions. The evidence indicates that compounds yielding amino acids were implanted into the surface of the moon by the solar wind, and the kind and amounts of amino acids found on the moon are closely similar to those found in meteorites. It is concluded that there is a common cosmochemical pattern for the moom and meteorites, and this offers evidence of a common course of cosmochemical reactions for carbon

Expatriation of Xyrichtys novacula (Pisces: Labridae) larvae: Evidence of rapid cross-slope exchange

Larvae of Xyrichtys novacula (Pisces: Labridae) have been collected in the Middle Atlantic Bight (MAB) hundreds of kilometers north of reported adult ranges by both the Marine Monitoring and Assessment Program (MARMAP) and by our ichthyoplankton cruises. These larvae could be from a previously unknown population north of Cape Hatteras or they could have been transported north from southern populations. In order to examine these two hypotheses both biological and physical oceanographic data were considered, including size-specific larval distribution, larval age, vertical distribution of larvae, satellite imagery of sea surface temperature, and temperature and salinity measurements. Larvae captured during our 1988 ichthyoplankton cruises ranged from 3.11 mm to 13.13 mm in length with small larvae (≤5 mm) found in association with the shelf break and larger larvae (\u3e5 mm) found distributed across the outer shelf and shelf break. Based on aging of daily otolith increments larval age was found to range from 7 to 36 days and backcalculated birthdates, derived from estimated age and date of capture, were found to be from mid-June to early August. Larvae occurred predominantly near the surface (≤10 m) at night and deeper (\u3e10 m) during the day. Concurrent hydrographic data revealed that small larvae were found in shelf water (\u3c35 psu) but with underlying slope water (\u3e35 psu) at depths of 15–30 m suggesting that small larvae were in shelf water at night but either at the boundary with or within slope water during the day. Satellite imagery from 1988 revealed a warm-core ring offshore of our 1988 sampling area. An analysis of historical warm-core ring data from Northwest Atlantic Fisheries Organization data reports in conjunction with captures of X. novacula during the years 1984–1987 demonstrated that the presence of warm-core rings offshore was associated with the occurrence of X. novacula on the MAB shelf, north of Chesapeake Bay. The feasibility of northward transport associated with the Gulf Stream and cross-slope transport associated with a warm-core ring was examined with a simple model which demonstrated that the required transport velocities were within the range of velocities presented in the literature. It is suggested that larvae are rapidly transported from south of Cape Hatteras to the MAB shelf break by advection associated with the Gulf Stream and a concomitant cross-slope flow related with the western edge of warm-core rings