Diversity in mathematics assessment equals diversity in opinion?

We undertook a study to investigate the views of both students and staff in our department towards assessment in mathematics, as a precursor to considering increasing the diversity of assessment types. In a survey and focus group there was reasonable agreement amongst the students with regards major themes such as mode of assessment. However, this level of agreement was not seen amongst the staff, where discussions regarding diversity in mathematics assessment definitely revealed a difference of opinion. As a consequence, we feel that the greatest barriers to increasing diversity may be with staff, and so more efforts are needed to communicate to staff the advantages and disadvantages, in order to give them greater confidence in trying a range of assessment types.

A self-similar expansion model for use in solar wind transient propogation studies

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient’s speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient’s angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Electricity use in the commercial kitchen

Academic and industrial literature concerning the energy use of commercial kitchens is scarce. Electricity consumption data were collected from distribution board current transformers in a sample of fourteen UK public house-restaurants. This was set up to identify patterns of appliance use as well as to assess the total energy consumption of these establishments. The electricity consumption in the selected commercial kitchens was significantly higher than current literature estimates. On average, 63% of the premises’ electricity consumption was attributed to the catering activity. Key appliances that contributed to the samples average daily electricity consumption of the kitchen were identified as refrigeration (70 kWh, 41%), fryers (11 kWh, 13%), combination ovens (35 kWh, 12%), bain maries (27 kWh, 9%) and grills (37 kWh, 12%). Behavioural factors and poor maintenance were identified as major contributors to excessive electricity usage with potential savings of 70% and 45% respectively. Initiatives are required to influence operator behaviour, such as the expansion of mandatory energy labelling, improved feedback information and the use of behaviour change campaigns. Strict maintenance protocols and more appropriate sizing of refrigeration would be of great benefit to energy reduction.

Pre-Columbian raised-field agriculture and land use in the Bolivian Amazon

We present an integrated palaeoecological and archaeobotanical study of pre-Columbian raised-field agriculture in the Llanos de Moxos, a vast seasonally inundated forest–savanna mosaic in the Bolivian Amazon. Phytoliths from excavated raised-field soil units, together with pollen and charcoal in sediment cores from two oxbow lakes, were analysed to provide a history of land use and agriculture at the El Cerro raised-field site. The construction of raised fields involved the removal of savanna trees, and gallery forest was cleared from the area by AD 310. Despite the low fertility of Llanos de Moxos soils, we determined that pre-Columbian raised-field agriculture sufficiently improved soil conditions for maize cultivation. Fire was used as a common management practice until AD 1300, at which point, the land-use strategy shifted towards less frequent burning of savannas and raised fields. Alongside a reduction in the use of fire, sweet potato cultivation and the exploitation of Inga fruits formed part of a mixed resource strategy from AD 1300 to 1450. The pre-Columbian impact on the landscape began to lessen around AD 1450, as shown by an increase in savanna trees and gallery forest. Although agriculture at the site began to decline prior to European arrival, the abandonment of raised fields was protracted, with evidence of sweet potato cultivation occurring as late as AD 1800.

Technical note: a simple procedure for removing temporal discontinuities in ERA-Interim upper stratospheric temperatures for use in nudged chemistry-climate model simulations

This note describes a simple procedure for removing unphysical temporal discontinuities in ERA-Interim upper stratospheric global mean temperatures in March 1985 and August 1998 that have arisen due to changes in satellite radiance data used in the assimilation. The derived temperature adjustments (offsets) are suitable for use in stratosphere-resolving chemistry-climate models that are nudged (relaxed) to ERA-Interim winds and temperatures. Simulations using a nudged version of the Canadian Middle Atmosphere Model (CMAM) show that the inclusion of the temperature adjustments produces temperature time series that are devoid of the large jumps in 1985 and 1998. Due to its strong temperature dependence, the simulated upper stratospheric ozone is also shown to vary smoothly in time, unlike in a nudged simulation without the adjustments where abrupt changes in ozone occur at the times of the temperature jumps. While the adjustments to the ERA-Interim temperatures remove significant artefacts in the nudged CMAM simulation, spurious transient effects that arise due to water vapour and persist for about 5 yr after the 1979 switch to ERA-Interim data are identified, underlining the need for caution when analysing trends in runs nudged to reanalyses.

A low-cost wireless temperature sensor: evaluation for use in environmental applications

With a wide range of applications benefiting from dense network air temperature observations but with limitations of costs, existing siting guidelines and risk of damage to sensors, new methods are required to gain a high resolution understanding of the spatio-temporal patterns of urban meteorological phenomena such as the urban heat island or precision farming needs. With the launch of a new generation of low cost sensors it is possible to deploy a network to monitor air temperature at finer spatial resolutions. Here we investigate the Aginova Sentinel Micro (ASM) sensor with a bespoke radiation shield (together < US$150) which can provide secure near-real-time air temperature data to a server utilising existing (or user deployed) Wireless Fidelity (Wi-Fi) networks. This makes it ideally suited for deployment where wireless communications readily exist, notably urban areas. Assessment of the performance of the ASM relative to traceable standards in a water bath and atmospheric chamber show it to have good measurement accuracy with mean errors < ± 0.22 °C between -25 and 30 °C, with a time constant in ambient air of 110 ± 15 s. Subsequent field tests of it within the bespoke shield also had excellent performance (root-mean-square error = 0.13 °C) over a range of meteorological conditions relative to a traceable operational UK Met Office platinum resistance thermometer. These results indicate that the ASM and bespoke shield are more than fit-for-purpose for dense network deployment in urban areas at relatively low cost compared to existing observation techniques.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Phospholipid-based microemulsions suitable for use in foods

The preparation of nonaqueous microemulsions using food-acceptable components is reported. The effect of oil on the formation of microemulsions stabilized by lecithin (Epikuron 200) and containing propylene glycol as immiscible solvent was investigated. When the triglycerides were used as oil, three types of phase behavior were noted, namely, a two-phase cloudy region (occurring at low lecithin concentrations), a liquid crystalline (LC) phase (occurring at high surfactant and low oil concentrations), and a clear monophasic microemulsion region. The extent of this clear one-phase region was found to be dependent upon the molecular volume of the oil being solubilized. Large molecular volume oils, such as soybean and sunflower oils, produced a small microemulsion region, whereas the smallest molecular volume triglyceride, tributyrin, produced a large, clear monophasic region. Use of the ethyl ester, ethyl oleate, as oil produced a clear, monophasic region of a size comparable to that seen with tributyrin. Substitution of some of the propylene glycol with water greatly reduced the extent of the clear one-phase region and increased the extent of the liquid crystalline region. In contrast, ethanol enhanced the clear, monophasic region by decreasing the LC phase. Replacement of some of the lecithin with the micelle-forming nonionic surfactant Tween 80 to produce mixed lecithin/Tween 80 mixtures of weight ratios (Km) 1:2 and 1:3 did not significantly alter the phase behavior, although there was a marginal increase in the area of the two-phase, cloudy region of the phase diagram. The use of the lower phosphatidylcholine content lecithin, Epikuron 170, in place of Epikuron 200 resulted in a reduction in the LC region for all of the systems investigated. In conclusion, these studies show that it is possible to prepare one-phase, clear lecithin-based microemulsions over a wide range of compositions using components that are food-acceptable.

Modeling plant transpiration under limited soil water: comparison of different plant and soil hydraulic parameterizations and preliminary implications for their use in land surface models

Accurate estimates of how soil water stress affects plant transpiration are crucial for reliable land surface model (LSM) predictions. Current LSMs generally use a water stress factor, β, dependent on soil moisture content, θ, that ranges linearly between β = 1 for unstressed vegetation and β = 0 when wilting point is reached. This paper explores the feasibility of replacing the current approach with equations that use soil water potential as their independent variable, or with a set of equations that involve hydraulic and chemical signaling, thereby ensuring feedbacks between the entire soil–root–xylem–leaf system. A comparison with the original linear θ-based water stress parameterization, and with its improved curvi-linear version, was conducted. Assessment of model suitability was focused on their ability to simulate the correct (as derived from experimental data) curve shape of relative transpiration versus fraction of transpirable soil water. We used model sensitivity analyses under progressive soil drying conditions, employing two commonly used approaches to calculate water retention and hydraulic conductivity curves. Furthermore, for each of these hydraulic parameterizations we used two different parameter sets, for 3 soil texture types; a total of 12 soil hydraulic permutations. Results showed that the resulting transpiration reduction functions (TRFs) varied considerably among the models. The fact that soil hydraulic conductivity played a major role in the model that involved hydraulic and chemical signaling led to unrealistic values of β, and hence TRF, for many soil hydraulic parameter sets. However, this model is much better equipped to simulate the behavior of different plant species. Based on these findings, we only recommend implementation of this approach into LSMs if great care with choice of soil hydraulic parameters is taken

Agroforestry: integrating apple and arable production as an approach to reducing copper use in organic and low-input apple production

Integrating top fruit production into an agroforestry system, where trees are integrated with arable crop production may have a beneficial effect on the control of plant pathogens such as scab (Venturia inaequalis). Apple yields and pest and disease levels were assessed in a novel apple/arable agroforestry system in Suffolk, and compared with a modern local organic orchard in 2012. Despite 2012 being a very bad year for apple production in the UK, apple yields in the agroforestry system appeared to be comparable with standard figures when scaled up from 2.5% land area under apple production to 100% apples, and even at just 2.5% cover, outperformed the organic orchard used for comparison. Initial indications are that scab levels were over twice as high in the organic orchard than in the agroforestry, indicating that this approach may offer some potential in reducing copper use in organic apple production. However, further research will be required to confirm these early results.