Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

Hillslope scale surface runoff, sediment, and nutrient losses associated with tramline wheelings

Research on arable sandy loam and silty clay loam soils on 4° slopes in England has shown that tramlines (i.e. the unseeded wheeling areas used to facilitate spraying operations in cereal crops) can represent the most important pathway for phosphorus and sediment loss from moderately sloping fields. Detailed monitoring over the October–March period in winters 2005–2006 and 2006–2007 included event-based sampling of surface runoff, suspended and particulate sediment, and dissolved and particulate phosphorus from hillslope segments (each ∼300–800 m2) established in a randomized block design with four replicates of each treatment at each of two sites on lighter and heavier soils. Experimental treatments assessed losses from the cropped area without tramlines, and from the uncropped tramline area, and were compared to losses from tramlines which had been disrupted once in the autumn with a shallow tine. On the lighter soil, the effects of removal or shallow incorporation of straw residues was also determined. Research on both sandy and silty clay loam soils across two winters showed that tramline wheelings represented the dominant pathway for surface runoff and transport of sediment, phosphorus and nitrogen from cereal crops on moderate slopes. Results indicated 5·5–15·8% of rainfall lost as runoff, and losses of 0·8–2·9 kg TP ha−1 and 0·3–4·8 t ha−1 sediment in tramline treatments, compared to only 0·2–1·7% rainfall lost as runoff, and losses of 0·0–0·2 kg TP ha−1 and 0·003–0·3 t ha−1 sediment from treatments without tramlines or those where tramlines had been disrupted. The novel shallow disruption of tramline wheelings using a tine once following the autumn spray operation consistently and dramatically reduced (p < 0·001) surface runoff and loads of sediment, total nitrogen and total phosphorus to levels similar to those measured in cropped areas between tramlines. Results suggest that options for managing tramline wheelings warrant further refinement and evaluation with a view to incorporating them into spatially-targeted farm-level management planning using national or catchment-based agri-environment policy instruments aimed at reducing diffuse pollution from land to surface water systems. Copyright © 2010 John Wiley & Sons, Ltd.

Determining the cost of in-field mitigation options to reduce sediment and phosphorus loss

The Mitigation Options for Phosphorus and Sediment (MOPS) project investigated the effectiveness of within-field control measures (tramline management, straw residue management, type of cultivation and direction, and vegetative buffers) in terms of mitigating sediment and phosphorus loss from winter-sown combinable cereal crops using three case study sites. To determine the cost of the approaches, simple financial spreadsheet models were constructed at both farm and regional levels. Taking into account crop areas, crop rotation margins per hectare were calculated to reflect the costs of crop establishment, fertiliser and agro-chemical applications, harvesting, and the associated labour and machinery costs. Variable and operating costs associated with each mitigation option were then incorporated to demonstrate the impact on the relevant crop enterprise and crop rotation margins. These costs were then compared to runoff, sediment and phosphorus loss data obtained from monitoring hillslope-length scale field plots. Each of the mitigation options explored in this study had potential for reducing sediment and phosphorus losses from arable land under cereal crops. Sediment losses were reduced from between 9 kg ha−1 to as much as 4780 kg ha−1 with a corresponding reduction in phosphorus loss from 0.03 kg ha−1 to 2.89 kg ha−1. In percentage terms reductions of phosphorus were between 9% and 99%. Impacts on crop rotation margins also varied. Minimum tillage resulted in cost savings (up to £50 ha−1) whilst other options showed increased costs (up to £19 ha−1 for straw residue incorporation). Overall, the results indicate that each of the options has potential for on-farm implementation. However, tramline management appeared to have the greatest potential for reducing runoff, sediment, and phosphorus losses from arable land (between 69% and 99%) and is likely to be considered cost-effective with only a small additional cost of £2–4 ha−1, although further work is needed to evaluate alternative tramline management methods. Tramline management is also the only option not incorporated within current policy mechanisms associated with reducing soil erosion and phosphorus loss and in light of its potential is an approach that should be encouraged once further evidence is available.

Impact of serving method on the consumption of nutritional supplement drinks: randomised trial in older adults with cognitive impairment

Aim: To analyse the influence of serving method on compliance and consumption of nutritional supplement drinks in older adults with cognitive impairment. Background: Oral nutritional supplement drinks have positive benefits on increasing nutritional status within undernourished elderly people leading to weight gain. However, consumption of these drinks is low and therefore limits their effectiveness. Design: This study was a non blind randomised control trial where participants either consumed nutritional supplement drinks in a glass/beaker or consumed them through a straw inserted directly into the container. Method: Participants with longstanding cognitive impairment were recruited from nursing homes (n=31) and hospitals (n=14). Participants were randomised to serving method. Nursing and care staff were instructed to give the supplement drinks three times per day on alternate days over a week by the allocated serving method. The researcher weighed the amount of supplement drink remaining after consumption. Data were collected over 12 months in 2011-2012. Results: 45 people participated in this study mean age 86.7 (SD 7.5 ) years. After randomisation there was no significant difference between the baseline characteristics of the two groups. Participants randomised to consume nutritional drinks from a glass / beaker drank significantly more than those who consumed them via a straw inserted directly into the container. However, supplements allocated to be given in a glass/beaker were more frequently omitted. Conclusion: Nutritional supplement drinks should be given to people with dementia who are able to feed themselves in a glass or a beaker if staffing resources allow (NIHR CSP ref 31101).

Wall materials and techniques available for low cost housing in Khartoum from a sustainability point of view

Khartoum like many cities in least developing countries (LDCs) still witnesses huge influx of people. Accommodation of the new comers leads to encroachment on the cultivation land leads to sprawl expansion of Greater Khartoum. The city expanded in diameter from 16.8 km in 1955 to 802.5 km in 1998. Most of this horizontal expansion was residential. In 2008 Khartoum accommodated 29% of the urban population of Sudan. Today Khartoum is considered as one of 43 major cities in Africa that accommodates more than 1 million inhabitants. Most of new comers live in the outskirts of the city e.g. Dar El-Salam and Mayo neighbourhoods. The majority of those new comers built their houses especially the walls from mud, wood, straw and sacks. Selection of building materials usually depends on its price regardless of the environmental impact, quality, thermal performance and life of the material. Most of the time, this results in increasing the cost with variables of impacts over the environment during the life of the building. Therefore, consideration of the environmental impacts, social impacts and economic impacts is crucial in the selection of any building material. Decreasing such impacts could lead to more sustainable housing. Comparing the sustainability of the available wall building materials for low cost housing in Khartoum is carried out through the life cycle assessment (LCA) technique. The purpose of this paper is to compare the most available local building materials for walls for the urban poor of Khartoum from a sustainability point of view by going through the manufacturing of the materials, the use of these materials and then the disposal of the materials after their life comes to an end. Findings reveal that traditional red bricks couldn’t be considered as a sustainable wall building material that will draw the future of the low cost housing in Greater Khartoum. On the other hand, results of the comparison lead to draw attention to the wide range of the soil techniques and to its potentials to be a promising sustainable wall material for urban low cost housing in Khartoum.

Biochar alteration of the sorption of substrates and products in Soil Enzyme Assays

Pine wood and barley straw biochar amendments to Kettering and Cameroon sandy silt loam soils (15, 30, or 150 mg biochar g−1 soil) caused significant reductions (up to 80%,

The effects of tannin-containing ground pine bark diet upon nutrient digestion, nitrogen balance, and mineral retention in meat goats

Background Pine bark is a rich source of phytochemical compounds including tannins, phenolic acids, anthocyanins, and fatty acids. These phytochemicals have potential to significantly impact on animal health and animal production. The goal of this work is to measure the effects of tannins in ground pine bark as a partial feed replacement on feed intake, dietary apparent digestibility, nitrogen balance, and mineral retention in meat goats. Results Eighteen Kiko cross goats (initial BW = 31.8 ± 1.49 kg) were randomly assigned to three treatment groups (n = 6). Dietary treatments were tested: control (0 % pine bark powder (PB) and 30 % wheat straw (WS)); 15 % PB and 15 % WS, and 30 % PB and 0 % WS. Although dry matter (DM) intake and digestibility were not affected (P > 0.10) by feeding PB, neutral detergent fiber (linear; P = 0.01), acid detergent fiber (linear; P = 0.001) and lignin digestibility (linear; P = 0.01) decreased, and crude protein (CP) digestibility tended to decrease (P = 0.09) as PB increased in the diet, apparent retention of Ca (P = 0.09), P (P = 0.03), Mg (P = 0.01), Mn (P = 0.01), Zn (P = 0.01) and Fe (P = 0.09) also increased linearly. Nitrogen intake and fecal N excretion were not affected (P > 0.05) by addition of PB in the diet, but N balance in the body was quadratically increased (P < 0.01) in the 15 % PB diet compared to other diets. This may be due to more rumen escape protein and less excreted N in the urine with the 15 % PB diet. The study showed that a moderate level of tannin-containing pine bark supplementation could improve gastrointestinal nitrogen balance with the aim of improving animal performance. Conclusion These results suggest that tannin-containing PB has negative impact on fiber, lignin, and protein digestibility, but positively impacted on N-balance.