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.

Pre-Raphaelitism, science and the arts in 'The Germ'

This article demonstrates for the first time how dense the references to science are within the Pre-Raphaelite periodical 'The Germ' (1850). By reading the essays from this magazine together, as they were first published, it is possible to see how thoroughly the Pre-Raphaelites theorised their artistic project in terms of a particular mid-Victorian ideal of science. At the same time, the magazine became a forum in which the question of how far the arts ought to take account of science could be debated. In this debate, the competing visions of Pre-Raphaelitism discussed in Holman Hunt’s later accounts of the movement can be seen emerging at a very early stage in its history.

Secondary school teachers' perspectives on teaching about topics that bridge science and religion

The question of where to locate teaching about the relationships between science and religion has produced a long-running debate. Currently, Science and Religious Education (RE) are statutory subjects in England and are taught in secondary schools by different teachers. This paper reports on an interview study in which 16 teachers gave their perceptions of their roles and responsibilities when teaching topics that bridge science and religion and the extent to which they collaborated with teachers in the other subject area. We found that in this sample, teachers reported very little collaboration between the curriculum areas. Although the science curriculum makes no mention of religion, all the science teachers said that their approaches to such topics were affected by their recognition that some pupils hold religious beliefs. All the RE teachers reported struggling to ensure students know of a range of views about how science and religion relate. The paper concludes with a discussion about implications for curriculum design and teacher training.

Attribution of extreme weather events in Africa: A preliminary exploration of the science and policy implications

At the most recent session of the Conference of the Parties (COP19) in Warsaw (November 2013) the Warsaw international mechanism for loss and damage associated with climate change impacts was established under the United Nations Framework Convention on Climate Change (UNFCCC). The mechanism aims at promoting the implementation of approaches to address loss and damage associated with the adverse effects of climate change. Specifically, it aims to enhance understanding of risk management approaches to address loss and damage. Understanding risks associated with impacts due to highly predictable (slow onset) events like sea-level rise is relatively straightforward whereas assessing the effects of climate change on extreme weather events and their impacts is much more difficult. However, extreme weather events are a significant cause of loss of life and livelihoods, particularly in vulnerable countries and communities in Africa. The emerging science of probabilistic event attribution is relevant as it provides scientific evidence on the contribution of anthropogenic climate change to changes in risk of extreme events. It thus provides the opportunity to explore scientifically-backed assessments of the human influence on such events. However, different ways of framing attribution questions can lead to very different assessments of change in risk. Here we explain the methods of, and implications of different approaches to attributing extreme weather events with a focus on Africa. Crucially, it demonstrates that defining the most appropriate attribution question to ask is not a science decision but needs to be made in dialogue with those stakeholders who will use the answers.

Whole life thinking and engineering the future

Whole-life thinking for engineers working on the built environment has become more important in a fast changing world.Engineers are increasingly concerned with complex systems, in which the parts interact with each other and with the outside world in many ways – the relationships between the parts determine how the system behaves. Systems thinking provides one approach to developing a more robust whole life approach. Systems thinking is a process of understanding how things influence one another within a wider perspective. Complexity, chaos, and risk are endemic in all major projects. New approaches are needed to produce more reliable whole life predictions. Best value, rather than lowest cost can be achieved by using whole-life appraisal as part of the design and delivery strategy.

How students view the boundaries between their science and religious education concerning the origins of life and the universe

Internationally in secondary schools, lessons are typically taught by subject specialists, raising the question of how to accommodate teaching which bridges the sciences and humanities. This is the first study to look at how students make sense of the teaching they receive in two subjects (science and religious education) when one subject’s curriculum explicitly refers to cross-disciplinary study and the other does not. Interviews with 61 students in seven schools in England suggested that students perceive a permeable boundary between science and their learning in science lessons and also a permeable boundary between religion and their learning in RE lessons, yet perceive a firm boundary between science lessons and RE lessons. We concluded that it is unreasonable to expect students to transfer instruction about cross-disciplinary perspectives across such impermeable subject boundaries. Finally we consider the implications of these findings for the successful management of cross-disciplinary education.

Garlic powder and wheat bran as fillers: Their effect on the physicochemical properties of edible biocomposites

Biocomposites with two different fillers, garlic and wheat bran, were studied. They were based on cassava starch and contained glycerol as a plasticizer and potassium sorbate as an antimicrobial agent and were characterized by scanning electron microscopy (SEM), differential scanning calorimetry (DSC) and infrared spectroscopy (IR). The mechanical performance at room and lower temperatures was also studied. SEM micrographies of fractured surfaces of the wheat bran composite films showed some ruptured particles of fiber while fibrils of garlic on the order of nanometers were observed when garlic composite films were studied. Mechanical tests, at room temperature, showed that the addition of wheat bran led to an increment in the storage modulus (E`) and hardening and a decrease in Tan delta, while the garlic composite showed a diminishing in the E` and hardening and did not produce significant changes in Tan delta values when compared with systems without fillers (matrix). In the range between -90 degrees C and 20 degrees C. all the materials studied presented two peaks in the Tan delta curve. In the case of the wheat bran composite, both relaxation peaks shifted slightly to higher temperatures, broadened and diminished their intensity when compared with those of the matrix; however garlic composite showed a similar behavior to the matrix. DSC thermograms of aqueous systems showed a slight shift of gelatinization temperature (T(gelatinization)) to higher values when the fillers were present. Thermograms of films showed that both, garlic and wheat bran composites, had a lower melting point than the matrix. IR data indicated that interaction between starch and fillers determined an increase in the availability of hydroxyl groups to be involved in a dynamic exchange with water. (C) 2010 Elsevier B.V. All rights reserved.

Study of some physical properties of biodegradable films based on blends of gelatin and poly(vinyl alcohol) using a response-surface methodology

The aim of this work was to study the effect of the hydrolysis degree (HD) and the concentration (C(PVA)) Of two types of poly(vinyl alcohol) (PVA) and of the type (glycerol and sorbitol) and the concentration (C(P)) of plasticizers on some physical properties of biodegradable films based on blends of gelatin and PVA Using a response-surface methodology. The films were prepared with a film forming solutions (FFS) with 2 g of macromolecules (gelatin+PVA)/100 g de FFS. The responses analyzed were the mechanical properties, the solubility, the moisture Content. the color difference and the opacity. The linear model was statistically significant and predictive for puncture force and deformation. elongation at break, solubility in water, Moisture content and opacity. The CPVA affected strongly the elongation at break of the films. The interaction of the HD and the C(P) affected this property. Moreover. the puncture force was affected slightly by the C(PVA). Concerning the Solubility in water, the reduction of the HD increased it and this effect was greater for high CPVA Values. In general. the most important effect observed in the physical properties of the films was that of the plasticizer type and concentration. The PVA hydrolysis degree and concentration have an important effect only for the elongation at break, puncture deformation and solubility in water. (C) 2008 Elsevier B.V. All rights reserved.

Spallation product distributions and neutron multiplicities for accelerator-driven system using the CRISP code

Neutron multiplicities for several targets and spallation products of proton-induced reactions in thin targets of interest to an accelerator-driven system obtained with the CRISP code have been reported. This code is a Monte Carlo calculation that simulates the intranuclear cascade and evaporationl fission competition processes. Results are compared with experimental data, and agreement between each other can be considered quite satisfactory in a very broad energy range of incitant particles and different targets.

Thin films of carbohydrate based surfactants and carboxymethylcellulose acetate butyrate mixtures: Morphology and thermal behavior

Thin films of mixtures containing carboxymethylcellulose acetate butyrate (CMCAB) and carbohydrate based surfactant, namely, sorbitan monopalmitate (Span 40) or poly(oxyethylene) sorbitan monopalmitate (Tween 40) were spin-coated onto silicon wafers. The effect of surfactant concentration on resulting film morphology and surface toughness Was Studied by atomic force microscopy (AFM). Upon increasing the concentration of Span 40 in the mixture, films became rougher and more heterogeneous, indicating surface enrichment by Span 40 molecules. In the case of mixtures composed by CMCAB and Tween 40, the increase of Tween 40 in the mixture led to smoother and more homogeneous films, indicating compatibility between both components. Differential scanning calorimetry (DSC) revealed that Span 40 and Tween 40 act as plasticizers for CMCAB, leading to dramatic reduction of glass transition temperature of CMCAB, namely, Delta T(g) = -158 degrees C and Delta T(g)=-179 degrees C. respectively. (C) 2008 Elsevier B.V. All rights reserved.

Paper Microzone Plates

This paper describes 96- and 384-microzone plates fabricated in paper as alternatives to conventional multi-well plates fabricated in molded polymers. Paper-based plates are functionally related to plastic well plates, but they offer new capabilities. For example, paper-microzone plates are thin (similar to 180 mu m), require small volumes of sample (5 mu L per zone), and can be manufactured from inexpensive materials ($0.05 per plate). The paper-based plates are fabricated by patterning sheets of paper, using photolithography, into hydrophilic zones surrounded by hydrophobic polymeric barriers. This photolithography used an inexpensive formulation photoresist that allows rapid (similar to 15 min) prototyping of paper-based plates. These plates are compatible with conventional microplate readers for quantitative absorbance and fluorescence measurements. The limit of detection per zone loaded for fluorescence was 125 fmol for fluorescein isothiocyanate-labeled bovine serum albumin, and this level corresponds to 0.02 the quantity of analyte per well used to achieve comparable signal-to-noise in a 96-well plastic plate (using a solution of 25 nM labeled protein). The limits of detection for absorbance on paper was aproximately 50 pmol per zone for both Coomassie Brilliant Blue and Amaranth dyes; these values were 0.4 that required for the plastic plate. Demonstration of quantitative colorimetric correlations using a scanner or camera to image the zones and to measure the intensity of color, makes it possible to conduct assays without a microplate reader.