The Essence of Mathematics Through Elementary Problems

"It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

The Essence of Mathematics Through Elementary Problems

"It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

Impact of ingredients on the elemental content of baby foods

The levels of the minerals: Ca, K, Mg, Na, P, and the trace elements: Cd, Cu, Fe, Mn, Ni, Pb, Se, Zn were determined in foods for 4–6, 7+ and 10+ months old babies in a brand available on the UK market. The mineral contents in the vegetarian meals for all the age groups were similar, in contrast, when compared to the non-vegetarian options, the Ca, Na and P levels were higher in the former. Both the trace elements and minerals levels in the 4–6 months vegetarian meal were the lowest of all the products analysed. The Cu, Se and Zn levels in all the meals were comparable to those in mature human breast milk. Calculations of the following molar ratios: Zn:Cu, Fe:Zn, and Fe:Mn, pairs of elements that have been shown to interaction antagonistically, were higher in the vegetarian meals

Homogenising the upper continental crust : the Si isotope evolution of the crust recorded by ancient glacial diamictites

This work was supported by PhD funding to MM by the University of St Andrews School of Earth and Environmental Sciences and the Handsel scheme, as well as by NERC grant NE/R002134/1 to PS and NSF grant EAR-1321954 to RR and RG.Twenty-four composite samples of the fine-grained matrix of glacial diamictites deposited from the Mesoarchaean to Palaeozoic have been analysed for their silicon isotope composition and used to establish, for the first time, the long-term secular Si isotope record of the compositional evolution of upper continental crust (UCC). Diamictites with Archaean and Palaeoproterozoic Nd model ages show greater silicon isotope heterogeneity than those with younger model ages (irrespective of depositional age). We attribute the anomalously light Si isotope compositions of some diamictites with Archaean model ages to the presence of glacially milled banded iron formation (BIF), substantiated by the high iron content and Ge/Si in these samples. We infer that relatively heavy Si isotope signatures in some Palaeoproterozoic diamictites (all of which have Archaean Nd model ages) are due to contribution from tonalite-trondhjemite-granodiorites (TTGs), evidenced by the abundance of TTG clasts. By the Neoproterozoic (with model ages ranging from 2.3 to 1.8 Ga), diamictite Si isotope compositions exhibit a range comparable to modern UCC. This reduced variability through time is interpreted as reflecting the decreasing importance of BIF and TTG in post-Archaean continental crust. The secular evolution of Si isotopes in the diamictites offers an independent test of models for the emergence of stable cratons and the onset of horizontal mobile-lid tectonism. The early Archaean UCC was heterogeneous and incorporated significant amounts of isotopically light BIF, but following the late Archaean stabilisation of cratons, coupled with the oxygenation of the atmosphere that led to the reduced neoformation of BIF and diminishing quantities of TTGs, the UCC became increasingly homogeneous. This homogenisation likely occurred via reworking of preexisting crust, as evidenced by Archaean Nd model ages recorded in younger diamictites.Publisher PDFPeer reviewe

Long-wavelength TCF-based fluorescence probes for the detection and intracellular imaging of biological thiols

Two ‘turn on’ TCF-based fluorescence probes were developed for the detection of biological thiols (TCF-GSH and TCFCl-GSH). TCF-GSH was shown to have a high sensitivity towards glutathione (GSH) with a 0.28 μM limit of detection. Unfortunately, at higher GSH concentrations the fluorescence intensity of TCF-GSH decreased and toxicity was observed for TCF-GSH in live cells. However, TCFCl-GSH was shown to be able to detect GSH at biologically relevant concentrations with a 0.45 μM limit of detection. No toxicity was found for TCFCl-GSH and a clear ‘turn on’ with good photostability was observed for the exogenous addition of GSH, Cys and HCys. Furthermore, TCFCl-GSH was used to evaluate the effects of drug treatment on the levels of GSH in live cells

Genic regions of a large salamander genome contain long introns and novel genes

BACKGROUND: The basis of genome size variation remains an outstanding question because DNA sequence data are lacking for organisms with large genomes. Sixteen BAC clones from the Mexican axolotl (Ambystoma mexicanum: c-value = 32 x 10(9) bp) were isolated and sequenced to characterize the structure of genic regions. RESULTS: Annotation of genes within BACs showed that axolotl introns are on average 10x longer than orthologous vertebrate introns and they are predicted to contain more functional elements, including miRNAs and snoRNAs. Loci were discovered within BACs for two novel EST transcripts that are differentially expressed during spinal cord regeneration and skin metamorphosis. Unexpectedly, a third novel gene was also discovered while manually annotating BACs. Analysis of human-axolotl protein-coding sequences suggests there are 2% more lineage specific genes in the axolotl genome than the human genome, but the great majority (86%) of genes between axolotl and human are predicted to be 1:1 orthologs. Considering that axolotl genes are on average 5x larger than human genes, the genic component of the salamander genome is estimated to be incredibly large, approximately 2.8 gigabases! CONCLUSION: This study shows that a large salamander genome has a correspondingly large genic component, primarily because genes have incredibly long introns. These intronic sequences may harbor novel coding and non-coding sequences that regulate biological processes that are unique to salamanders

What cost components are relevant for economic evaluations of palliative care, and what approaches are used to measure these costs? A systematic review

BACKGROUND: It is important to understand the costs of palliative and end-of-life care in order to inform decisions regarding cost allocation. However, economic research in palliative care is very limited and little is known about the range and extent of the costs that are involved in palliative care provision. AIM: To undertake a systematic review of the health and social care literature to determine the range of financial costs related to a palliative care approach and explore approaches used to measure these costs. DESIGN: A systematic review of empirical literature with thematic synthesis. Study quality was evaluated using the Weight of Evidence Framework. DATA SOURCES: The databases CINAHL, Cochrane, PsycINFO and Medline were searched from 1995 to November 2015 for empirical studies which presented data on the financial costs associated with palliative care. RESULTS: A total of 38 papers met our inclusion criteria. Components of palliative care costs were incurred within four broad domains: hospital care, community or home-based care, hospice care and informal care. These costs could be considered from the economic viewpoint of three providers: state or government, insurers/third-party/not-for-profit organisations and patient and family and/or society. A wide variety of costing approaches were used to derive costs. CONCLUSION: The evidence base regarding the economics of palliative care is sparse, particularly relating to the full economic costs of palliative care. Our review provides a framework for considering these costs from a variety of economic viewpoints; however, further research is required to develop and refine methodologies

Boronate ester cross-linked PVA hydrogels for the capture and H2O2-mediated release of active fluorophores

A new set of PVA hydrogels were formed using the boronate ester fluorescent probe, PF1 and the novel boronate fluorescent probe PT1 as the covalent crosslinkers. Treatment with aqueous H2O2 allowed triggered release of the fluorescent dye accompanied by complete dissolution of the hydroge

QTL and candidate gene mapping for polyphenolic composition in apple fruit

<p>Abstract</p> <p>Background</p> <p>The polyphenolic products of the phenylpropanoid pathway, including proanthocyanidins, anthocyanins and flavonols, possess antioxidant properties that may provide health benefits. To investigate the genetic architecture of control of their biosynthesis in apple fruit, various polyphenolic compounds were quantified in progeny from a 'Royal Gala' × 'Braeburn' apple population segregating for antioxidant content, using ultra high performance liquid chromatography of extracts derived from fruit cortex and skin.</p> <p>Results</p> <p>Construction of genetic maps for 'Royal Gala' and 'Braeburn' enabled detection of 79 quantitative trait loci (QTL) for content of 17 fruit polyphenolic compounds. Seven QTL clusters were stable across two years of harvest and included QTLs for content of flavanols, flavonols, anthocyanins and hydroxycinnamic acids. Alignment of the parental genetic maps with the apple whole genome sequence <it>in silico </it>enabled screening for co-segregation with the QTLs of a range of candidate genes coding for enzymes in the polyphenolic biosynthetic pathway. This co-location was confirmed by genetic mapping of markers derived from the gene sequences. <it>Leucoanthocyanidin reductase </it>(<it>LAR1</it>) co-located with a QTL cluster for the fruit flavanols catechin, epicatechin, procyanidin dimer and five unknown procyanidin oligomers identified near the top of linkage group (LG) 16, while <it>hydroxy cinnamate/quinate transferase </it>(<it>HCT</it>/<it>HQT</it>) co-located with a QTL for chlorogenic acid concentration mapping near the bottom of LG 17.</p> <p>Conclusion</p> <p>We conclude that <it>LAR1 </it>and <it>HCT</it>/<it>HQT </it>are likely to influence the concentration of these compounds in apple fruit and provide useful allele-specific markers for marker assisted selection of trees bearing fruit with healthy attributes.</p