Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

Utilisation of dried shiitake, black ear and silver ear mushrooms into sorghum biscuits manipulates the predictive glycaemic response in relation to variations in biscuit physical characteristics

The nutritional quality of gluten-free products is important to the health of individuals with coeliac disease. Mushrooms are good sources of vitamins, dietary fibres and proteins, and are a low-calorie option that can be used in gluten-free diets to improve their nutritional value. The effects of incorporating dried mushrooms on the hydration and pasting properties of sorghum flour, as well as the physicochemical characteristics and in vitro glycaemic response of sorghum biscuits were studied. Sorghum flour enriched with mushroom powders exhibited higher water absorption capacity and swelling power compared with the control (P < 0.05). The addition of shiitake (Lentinula edodes) mushroom significantly decreased the pasting viscosities, while the addition of black ear (Auricularia auricula) and silver ear (Tremella fuciformis) mushroom increased viscosity values (P < 0.05). Biscuit diameter, thickness and weight loss were reduced with increasing mushroom powder addition, and the colour parameters of biscuits were affected significantly. Enrichment with shiitake and black ear mushroom increased the hardness of biscuits (P < 0.05). Inclusion of mushroom powders significantly reduced the predicted glycaemic response of sorghum biscuits (P < 0.05). Correlation analysis was conducted to illustrate that hydration dynamics (such as water absorption capacity and swelling power) were negatively correlated with glycaemic response (P < 0.001)

Zircon ages in granulite facies rocks: decoupling from geochemistry above 850 °C?

Granulite facies rocks frequently show a large spread in their zircon ages, the interpretation of which raises questions: Has the isotopic system been disturbed? By what process(es) and conditions did the alteration occur? Can the dates be regarded as real ages, reflecting several growth episodes? Furthermore, under some circumstances of (ultra-)high-temperature metamorphism, decoupling of zircon U–Pb dates from their trace element geochemistry has been reported. Understanding these processes is crucial to help interpret such dates in the context of the P–T history. Our study presents evidence for decoupling in zircon from the highest grade metapelites (> 850 °C) taken along a continuous high-temperature metamorphic field gradient in the Ivrea Zone (NW Italy). These rocks represent a well-characterised segment of Permian lower continental crust with a protracted high-temperature history. Cathodoluminescence images reveal that zircons in the mid-amphibolite facies preserve mainly detrital cores with narrow overgrowths. In the upper amphibolite and granulite facies, preserved detrital cores decrease and metamorphic zircon increases in quantity. Across all samples we document a sequence of four rim generations based on textures. U–Pb dates, Th/U ratios and Ti-in-zircon concentrations show an essentially continuous evolution with increasing metamorphic grade, except in the samples from the granulite facies, which display significant scatter in age and chemistry. We associate the observed decoupling of zircon systematics in high-grade non-metamict zircon with disturbance processes related to differences in behaviour of non-formula elements (i.e. Pb, Th, U, Ti) at high-temperature conditions, notably differences in compatibility within the crystal structure

The impact of urea-induced unfolding on the redox process of immobilised cytochrome c

We have studied the effect of urea-induced unfolding on the electron transfer process of yeast iso-1-cytochrome c and its mutant K72AK73AK79A adsorbed on electrodes coated by mixed 11-mercapto-1-undecanoic acid/11-mercapto-1-undecanol self-assembled monolayers. Electrochemical measurements, complemented by surface enhanced resonance Raman studies, indicate two distinct states of the adsorbed proteins that mainly differ with respect to the ligation pattern of the haem. The native state, in which the haem is axially coordinated by Met80 and His18, displays a reduction potential that slightly shifts to negative values with increasing urea concentration. At urea concentrations higher than 6 M, a second state prevails in which the Met80 ligand is replaced by an additional histidine residue. This structural change in the haem pocket is associated with an approximately 0.4 V shift of the reduction potential to negative values. These two states were found for both the wild-type protein and the mutant in which lysine residues 72, 73 and 79 had been substituted by alanines. The analysis of the reduction potentials, the reaction enthalpies and entropies as well as the rate constants indicates that these three lysine residues have an important effect on stabilising the protein structure in the adsorbed state and facilitating the electron transfer dynamics

Early Childhood Caries among a Bedouin community residing in the eastern outskirts of Jerusalem

<p>Abstract</p> <p>Background</p> <p>ECC is commonly prevalent among underprivileged populations. The Jahalin Bedouin are a severely deprived, previously nomadic tribe, dwelling on the eastern outskirts of Jerusalem. The aim of this study was to assess ECC prevalence and potentially associated variables.</p> <p>Methods</p> <p>102 children aged 12–36 months were visually examined for caries, mothers' anterior dentition was visually subjectively appraised, demographic and health behavior data were collected by interview.</p> <p>Results</p> <p>Among children, 17.6% demonstrated ECC, among mothers, 37.3% revealed "fairly bad" anterior teeth. Among children drinking bottles there was about twice the level of ECC (20.3%) than those breast-fed (13.2%). ECC was found only among children aged more than one year (p < 0.001); more prevalent ECC (55.6%) was found among large (10–13 children) families than among smaller families (1–5 children: 13.5%, 6–9 children: 15.6%) (p = 0.009); ECC was more prevalent among children of less educated mothers (p = 0.037); ECC was more prevalent among mothers with "fairly poor" anterior dentition (p = 0.04). Oral hygiene practices were poor.</p> <p>Conclusion</p> <p>ECC levels in this community were not very high but neither low. This changing population might be on the verge of a wider dental disease "epidemic". Public health efforts clearly need to be invested towards the oral health and general welfare of this community.</p

Permian high-temperature metamorphism in the Western Alps (NW Italy)

During the late Palaeozoic, lithospheric thinning in part of the Alpine realm caused high-temperature low-to-medium pressure metamorphism and partial melting in the lower crust. Permian metamorphism and magmatism has extensively been recorded and dated in the Central, Eastern, and Southern Alps. However, Permian metamorphic ages in the Western Alps so far are constrained by very few and sparsely distributed data. The present study fills this gap. We present U/Pb ages of metamorphic zircon from several Adria-derived continental units now situated in the Western Alps, defining a range between 286 and 266 Ma. Trace element thermometry yields temperatures of 580-890°C from Ti-in-zircon and 630-850°C from Zr-in-rutile for Permian metamorphic rims. These temperature estimates, together with preserved mineral assemblages (garnet-prismatic sillimanite-biotite-plagioclase-quartz-K-feldspar-rutile), define pervasive upper-amphibolite to granulite facies conditions for Permian metamorphism. U/Pb ages from this study are similar to Permian ages reported for the Ivrea Zone in the Southern Alps and Austroalpine units in the Central and Eastern Alps. Regional comparison across the former Adriatic and European margin reveals a complex pattern of ages reported from late Palaeozoic magmatic and metamorphic rocks (and relics thereof): two late Variscan age groups (~330 and ~300 Ma) are followed seamlessly by a broad range of Permian ages (300-250 Ma). The former are associated with late-orogenic collapse; in samples from this study these are weakly represented. Clearly, dominant is the Permian group, which is related to crustal thinning, hinting to a possible initiation of continental rifting along a passive margin