A new estimate for the approximation of functions by Hermite-Fejér interpolation polynomials

AbstractA new estimate is derived for the error committed in approximating a continuous function by Hermite-Fejér interpolation polynomials on the Chebyshev nodes of the first kind. The estimate obtained reflects the fact that the polynomials interpolate the function which is being approximated

Nomenclature of the hydrotalcite supergroup: Natural layered double hydroxides

Layered double hydroxide (LDH) compounds are characterized by structures in which layers with a brucite-like structure carry a net positive charge, usually due to the partial substitution of trivalent octahedrally coordinated cations for divalent cations, giving a general layer formula [( M 2+ 1-x M 3+ x )(OH)2] x +. This positive charge is balanced by anions which are intercalated between the layers. Intercalated molecular water typically provides hydrogen bonding between the brucite layers. In addition to synthetic compounds, some of which have significant industrial applications, more than 40 mineral species conform to this description. Hydrotalcite, Mg6Al2(OH) 16[CO3]•4H2O, as the longest-known example, is the archetype of this supergroup of minerals. We review the history, chemistry, crystal structure, polytypic variation and status of all hydrotalcite-supergroup species reported to date. The dominant divalent cations, M 2+, that have been reported in hydrotalcite supergroup minerals are Mg, Ca, Mn, Fe, Ni, Cu and Zn; the dominant trivalent cations, M 3+, are Al, Mn, Fe, Co and Ni. The most common intercalated anions are (CO3)2-, (SO4)2- and Cl -; and OH-, S2- and [Sb(OH)6] - have also been reported. Some species contain intercalated cationic or neutral complexes such as [Na(H2O)6]+ or [MgSO4]0. We define eight groups within the supergroup on the basis of a combination of criteria. These are (1) the hydrotalcite group, with M 2+:M 3+ = 3:1 (layer spacing ∼7.8 Å); (2) the quintinite group, with M 2+:M 3+ = 2:1 (layer spacing ∼7.8 Å); (3) the fougèrite group, with M 2+ = Fe2+, M 3+ = Fe3+ in a range of ratios, and with O2- replacing OH- in the brucite module to maintain charge balance (layer spacing ∼7.8 Å); (4) the woodwardite group, with variable M 2+:M 3+ and interlayer [SO4] 2-, leading to an expanded layer spacing of ∼8.9 Å; (5) the cualstibite group, with interlayer [Sb(OH)6]- and a layer spacing of ∼9.7 Å; (6) the glaucocerinite group, with interlayer [SO4]2- as in the woodwardite group, and with additional interlayer H2O molecules that further expand the layer spacing to ∼11 Å; (7) the wermlandite group, with a layer spacing of ∼11 Å, in which cationic complexes occur with anions between the brucite-like layers; and (8) the hydrocalumite group, with M 2+ = Ca2+ and M 3+ = Al, which contains brucite-like layers in which the Ca:Al ratio is 2:1 and the large cation, Ca2+, is coordinated to a seventh ligand of 'interlayer' water. The principal mineral status changes are as follows. (1) The names manasseite, sjögrenite and barbertonite are discredited; these minerals are the 2H polytypes of hydrotalcite, pyroaurite and stichtite, respectively. Cyanophyllite is discredited as it is the 1M polytype of cualstibite. (2) The mineral formerly described as fougèrite has been found to be an intimate intergrowth of two phases with distinct Fe 2+:Fe3+ ratios. The phase with Fe2+:Fe 3+ = 2:1 retains the name fougèrite; that with Fe 2+:Fe3+ = 1:2 is defined as the new species trébeurdenite. (3) The new minerals omsite (IMA2012-025), Ni 2Fe3+(OH)6[Sb(OH)6], and mössbauerite (IMA2012-049), Fe3+ 6O 4(OH)8[CO3]•3H2O, which are both in the hydrotalcite supergroup are included in the discussion. (4) Jamborite, carrboydite, zincaluminite, motukoreaite, natroglaucocerinite, brugnatellite and muskoxite are identified as questionable species which need further investigation in order to verify their structure and composition. (5) The ranges of compositions currently ascribed to motukoreaite and muskoxite may each represent more than one species. The same applies to the approved species hydrowoodwardite and hydrocalumite. (6) Several unnamed minerals have been reported which are likely to represent additional species within the supergroup. This report has been approved by the Commission on New Minerals, Nomenclature and Classification (CNMNC) of the International Mineralogical Association, voting proposal 12-B. We also propose a compact notation for identifying synthetic LDH phases, for use by chemists as a preferred alternative to the current widespread misuse of mineral names. © 2012 Mineralogical Society.Fil: Mills, S.J.. Museum Victoria; AustraliaFil: Christy, A.G.. Australian National University. Centre for Advanced Microscopy; AustraliaFil: Génin, J. M. R.. CNRS-Université de Lorraine; FranciaFil: Kameda, T.. Tohoku University. Graduate School of Environmental Studies; JapónFil: Colombo, Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Ciencias de la Tierra. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Centro de Investigaciones en Ciencias de la Tierra; Argentin

Postnatal depression - an examination of psychosocial factors

Postnatal depression (PND) has been underreported in South Africa. This retrospective study investigated factors which appear to predispose women to PND. Two groups, one consisting of women who suffered from PND and the other of women free of this complaint, provided information on a number of biological, psychological and social factors. In line with current opinion it was found that no single causative factor could be isolated but that a variety of factors may contribute to the problem. Among the factors which distinguishedJhe two groups were the mothers' emotional health during pregnancy, complications after birth, marital relations, relationship with their own mothers, social support and preparation for motherhood. An alarming finding was that a large proportion of the PND sufferers had not known of the disorder's existence before their own diagnosis

Effect of interventions incorporating personalised cancer risk information on intentions and behaviour: A systematic review and meta-analysis of randomised controlled trials

Objective To provide a comprehensive review of the impact on intention to change health-related behaviours and health-related behaviours themselves, including screening uptake, of interventions incorporating information about cancer risk targeted at the general adult population. Design A systematic review and random-effects meta-analysis. Data sources An electronic search of MEDLINE, EMBASE, CINAHL and PsycINFO from 1 January 2000 to 1 July 2017. Inclusion criteria Randomised controlled trials of interventions including provision of a personal estimate of future cancer risk based on two or more non-genetic variables to adults recruited from the general population that include at least one behavioural outcome. Results We included 19 studies reporting 12 outcomes. There was significant heterogeneity in interventions and outcomes between studies. There is evidence that interventions incorporating personalised cancer risk information do not affect intention to attend or attendance at screening (relative risk 1.00 (0.97-1.03)). There is limited evidence that they increase smoking abstinence, sun protection, adult skin self-examination and breast examination, and decrease intention to tan. However, they do not increase smoking cessation, parental child skin examination or intention to protect skin. No studies assessed changes in diet, alcohol consumption or physical activity. Conclusions Interventions incorporating personalised cancer risk information do not affect uptake of screening, but there is limited evidence of effect on some health-related behaviours. Further research, ideally including objective measures of behaviour, is needed before cancer risk information is incorporated into routine practice for health promotion in the general population. Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted

Direct sublattice imaging of interface dislocation structures in CdTe/GaAs(001)

This paper presents directly interpretable atomic resolution images of dislocation structures at interfaces in CdTe/GaAs(001) systems. This is achieved using the technique of Z-contrast imaging in a 300 kV scanning transmission electron microscope in conjunction with maximum entropy image analysis. In addition to being used to further the understanding of the relation between growth conditions and exhibited properties, the data presented provides direct information on the atomic arrangements at dislocation cores

CNMNC guidelines for the nomenclature of polymorphs and polysomes

peer reviewe

External and intrinsic anchoring in nematic liquid crystals: A Monte Carlo study

We present a Monte Carlo study of external surface anchoring in nematic cells with partially disordered solid substrates, as well as of intrinsic anchoring at free nematic interfaces. The simulations are based on the simple hexagonal lattice model with a spatially anisotropic intermolecular potential. We estimate the corresponding extrapolation length $b$ by imposing an elastic deformation in a hybrid cell-like nematic sample. Our estimates for $b$ increase with increasing surface disorder and are essentially temperature--independent. Experimental values of $b$ are approached only when both the coupling of nematic molecules with the substrate and the anisotropy of nematic--nematic interactions are weak.Comment: Revisions primarily in section I

Evaluation of a general practice based Hepatitis C virus screening intervention

In 2003 an estimated 37,500 of Scotland's population was chronically infected with HCV; 44% were undiagnosed former injecting drug users (IDU) - a priority group for arrival therapy. Aims to evaluate a hepatitis C virus (HCV) screening intervention. Outcomes measures among two similar general practice populations in an area of high HCV and drug use prevalence, one of which was exposed to an HCV screening intervention, were compared. Thirty to fifty four year old attendees of the intervention practice were opportunistically offered testing and counselling, where clinically appropriate, (November 2003 - April 2004). Outcomes: HCV test uptake, case detection, referral and treatment administration rates. Of 584 eligible attendees, 421 (72%) were offered and 117 (28%) accepted testing in the intervention practice; no testing was undertaken in the comparison practice. Prevalences of HCV antibody were 13% (15/117), 75% (3/4) and 91% (10/11) among all tested persons, current IDUs and former IDUs respectively. For 4/15 (27%) evidence of binge drinking following the receipt of their positive result, was available. Of the 11 referred to specialist care because they were HCV RNA positive, nine attended at least one appointment. Two received treatment: one had achieved a sustained viral response as of February 2008. While non targeted HCV screening in the general practice setting can detect infected former IDU, the low diagnostic yield among non IDUs limited the effectiveness of the intervention. A more targeted approach for identifying former IDUs is recommended. Additionally, the low uptake of treatment among chronically infected persons four years after diagnosis demonstrates the difficulties in clinically managing such individuals. Strategies, including support for those with a history of problem alcohol use, to improve treatment uptake are required

Plasma-polymerized pericyte patches improve healing of murine wounds through increased angiogenesis and reduced inflammation

Pericytes have the potential to be developed as a cell therapy for the treatment of wounds; however, the efficacy of any cell therapy relies on the successful delivery of intact and functioning cells. Here, the effect of delivering pericytes on wound repair was assessed alongside the development of a surface-functionalized pericyte patch. Plasma polymerization (PP) was used to functionalize the surface of silicone patches with heptylamine (HA) or acrylic acid (AA) monomers. Human pericytes were subsequently delivered to murine excisional wounds by intradermal injection or using the pericyte-laden patches and the comparative effects on wound healing, inflammation and revascularization determined. The AA surface provided the superior transfer of the cells to de-epidermized dermis. Excisional murine wounds treated either with pericytes injected directly into the wound or with the pericyte-laden AA patches showed improved healing with decreased neutrophil infiltration and reduced numbers of macrophages in the wounds. Pericyte delivery also enhanced angiogenesis through a mechanism independent of VEGF signalling. Pericytes, when delivered to wounds, improved healing responses by dampening inflammation and promoting angiogenesis. Delivery of pericytes using PP-AA-functionalized patches was equally as effective as direct injection of pericytes into wounds. Pericyte-functionalized dressings may therefore be a clinically relevant approach for the treatment of wounds.Hannah M. Thomas, Parinaz Ahangar, Robert Fitridge, Giles T.S. Kirby, Stuart J. Mills and Allison J. Cowi

Attenuation of flightless I increases human pericyte proliferation, migration and angiogenic functions and improves healing in murine diabetic wounds

Pericytes are peri-vascular mural cells which have an important role in the homeostatic regulation of inflammatory and angiogenic processes. Flightless I (Flii) is a cytoskeletal protein involved in regulating cellular functions, but its involvement in pericyte activities during wound healing is unknown. Exacerbated inflammation and reduced angiogenesis are hallmarks of impaired diabetic healing responses, and strategies aimed at regulating these processes are vital for improving healing outcomes. To determine the effect of altering Flii expression on pericyte function, in vitro and in vivo studies were performed to assess the effect on healing, inflammation and angiogenesis in diabetic wounds. Here, we demonstrated that human diabetic wounds display upregulated expression of the Flii protein in conjunction with a depletion in the number of platelet derived growth factor receptor β (PDGFRβ) +/ neural glial antigen 2 (NG2) + pericytes present in the dermis. Human pericytes were found to be positive for Flii and attenuating its expression in vitro through siRNA knockdown led to enhanced proliferation, migration and angiogenic functions. Genetic knockdown of Flii in a streptozotocin-induced murine model of diabetes led to increased numbers of pericytes within the wound. This was associated with dampened inflammation, an increased rate of angiogenic repair and improved wound healing. Our findings show that Flii expression directly impacts pericyte functions, including proliferation, motility and angiogenic responses. This suggests that Flii regulation of pericyte function may be in part responsible for the changes in pericyte-related processes observed in diabetic wounds.Hannah M Thomas, Parinaz Ahangar, Benjamin R Hofma, Xanthe L Strudwick, Robert Fitridge, Stuart J Mills and Allison J Cowi