On Frèchet algebras of power series

If the indeterminate X in a Frèchet algebra A of power series is a power series generator for A, then either A is the algebra of all formal power series or is the Beurling-Frèchet algebra on non-negative integers defined by a sequence of weights. Let the topology of A be defined by a sequence of norms. Then A is an inverse limit of a sequence of Banach algebras of power series if and only if each norm in the defining sequence satisfies certain closability condition and an equicontinuity condition due to Loy. A non-Banach uniform Frèchet algebra with a power series generator is a nuclear space. A number of examples are discussed; and a functional analytic description of the holomorphic function algebra on a simply connected planar domain is obtained

Numerical solution of fractional integro-differential equations with nonlocal conditions

In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem

A Beurling algebra is semisimple: an Elementary proof

The Beurling algebra L1(G,ω)on a locally compact Abelian group G with a measurable weight ω is shown to be semisimple. This gives an elementary proof of a result that is implicit in the work of M.C. White (1991), where the arguments are based on amenable (not necessarily Abelian) groups

The Scientific Temper of Climate Change Coverage in Indian Newspapers

Despite the efforts of several science communication organizations, coverage of science and science based issues remains very low in the worldwide media in general and Indian media, in particular. In contrast, the Indian media has seen an escalation of climate change reporting in the last decade. Climate change being an issue with far reaching social and economic implications, coverage of the issue is likely to have policy implications. Media coverage of scientific issues to a large extent informs policy decisions. Thus scientific coverage of an issue like climate change will result in scientific policies. In order to ensure this, the scientific temper of coverage of an issue like climate change needs to be tracked. This study of the scientific temper of climate change coverage in three mainstream English language newspapers published from New Delhi, Mumbai and Chennai shows that there has been very little attempt to involve science and scientists in the reportage. Majority of the news reports have used politicians as primary claim makers and have been sourced from the UN or IPCC reports. In comparison the number of reports using scientists as the primary claim makers and sourced from peer-reviewed journals is very low and has remained almost constant over the years

Obstetric consequences of subfertility: a retrospective cohort study

Objective To compare the risk of adverse pregnancy outcomes in women with and without subfertility and to investigate whether fertility treatment contributes to the adverse outcomes. Design Register‐based retrospective cohort study. Setting Aberdeen, Scotland Population The exposed group included women with subfertility attending Aberdeen Fertility Clinic between 1989 and 2008 and delivering a singleton (n = 3188) or twin (n = 350) at Aberdeen Maternity Hospital between 1992 and 2009. The unexposed cohort included the remainder of women (singleton n = 52443, twin n = 1125) delivering at Aberdeen Maternity Hospital between 1992 and 2009. Methods The Aberdeen Fertility Centre database and Aberdeen Maternity and Neonatal Databank were linked using Community Health Index numbers. Regression models were used to calculate risk ratios and 95% confidence intervals adjusting for potential confounders. Main outcome measures Maternal outcomes including pre‐eclampsia, antepartum haemorrhage, preterm birth, induction of labour; delivery outcomes including operative vaginal delivery, caesarean section; and offspring outcomes including low birthweight, stillbirth and neonatal death. Results Women with a history of subfertility who delivered a singleton were at a higher risk of pre‐eclampsia [adjusted risk ratios (aRR) 1.18, 95% confidence intervals (CI) 1.02–1.37], antepartum haemorrhage (aRR 1.32, 95% CI 1.18–1.47), induction of labour (aRR 1.21, 95% CI 1.11–1.31) and very preterm delivery (<32 weeks) (aRR 1.96, 95% CI 1.53–2.49). Subfertile women delivering twins were at a higher risk of being delivered by emergency caesarean section (aRR 2.14, 95% CI 1.26–3.66). There were no significant differences in adverse outcomes for singleton pregnancies between the treated and untreated subfertile couples. Conclusion Subfertility per se, rather than fertility treatment, was associated with increased risk of adverse outcomes in singleton pregnancies

Electrocardiography in people living at high altitude of Nepal.

OBJECTIVE: The main objective of this study was to estimate the prevalence of coronary heart disease (CHD) of high-altitude populations in Nepal determined by an ECG recordings and a medical history. METHODS: We carried out a cross-sectional survey of cardiovascular disease and risk factors among people living at four different altitude levels, all above 2800 m, in the Mustang and Humla districts of Nepal. 12-lead ECGs were recorded on 485 participants. ECG recordings were categorised as definitely abnormal, borderline or normal. RESULTS: No participant had Q waves to suggest past Q-wave infarction. Overall, 5.6% (95% CI 3.7 to 8.0) of participants gave a self-report of CHD. The prevalence of abnormal (or borderline abnormal) ECG was 19.6% (95% CI 16.1 to 23.4). The main abnormalities were: right axis deviation in 5.4% (95% CI 3.5 to 7.7) and left ventricular hypertrophy by voltage criteria in 3.5% (95% CI 2.0 to 5.5). ECG abnormalities were mainly on the left side of the heart for Mustang participants (Tibetan origin) and on the right side for Humla participants (Indo-Aryans). There was a moderate association between the probability of abnormal (or borderline abnormal) ECG and altitude when adjusted for potential confounding variables in a multivariate logistic model; with an OR for association per 1000 m elevation of altitude of 2.83 (95% CI 1.07 to 7.45), p=0.03. CONCLUSIONS: Electrocardiographic evidence suggests that although high-altitude populations do not have a high prevalence of CHD, abnormal ECG findings increase by altitude and risk pattern varies by ethnicity

Frechet algebras with a Laurent series generator and the annulus algebras

Banach and Frechet algebras with a Laurent series generator are investigated leading, via the discrete Beurling algebras, to functional analytic characterisations of the holomorphic function algebras on the annulus as well as the C∞-algebra on the unit circle

Preferential stiffness and the crack-tip fields of an elastic porous solid based on the density-dependent moduli model

In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused by damaged pores in many porous bodies such as ceramics, concrete and human bones. To that end, we revisit a new class of implicit constitutive relations under the assumption of small deformation. Although the constitutive relationship \textit{appears linear} in both the Cauchy stress and linearized strain, the governing equation bestowed from the balance of linear momentum results in a quasi-linear partial differential equation (PDE) system. For the linearization and obtaining a sequence of elliptic PDEs, we propose the solution algorithm comprise a \textit{Newton\u27s method} coupled with a bilinear continuous Galerkin-type finite elements for the discretization. Our algorithm exhibits an optimal rate of convergence for a manufactured solution. In the numerical experiments, we set the boundary value problems (BVPs) with edge crack {under different modes of loading (i.e., the pure mode-I, II, and the mixed-mode). From the numerical results, we find that the density-dependent moduli model describes diverse phenomena that are not captured within the framework of classical linearized elasticity. In particular,numerical solutions clearly indicate that the nonlinear \textit{modeling} parameter depending on its sign and magnitude can control preferential mechanical stiffness along with the change of volumetric strain; larger the parameter is in the positive value}, the responses are such that the strength of porous solid gets weaker against the tensile loading while stiffer against the in-plane shear (or compressive) loading, which is vice versa for the negative value of it