A Refinement of Jensen's Discrete Inequality for Differentiable Convex Functions

A refinement of Jensen’s discrete inequality and applications for the celebrated Arithmetic Mean – Geometric Mean – Harmonc Mean inequality and Cauchy-Schwartz-Bunikowski inequality are pointed out

New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case

We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.Comment: Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures

On inequalities of Jensen-Ostrowski type

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of (Formula Presented), with various assumptions on the absolutely continuous function f:[a,b]→C and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting λ=0 and ζ=∫Ωgdμ, respectively. In particular, we obtain some bounds for the discrepancy in Jensen’s integral inequality. Applications of these inequalities for f-divergence measures are also given

Economic evaluation of ASCOT-BPLA: Antihypertensive treatment with an amlodipine-based regimen is cost-effective compared to an atenolol-based regimen

Copyright © 2010 BMJ Publishing Group Ltd & British Cardiovascular Society. Internal or personal use of this material is permitted. However, permission to reprint/republish this material must be obtained from the Publisher.Objective: To compare the cost effectiveness of an amlodipine-based strategy and an atenolol-based strategy in the treatment of hypertension in the UK and Sweden. Design: A prospective, randomised trial complemented with a Markov model to assess long-term costs and health effects. Setting: Primary care. Patients: Patients with moderate hypertension and three or more additional risk factors. Interventions: Amlodipine 5–10 mg with perindopril 4–8 mg added as needed or atenolol 50–100 mg with bendroflumethiazide 1.25–2.5 mg and potassium added as needed Main outcome measures: Cost per cardiovascular event and procedure avoided, and cost per quality-adjusted life-year gained. Results: In the UK, the cost to avoid one cardiovascular event or procedure would be €18 965, and the cost to gain one quality-adjusted life-year would be €21 875. The corresponding figures for Sweden were €13 210 and €16 856. Conclusions: Compared with the thresholds applied by NICE and in the Swedish National Board of Health and Welfare’s Guidelines for Cardiac Care, an amlodipine-based regimen is cost effective for the treatment of hypertension compared with an atenolol-based regimen in the population studied.The study was supported by the principal funding source, Pfizer, New York, USA

ASCORE: an up-to-date cardiovascular risk score for hypertensive patients reflecting contemporary clinical practice developed using the (ASCOT-BPLA) trial data.

A number of risk scores already exist to predict cardiovascular (CV) events. However, scores developed with data collected some time ago might not accurately predict the CV risk of contemporary hypertensive patients that benefit from more modern treatments and management. Using data from the randomised clinical trial Anglo-Scandinavian Cardiac Outcomes Trial-BPLA, with 15 955 hypertensive patients without previous CV disease receiving contemporary preventive CV management, we developed a new risk score predicting the 5-year risk of a first CV event (CV death, myocardial infarction or stroke). Cox proportional hazard models were used to develop a risk equation from baseline predictors. The final risk model (ASCORE) included age, sex, smoking, diabetes, previous blood pressure (BP) treatment, systolic BP, total cholesterol, high-density lipoprotein-cholesterol, fasting glucose and creatinine baseline variables. A simplified model (ASCORE-S) excluding laboratory variables was also derived. Both models showed very good internal validity. User-friendly integer score tables are reported for both models. Applying the latest Framingham risk score to our data significantly overpredicted the observed 5-year risk of the composite CV outcome. We conclude that risk scores derived using older databases (such as Framingham) may overestimate the CV risk of patients receiving current BP treatments; therefore, 'updated' risk scores are needed for current patients