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

q-Integral inequalities associated with some fractional q-integral operators

In recent years fractional q-integral inequalities have been investigated by many authors. Therefore, the fractional q-integral inequalities have become one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Here, we aim to establish some new fractional q-integral inequality by using fractional q-integral operators. Relevant connections of the results presented here with earlier ones are also pointed out

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

Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass

Exact solutions of Schrodinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass, Point canonical transformation, Effective mass Schr\"{o}dinger equation.Comment: 9 page

Evaluation of C-reactive protein prior to and on-treatment as a predictor of benefit from atorvastatin: observations from the Anglo-Scandinavian Cardiac Outcomes Trial

<p><b>Aims:</b> We tested whether on-statin C-reactive protein is associated with cardiovascular (CV) outcome in the Anglo-Scandinavian Cardiac Outcomes Trial (ASCOT).</p> <p><b>Methods and results:</b> ASCOT randomized a subset of 4853 patients with total cholesterol ≤6.5 mmol/L (250 mg/dL) to atorvastatin or placebo. In a case–control study during 5.5-year follow-up, 485 CV cases were age- and sex-matched with 1367 controls. Baseline LDL-cholesterol (LDL-c) and log-transformed C-reactive protein predicted CV events [odds ratio (OR) per 1 standard deviation (SD) 1.31 (95% confidence interval {CI}: 1.10, 1.56), P = 0.002 and OR 1.19 (1.05, 1.34), P = 0.006, respectively]. Including baseline C-reactive protein into a Framingham risk model very modestly improved risk prediction. Baseline C-reactive protein did not indicate the magnitude of the atorvastatin effect on CV outcome (P = 0.54). At 6 months, atorvastatin reduced median LDL-c by 40.3% and median C-reactive protein by 27.4%. In those randomized to atorvastatin, lower on-treatment LDL-c at 6 months was associated with a significant reduction in subsequent CV events [OR 0.41 (0.22, 0.75), P = 0.004] comparing those above and below the median (2.1 mmol/L). In contrast, C-reactive protein below the median (1.83 mg/L) compared with C-reactive protein above the median was not associated with a significant reduction in CV events [OR 0.86 (0.49, 1.51), P = 0.60]. Consequently, addition of on-treatment C-reactive protein to LDL-c did not improve prediction of statin efficacy.</p> <p><b>Conclusion:</b> Among these hypertensive patients selected on the basis of traditional CV risk factors, C-reactive protein did not usefully improve the prediction of CV events and, critically, reduction in C-reactive protein associated with statin therapy was not a predictor of CV outcome alone or in combination with LDL-c.</p&gt

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review

Three-point function of semiclassical states at weak coupling

We give the derivation of the previously announced analytic expression for the correlation function of three heavy non-BPS operators in N=4 super-Yang-Mills theory at weak coupling. The three operators belong to three different su(2) sectors and are dual to three classical strings moving on the sphere. Our computation is based on the reformulation of the problem in terms of the Bethe Ansatz for periodic XXX spin-1/2 chains. In these terms the three operators are described by long-wave-length excitations over the ferromagnetic vacuum, for which the number of the overturned spins is a finite fraction of the length of the chain, and the classical limit is known as the Sutherland limit. Technically our main result is a factorized operator expression for the scalar product of two Bethe states. The derivation is based on a fermionic representation of Slavnov's determinant formula, and a subsequent bosonisation.Comment: 28 pages, 5 figures, cosmetic changes and more typos corrected in v