New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations

In the paper, new upper bounds in the second Kershaw’s double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are refined

On the approximation of the Wallis ratio

In this review article, we study the recent investigations and developments on the Wallis ratio. Some best constants for the approximation of the Wallis ratio are introduced. Some double inequalities for bounding the Wallis ratio are also introduced

More supplements to a class of logarithmically completely monotonic functions associated with the gamma function

In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on $(0,\infty)$. As applications of the necessary and sufficient condition, some inequalities for bounding the psi and polygamma functions and the ratio of two gamma functions are derived.Comment: 8 page

The characteristics of impaired fasting glucose associated with obesity and dyslipidaemia in a Chinese population

<p>Abstract</p> <p>Background</p> <p>Different populations have diverse patterns of relationships between Impaired Fasting Glucose (IFG) and obesity and lipid markers, it is important to investigate the characteristics of associations between IFG and other related risk factors including body mass index (BMI), waist circumstance (WC), serum lipids and blood pressure (BP) in a Chinese population.</p> <p>Methods</p> <p>This was a case-control study of 648 IFG subjects and 1,296 controls derived from a large-scale, community-based, cross-sectional survey of 10,867 participants. Each subject received a face-to-face interview, physical examination, and blood tests, including fasting blood glucose and lipids. Student's <it>t</it>-test, Chi-square test, Spearman correlation and multiple logistic regressions were used for the statistical analyses.</p> <p>Results</p> <p>Fasting plasma glucose (FPG) was positively correlated with BMI, WC, systolic blood pressure (SBP), diastolic blood pressure (DBP), triglyceride (TG), and total cholesterol (TC), and was negatively correlated with high density lipoprotein-cholesterol (HDL-C) (all p < 0.05). BMI was more strongly correlated with IFG than with WC. The correlation coefficient of FPG was remarkably higher with TG (0.244) than with TC (0.134) and HDL-C (-0.192). TG was an important predictor of IFG, with odds ratios of 1.76 (95%CI: 1.31-2.36) for subjects with borderline high TG level (1.70 mmol/l ≤ TG < 2.26 mmol/l) and 3.13 (95% CI: 2.50-3.91) for those with higher TG level (TG ≥ 2.26 mmol/l), when comparing to subjects with TG < 1.70 mmol/l. There was a significant dose-response relationship between the number of abnormal variables and increased risk of IFG.</p> <p>Conclusions</p> <p>In this Chinese population, both BMI and WC were important predictors of IFG. Abnormal TG as a lipid marker was more strongly associated with IFG than were TC and HDL-C. These factors should be taken into consideration simultaneously for prevention of IFG.</p

A Class of k-Log-Convex Functions and their Applications to Some Special Functions

Let a and b be two real numbers, f a positive and differentiable function on an interval I. The authors establish the i-log-convex or i-log-concave properties for i ∈ N of the function for k ∈ N is monotonic and apply these properties to to deduce some known and new conclusions related to some special functions such as the gamma function, Riemann&apos;s zeta function, complete elliptic integrals, exponential mean and extended mean values