Solvability of iterative systems of three-point boundary value problems

We establish a criterion for the existence of at least one positive solution for the iterative system of three-point boundary value problems by determining the eigenvalues λi, 1 ≤ i ≤ n, using Guo–Krasnosel’skii fixed point theorem.Publisher's Versio

Association of triglycerides/high density lipoprotein cholesterol ratio with insulin resistance in polycystic ovary syndrome

Background: Insulin resistance (IR) is frequently observed in women with polycystic ovary syndrome (PCOS). Recent studies advocated that triglyceride to high-density lipoprotein cholesterol ratio (TG/HDL-C) can be used as a simple clinical indicator of IR. Hence, the present study was performed to investigate the use of TG/HDL-C and its association with IR in PCOS.Methods: Forty-one patients with PCOS and 40 healthy age matched women were randomly enrolled. Demographic and clinical characteristics were obtained. Insulin resistance was defined by the homeostasis model assessment for insulin resistance (HOMA-IR) and quantitative insulin sensitivity check index (QUICKI).Results: In PCOS group, the insulin, HOMA-IR and TG/HDL-C ratio were significantly higher (p=0.001) than controls while, QUICKI was lower (p=0.001). Insulin, HOMA-IR were positively correlated with TG/HDL-C (ρ=0.303, p=0.006 and ρ=0.312, p=0.005 respectively) while, QUICKI was negatively correlated (ρ=-0.698, p=0.001). In receiver operating characteristic (ROC) analysis, area under the curve (AUC) for model based on QUICKI levels was better 0.898 (95% CI: 0.811-0.955, p=0.001) than HOMA-IR 0.636 (95% CI: 0.522-0.740, p=0.03). A cut-off value 3.23 for TG/HDL-C is proposed from the model based on QUICKI with best combination of sensitivity 83.3% and specificity 86.7%.Conclusions: Results of present study support that TG/HDL-C ratio may be a simple indicator of IR in PCOS patients which helps clinicians to identify IR in small centers, where the assays for insulin measurement are not available

Existence of symmetric positive solutions for lidstone type integral boundary value problems

This paper establishes the existence of even number of symmetric positive solutions for the even order differential equation (−1)n u (2n) (t) = f(t, u(t)), t ∈ (0, 1), satisfying Lidstone type integral boundary conditions of the form u (2i) (0) = u (2i) (1) = Z 1 0 ai+1(x)u (2i) (x)dx, for 0 ≤ i ≤ n − 1, where n ≥ 1, by applying Avery–Henderson fixed point theorem.Publisher's Versio

A study on metabolic variables and its association with high sensitive C-reactive protein in obese children and adolescents

Obesity in children and adolescents predispose to the development of obesity in adulthood and subsequent cardiovascular disease. High-sensitivity C-reactive protein (hsCRP) is a marker of low grade inflammatory state, which characterizes an atherosclerotic process. The aim of this study was to assess the metabolic abnormalities and its association with hsCRP in obese children and adolescents. A total of 62 obese children and adolescents and 24 healthy children and adolescents with a normal weight were recruited. In all subjects, anthropometric and biochemical parameters were measured. Body mass index (BMI) and blood pressure were significantly higher in the obese children and adolescents than the control. Obese children had significantly higher hsCRP levels (P < 0.001), total cholesterol, triglyceride, low-density lipoprotein-cholesterol (LDL-C) and lower high-density lipoprotein-cholesterol than the control group. Furthermore, homeostatic model assessment-insulin resistance (HOMA-IR) was significantly higher in obese children compared with the normal weight children. Furthermore, hsCRP showed a positive correlation with BMI (r = 0.357; P = 0.028), total cholesterol (r = 0.367; P = 0.008) and LDL-C (r = 0.356; P = 0.01), insulin (r = 0.311; P = 0.026) and not with HOMA-IR (r = 0.244; P = 0.084)). In conclusion, obese children and adolescents have significantly increased hsCRP compared with a normal weight group. Early intervention and prevention of obesity in children and adolescents decreases cardiovascular disease in later life