On Bilinear Hardy Inequality and Corresponding Geometric Mean Inequality

The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case $1< q, p_1, p_2<\infty$ with $q \geq \max(p_1,p_2)$

Prevalence and component analysis of metabolic syndrome: An Indian atherosclerosis research study perspective

Asian Indians have a high predisposition to metabolic syndrome (MS) and coronary artery disease (CAD). The present study aimed to estimate MS prevalence in 531 Asian Indian families comprising of 2318 individuals. Anthropometrics and lipid profile were assessed. MS prevalence was estimated using standard Adult Treatment Panel III (ATP-III) and World Health Organisation (WHO) criteria and modified definitions which included lowered cut-offs for waist circumference (WC) (≥90 cm for men and ≥80 cm for women], body mass index (BMI) (≥23 kg/m2) and impaired fasting glucose (IFG) levels. ATP-III criteria identified a significantly higher proportion of people with MS (N = 933; 40.3%) compared with WHO (N = 708; 30.6%; p < 0.0001) while modified ATP-III showed maximum gain in percent prevalence among the revised criteria (17.3%; p = 0.0056). The IDF criteria identified similar proportion of subjects with MS (N = 809; 34.9%) as the revised WHO criteria (N = 792; 34.2%). The number of MS subjects was highest in the 50–59 years age group. MS was diagnosed a decade earlier in unaffected subjects compared with those with CAD/diabetes using the modified MS criteria. WC correlated significantly with BMI and waist–hip ratio (WHR) (p = 0.000). Among MS components, high density lipoprotein cholesterol and BMI contributed significantly in males (71.4% and 85.9%) and females (86.8% and 88.8%), respectively. The higher percentage contribution of WC among males and WHR among females indicates the influence of gynecoid/android pelvis on WHR measures. In conclusion, the revision of definition criteria for MS with lowered cut-offs for WC and BMI is critical for the accurate assessment of MS among Asian Indians

Hardy-type inequalities over balls in R^N for some bilinear and iterated operators

Some new multidimensional Hardy-type inequalites are proved and discussed. The cases with bilinear and iterated operators are considered and some equivalence theorems are proved

Equivalent integral conditions related to bilinear Hardy-type inequalities

Infinitely many, even scales of, equivalent conditions are derived to characterize the bilinear Hardy-type inequality under various ranges of parameters

Adult nontwin sib concordance rates for type 2 diabetes, hypertension and metabolic syndrome among Asian Indians: The Indian Atherosclerosis Research Study

Jayashree Shanker1, Saikat Kanjilal3, Veena S Rao2, Ganapathy Perumal1, Natesha B Khadrinarasimhiah2, Manjari Mukherjee4, Shamanna S Iyengar3, Vijay V Kakkar51Mary and Garry Weston Functional Genomics Unit, Thrombosis Research Institute, Bangalore, India; 2Tata Proteomics and Coagulation Unit, Thrombosis Research Institute, Bangalore, India; 3Cardiology Division, St. Johns&rsquo; Medical College and Hospital, Bangalore, India; 4University Department of Chemical Technology, Mumbai, India; 5Founder Chairman, Thrombosis Research Institute-London, UKAbstract: Diabetes (DM), hypertension (HTN), and metabolic syndrome (MS) are established cardiovascular risk factors with a complex etiology. The aim of the present study was to estimate the rates of concordance for the above coronary risk factors between siblings in Asian Indian families with premature coronary artery disease (CAD). Spouse concordance rates were used to evaluate the relative contribution of shared genes and lifestyle towards these traits. A total of 508 families comprising of 1250 sib-pairs and 463 corresponding spouse-pairs were analyzed. Concordance rates were manually determined. Plasma lipids were estimated by standard enzymatic assay. The concordance rates among sib-pairs for DM, HTN, and MS was 11% (N = 136), 14% (N = 174), and 23% (N = 287), while the corresponding concordance for spouse-pairs was 2.8% (N = 13), 6.3% (N = 29), and 28.1% (N = 130), respectively. Employing Chi-square test, sib-pairs showed significantly higher concordance for diabetes (p&nbsp;&lt; 0.0001) and hypertension (p 0.0001) while spouse-pairs had higher concordance for metabolic syndrome (p = 0.033) in our study. These findings suggest a probable dominant genetic component in the causation of DM and HTN and a predominantly nongenetic component for metabolic syndrome among Asian Indians.Keywords: sib-pairs, spouse-pairs, type 2 diabetes, hypertension, metabolic syndrome, concordance, CAD, Asian Indian