Abstract:
We use the definition of differential operators on noncommutative rings given by V.Lunts and A.Rosenberg to find the differential operators on Azumaya algebras and the Heisenberg algebras.

Abstract:
Diabetes is a chronic, potentially debilitating and often fatal disease. The prevalence of type 2 diabetes is increasing in all populations worldwide. The investigation was carried out to study the impact of barley grass powder (BGP) supplementation on the carbohydrate and lipid metabolism of stable type 2 diabetes mellitus (T2DM) subjects. A total of 59 stable type 2 diabetic subjects were enrolled in the study from pathology laboratories and divided into experimental (n=36) and control groups (n=23). BGP (1.2 g/day) in the form of capsules (n=4) was given to the experimental group subjects for a period of 60 days. Fasting blood sugar (FBS), glycated haemoglobin (HbA1c) and lipid profile levels were monitored at baseline and at 60 days. Paired t test was applied using Microsoft Office Excel 2003. Supplementation with BGP resulted in a significant decrease in FBS, HbA1c, total cholesterol (TC), low-density lipoprotein cholesterol (LDL-C) and non-high-density lipoprotein cholesterol (Non-HDL-C) and a significant increase in high-density lipoprotein cholesterol (HDL-C) levels. In conclusion, the results obtained suggest that BGP holds promise to be used as a functional food to optimise the health of diabetic subjects.

Abstract:
The algebra of quantum differential operators on graded algebras was introduced by V. Lunts and A. Rosenberg. D. Jordan, T. McCune and the second author have identified this algebra of quantum differential operators on the polynomial algebra with coefficients in an algebraically closed field of characteristic zero. It contains the first Weyl algebra and the quantum Weyl algebra as its subalgebras. In this paper we classify irreducible weight modules over the algebra of quantum differential operators on the polynomial algebra. Some classes of indecomposable modules are constructed in the case of positive characteristic and q root of unity.

Abstract:
After recalling the definitions and the properties of the generic base algebra and of the universal comodule algebra attached to a Hopf algebra by Aljadeff and the second-named author, we determine these algebras for the Taft algebras, the Hopf algebras E(n), and certain monomial Hopf algebras.

Abstract:
Many of the plant sources have excellent nutrient and non-nutrient properties which can be exploited to manage clinical conditions. The current study was undertaken to assess the impact of panchratna juice (Amla, Tulsi, Ginger, Mint and Turmeric) in the management of type 2 diabetes mellitus subjects. A total of 55 stable type 2 diabetics were enrolled from pathology laboratories and were given either fresh panchratna juice (n = 15) for 45 days or processed panchratna juice (n = 20) for 90 days and compared with diabetic controls (n = 20). Anthropometric profile, glycemic status and lipid profile were assessed on all the subjects at baseline, 45 days and 90 days. Students t test, paired t test and ANOVA were applied using Microsoft Excel. The results indicated that fresh panchratna juice or processed panchratna juice supplementation for long-term did not have any significant impact on the glycemic and lipemic status of diabetic subjects. Thus, the protective effects are lost with processing, and therefore, these plant sources should be consumed in their natural form.

Abstract:
Following the definitions of the algebras of differential operators, $\beta$-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free associative algebra. We further study their properties.

Abstract:
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal enveloping algebra and acts not through the differential operators of its representation ring but through the quantised differential operators of its representation ring. We present this situation for the quantum group of sl_2.

Abstract:
Following the definition of quantum differential operators given by Lunts and Rosenberg in (Sel. math., New ser. 3 (1997) 335--359), we show that the ring of quantum differential operators on the affine line is the ring generated by x and \del, the familiar differential operators on the line, along with two additional operators which we call \del^\beta^1 and \del^\beta^-1. We describe this ring both as a subring of the ring of graded endomorphisms and as a ring given by generators and relations. From this starting point, we are able to describe the ring of quantum differential operators on affine n-space and to construct the ring of global quantum differential operators on the projective line.

Abstract:
Background: Industrial and technological revolution has resulted in nutrition transition. This calls for analyzing the risk factor scenario in the industrial population. Objective: The objective was to map the prevalence and assess the risk factors of industrial employees. Materials and Methods: The employees of a large petrochemical industry were enrolled (N=269) for the study. Risk factors were elicited through a structured questionnaire. Parameters monitored were fasting blood sugar and lipid profile. Relative risk was calculated to find out significant predictor variables. Results: The employees had high prevalence of overweight (27%), obesity (22%), central obesity (48.7%), prehypertension (43.2%), hypertension (36.6%), and dyslipidemia (41.4%). They had erroneous dietary habits such as low intake of fruits and vegetables and high fat intake. Most of the employees had low physical activity levels. The prevalence of smoking (13.5%), tobacco (28.2%), and alcohol use (22.2%) were also high with 15.1% having multiple habits. One-fifth of the employees had metabolic syndrome (MS). Seven predictor variables, namely, family history, BMI, WHR, blood pressure, physical inactivity, TG, and TG/H were identified and used to develop the risk score card to identify people at high risk of CVD and DM. Conclusion: Multiple risk factor scenario among the industrial population studied calls for effective intervention strategies and policy changes to combat the burden of non-communicable diseases. The risk score card can be used to screen the high-risk group in the industrial population.