An extension of the general Struble's method for solving an nth order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues

This paper attempts to show the more suitability of the extended general Struble's technique than the unified Krylov-Bogoliubov-Mitropolskii (KBM) method in solving the problems that occur during the critical conditions. Recently a critically damped condition of an nth, n=2,3, … order weakly nonlinear autonomous ordinary differential equation has been investigated by the unified KBM method, in which the corresponding unperturbed equation has some real (negative) repeated eigenvalues. But there are more important critical conditions, which are still untouched. One of them occurs when a pair of complex eigenvalues is equal to another. It is complicated to formulate as well as to utilize the KBM method to investigate this condition. However, the extended general Struble's technique is applicable to both autonomous and non-autonomous systems. Solutions obtained for different critical conditions as well as for different initial conditions show a good agreement with the numerical solutions. The method is illustrated by an example of a fourth-order nonlinear differential equation whose unperturbed equation has repeated complex eigenvalues. A steady-state solution is determined for the non-autonomous equation. Moreover, a critical condition of a fourth-order nonlinear equation is investigated when two real eigenvalues of the unperturbed equation are non-positive and equal.     

The Association Between Small Dense Low Density Lipoprotein and Coronary Artery Disease in North Indian Patients

Pathogenesis of coronary artery disease (CAD) is multi-factorial and several conventional risk factors have been ascribed; LDL-C being one of the important risk factor. However Indian population studies with established CAD often show LDL levels within normal range in patients with proven CAD. We hypothesized that Small dense low density lipoprotein (sdLDL) being more atherogenic might correlate more strongly to the occurrence and severity of CAD. The aim of the study was to evaluate the association between serum small dense LDL level and angiographically documented coronary artery disease. This is a cross sectional case control study in which sdLDL were measured in 126 patients with CAD and in 64 patients without CAD. Total cholesterol, HDL Cholesterol, LDL cholesterol and triglycerides were measured by standard methods along with other traditional risk factors. Direct quantitative measurement of sdLDL was done by enzymatic analysis. Mean sdLDL level was higher in patients with coronary stenosis than patients without coronary stenosis (16.3 ± 6.8 vs. 10.1 ± 5.7 mg/dL respectively, (p < 0.001). There was significant correlation between mean sdLDL and severity of CAD as assessed by syntax score with mean sdLDL level in low, intermediate and high syntax score being 15.0 ± 5.8, 20.1 ± 6.7 and 22.7 ± 7.3 mg/dL respectively (p value <0.001). A cut off value of 10.02 mg/dL was associated with presence of CAD (95 % CI 0.82–0.93, p < 0.001) using ROC curve. In conclusion Indian patients with established CAD have higher sdLDL levels compared to individuals without CAD despite having comparable LDL levels.     

Paradigm wars, dialogue or dance: is rapprochement possible and/or desirable?

In focusing on the Kincheloe and Tobin paper, ‘The Much Exaggerated Death of Positivism,’ this forum explores the hegemony of positivism in the professional practices of a group of educators whose research expertise lies in the fields of science education, mathematics education and leadership education. Responding to the first question, ‘What is your personal/professional experience of the hegemony of positivism?’, four key issues arise: is positivism part of the external world or is it within us (and thus what is our agency)?, the role of positivism as a driver of Western cultural imperialism, dualism as the chief logic of positivism, and the difficulty of responding to positivism from a pluralist perspective. The second question, ‘Is rapprochement between positivism and other paradigms possible and/or desirable without being re-colonised?’, raises a number of key issues that, although relatively new to science education, are of increasing interest to cultural studies researchers keen to embrace alternative research paradigms with which to create culturally inclusive science curricula. The discussants reveal their personal experiences of being marginalised by the hegemony of positivism and give voice to a range of opinions about how best to respond. The integral perspective of spiral dynamics is proposed as a model of paradigm evolution, our fundamental assumptions about modern progress are questioned, and the non-dualist logic of dialectics is explored as a more inclusive rationality for researchers. In the spirit of counter-hegemonic cultural studies, the discussants draw on their personal Buddhist and Hindu perspectives to open new doorways into complex ontological systems lying beyond the simplistic materialism of crypto-positivism. We are given a glimpse of powerful means of generating new insights into the emergent universe (within and without) that an evolving science endeavours to explain.     

Field Experiences in High-Need,Urban Settings: Analysis of Current Practice and Insights for Change

High-need urban districts face many challenges in their efforts to overcome the large gaps in achievement demonstrated by their students. This study focuses on a strategy to overcome these challenges by better preparing future teachers for service in urban schools through quality field experiences at these sites. Teacher educators and urban school teachers who host teacher candidates during field experiences completed a questionnaire regarding their views about placements in high-need urban districts. A thematic analysis of their responses summarizes their beliefs about the most and least beneficial forms of field experiences, the most prevalent challenges in establishing quality field experiences, and the most successful strategies that facilitate the development of quality field experiences. The discussion compares the views of teacher educators with practicing teachers and recommends strategies to enhance field experiences in high-need, urban schools.     

Leading Differentiated Learning for the Gifted

This study examined similarities and differences in the perceptions of principals and teachers about the use of differentiated strategies for gifted learners and studied principals’ perceptions about schoolwide differentiation. Comparisons of these perceptions have been undoc-umented to date. Participants included 867 teachers and 120 principals from government schools in Sydney, Australia. A mixed methods approach was used, including online questionnaires and case studies of principals. Results revealed significant differences between the perceptions of principals and teachers about differentiated practices. The case studies demonstrate that exemplary principals continually enhance their understanding of differentiated learning and build their teachers’ collective capacity for educating gifted learners. The findings indicate the need for stronger pedagogical congruence between principals and teachers in educating the gifted, ongoing professional education of principals and teachers in gifted education, and effective leadership actions for schoolwide differentiated learning.     

Erythrocyte glutathione status in human visceral leishmaniasis

A glutathione redox cycle is a major antioxidant defense system for the detoxification of reactive oxygen species within erythrocytes. Reactive oxygen species such as superoxide anions, hydrogen peroxide and hydroxyl radicals are generated as a host defense mechanism for killing of engulfed Leishmania donovani, a causative agent of visceral leishmaniasis, are capable of damaging lipids and other biomolecules when produced in excess. Erythrocytes are most vulnerable to Reactive oxygen species. In present study we aimed to evaluate erythrocyte reduced glutathione (GSH) levels as an antioxidant and erythrocyte malondialdehyde (MDA) as a marker of lipid peroxidation. The study included twenty-five Visceral leishmaniasis patients and they were followed up after their complete chemotherapy with antileishmanial drugs (sodium stibogluconate) for 30 days. Forty six age and sex matched healthy individuals were taken as controls. GSH levels in erythrocytes of visceral leishmaniasis patients were increased in spite of significant increased erythrocyte MDA as compared to controls. Whereas erythrocyte GSH and MDA levels of follow up patients were decreased as compared to patients before treatment groups. We concluded that visceral leishmaniasis patients are in oxidative stress which most likely induces the endogenous antioxidant such as GSH or its poor utilization by cells.     

Effect of Tulsi (<Emphasis Type="Italic">Ocimum sanctum</Emphasis> Linn.) Supplementation on Metabolic Parameters and Liver Enzymes in Young Overweight and Obese Subjects

Ocimum sanctum Linn. (also known as Tulsi) is a sacred Indian plant, the beneficial role of which, in obesity and diabetes is described traditionally. This is a randomized, parallel group, open label pilot study to investigate the effect of O. sanctum on metabolic and biochemical parameters in thirty overweight/obese subjects, divided into two groups A and B. Group A (n = 16) received one 250 mg capsule of Tulsi (O. sanctum) extract twice daily in empty stomach for 8 weeks and group B (n = 14) received no intervention. Statistically significant improvements in the values of serum triglycerides (p = 0.019); low density lipoprotein (p = 0.001); high density lipoprotein (p = 0.001); very low density lipoprotein (p = 0.019); Body Mass Index, BMI (p = 0.005); plasma insulin (p = 0.021) and insulin resistance (p = 0.049) were observed after 8 weeks in the O. sanctum intervention group. The improvement in HDL-C in the intervention group when compared to the control group was also statistically significant (p = 0.037). There was no significant alteration of the liver enzymes SGOT and SGPT in both the intervention (p = 0.141; p = 0.074) and control arms (p = 0.102; p = 0.055) respectively. These observations clearly indicate the beneficial effects of O. sanctum on various biochemical parameters in young overweight/obese subjects.