Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs

Symmetries of the fundamental first integrals for scalar second-order ordinary differential equations (ODEs) which are linear or linearizable by point transformations have already been obtained. Firstly we show how one can determine the relationship between the symmetries and the first integrals of linear or linearizable scalar ODEs of order two. Secondly, a complete classification of point symmetries of first integrals of such linear ODEs is studied. As a consequence, we provide a counting theorem for the point symmetries of first integrals of scalar linearizable second-order ODEs. We show that there exists the 0-, 1-, 2-, or 3-point symmetry cases. It is shown that the maximal algebra case is unique

Reference values for glucose tolerance test in the urban Zimbabwean pregnant woman

A clinical study carried out in urban Zimbabwe on how to derive normal glucose values for the normal woman at different gestations of pregnancy.The oral glucose tolerance test is widely used as a screening test for impaired glucose tolerance. Criteria for abnormal results in pregnancy have been documented from different countries and in Zimbabwe, the North American values as proposed by O’Sulluvan and Mahan1 have been adopted. These standards were derived from populations on Western diets; also the glucose load was 100 g, the gestations were unselected and no allowance had been made for altered glucose tolerance with advancing gestation. The standards may also be inappropriate because of the differences in the nutritional status and the dietary habits of the two population groups. Others that have used a glucose load of 50 g have obtained significantly lower values than O’Sullivan and Mahan.2,3 Although in 1979 the WHO expert committee on diabetes4 recommended a standard glucose load of 75 g, many units, including ours, continue to use the 50 g load. The aim of this study was, therefore, to derive normal glucose values for the normal urban Zimbabwean woman at different gestations of pregnancy

HIV-1 Seroconversion Incidence Following Pregnancy and Delivery Among Women Seronegative at Recruitment in Harare, Zimbabwe

A CAJM article on the incidence of HIV amongst pregnant women in Zimbabwe.Objective: To estimate the incidence of HIV sero-conversion among women following pregnancy and' delivery. Design: A prospective cohort of women who were HIV negative at recruitment on first antenatal care visit. Materials and Methods: Pregnant women were invited to undergo voluntary confidential HIV counseling and blood draw for HIV testing during the first antenatal care visit as part of a prospective study of mother- to-child transmission of HIV-1. Repeat tests were conducted at delivery, six weeks post partum and at three monthly intervals until 24 months or on termination due to subsequent pregnancy, death or loss to follow up. Logistic regression modelling was used to determine independent predictors of HIV sero-conversion. Results: Among 372 HIV negative pregnant women who were enrolled, 66 sero-converted during follow up, resulting in a sero-incidence of 4.8 per 100 person years (95% confidence interval [Cl], 3.1 to 6.5). Women who did not seroconvert during the time of pregnancy or follow up were significantly more likely to have used a condom with their partners (OR = 0.68,95% Cl = 0.47 to 0.99). Women aged 17 years and below had the highest sero-conversion incidence (6.25%) followed by those aged 18 to 19 years (5.42%). Women who sero-converted and those who were HIV positive at recruitment were more likely to be married. Lack of education by the partner of a pregnant woman constituted a significant risk factor for HIV sero-conversion (OR = 2.8; 95% Cl = 1.1 toll.0). Conclusions: There is a high HIV sero-conversion incidence among women during pregnancy and following delivery, especially those aged 19 years and below. Being married does not protect the women from the risk of HIV sero-conversion. Strategies for HIV prevention should target pregnant women and their partners

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres

Microvascular complications in South African patients with long duration diabetes mellitus

Objective. To determine the prevalence of microvascular complications in South African black and Indian patients with long-duration diabetes mellitus (DM).Design. A retrospective analysis was undertaken of clinical records of 219 OM patients (132 black, 87 Indian) with longduration OM (over 10 years) attending a diabetes clinic in Durban. Data recorded on each subject included demographic details (age, gender, ethnic group, type of diabetes, age of onset and duration of diabetes), presence of retinopathy, markers of nephropathy and biochemical variables. The prevalence of complications and the clinical and biochemical parameters were evaluated for type 1 and type 2 diabetes and for each ethnic group.Results. Of the 219 patients, 47 had type 1 OM (36 blacks, 11 Indians) and 172 were classified as type 2 OM (96 blacks, 76 Indians). The mean age of onset of OM wa later in blacks than Indians, both for type 1 (P < 0.05) and type 2 OM (P < 0.01). In patients with type 1 OM, the prevalence of retinopathy was 53.2% (blacks 55.6%, Indians 45.5%), persistent proteinuria was found in 23.4% (blacks 25%, Indians 18.2%) and hypertension in 34%. 0 ethnic difference was found except for the prevalence of hyperten ion which was higher in blacks than Indians (41.7% v. 9.1%, P < 0.5). Onset of retinopathy from time of diabetes diagno is occurred earlier in blacks than Indians (13.0 ± 4.6 yrs v. 18.0 ± 4.6 yrs, P < 0.05). For the type 2 DM group, retinopathy was found in 64.5% (black v. Indian 68.8 v. 59.2%) and per istent proteinuria in 25% (black v. Indian 30.2 v. 1 .4%). Hypertension wa observed in 68% and wa more prevalent in blacks (84.4 v. 47.,*%, P < 0.01) There was an earlier onset of retinopathy (P < 0,05) and hypertension (P < 0.01) from time of diabetes diagnosis in blacks than Indians. In the type 1 OM group retinopathy was a sociated with a ignificantly longer duration of diabetes (P < 0.05) and higher glycated haemoglobin (HbA1) (P < 0.05). For type 2 DM subjects there was a significant association between retinopathy and longer duration of diabetes (P < 0.05) and higher systolic blood pressure (P < 0.05).Conclusion. 1his study has shown that there is a high prevalence of microvascular complications in South African patients with long-duration diabetes mellitus

Risky behaviour and psychosocial correlates in adolescents – is there a link with tuberculosis?

Objective: Reasons for the increase in incidence of Tuberculosis (TB) in late adolescence are poorly understood. One hypothesis is that psychological and behavioural variables associated with adolescence may increase risk of developing TB. The study aimed to determine whether psychosocial and behavioural variables affect incidence of TB disease in adolescents. Methods: A casecontrol study design was used in adolescents who were participants in a TB epidemiological study. Cases were adolescents diagnosed with TB disease. Approximately half of the controls had no TB disease but a positive TST indicative of latent TB. Half had neither TB disease nor latent TB. A self-administered questionnaire was completed by participants. The questionnaire consisted of a combination of standardised psychosocial instruments. Results: Of 292 participants, 62 were cases, 112 had latent TB and 118 neither TB disease nor latent TB. There were no significant differences in instrument scores between cases and controls. There was a trend for certain adverse life events to be more common in the TB-disease group. Conclusion: In adolescents, a trend for association between TB incidence and psychosocial and behavioural variables was not statistically significant. Given the trend, research with larger samples, and more comprehensive assessment of the relationship between stressors and TB, is warranted.Keywords: Tuberculosis; Adolescents; Self-injurious behaviour; Psychosocial factor

A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

Risky behaviour and psychosocial correlates in adolescents - is there a link with tuberculosis?

Reasons for the increase in incidence of Tuberculosis (TB) in late adolescence are poorly understood. One hypothesis is that psychological and behavioural variables associated with adolescence may increase risk of developing TB. The study aimed to determine whether psychosocial and behavioural variables affect incidence of TB disease in adolescents. Methods: A case control study design was used in adolescents who were participants in a TB epidemiological study. Cases were adolescents diagnosed with TB disease. Approximately half of the controls had no TB disease but a positive TST indicative of latent TB. Half had neither TB disease nor latent TB. A self-administered questionnaire was completed by participants. The questionnaire consisted of a combination of standardised psychosocial instruments. Results: Of 292 participants, 62 were cases, 112 had latent TB and 118 neither TB disease nor latent TB. There were no significant differences in instrument scores between cases and controls. There was a trend for certain adverse life events to be more common in the TB-disease group. Conclusion: In adolescents, a trend for association between TB incidence and psychosocial and behavioural variables was not statistically significant. Given the trend, research with larger samples, and more comprehensive assessment of the relationship between stressors and TB, is warranted