Numerical simulations for the Toda lattices Hamiltonian system: Higher order symplectic illustrative perspective.

In this paper we apply some higher order symplectic numerical methods to analyze the dynamics of 3-site Toda lattices (reduced to relative coordinates). We present benchmark numerical simulations that has been generated from the HOMsPY (Higher Order Methods in Python) library. These results provide detailed information of the underlying Hamiltonian system. These numerical simulations reinforce the claim that the symplectic numerical methods are highly accurate qualitatively and quantitatively when applied not only to Hamiltonian of the Toda lattices, but also to other physical models. Excepting exactly integrable models, these symplectic numerical schemes are superior, efficient, energy preserving and suitable for a long time integrations, unlike standard non-symplectic numerical methods which lacks preservation of energy (and other constants of motion, when such exist).

Role of ascorbic acid supplement in amelioration of anaemia in lead intoxication.

OBJECTIVE: To assess anaemia and oxidative stress in rats that were injected lead and to evaluate the possible effects of ascorbic acid supplementation on these parameters. METHODS: This randomised control trial study was conducted at the Army Medical College, Rawalpindi, Pakistan, from October 2007 to September 2008, and comprised Sprague Dawley rats. The rats were randomly divided into three groups. The rats in Group 1 were given weekly injections of sodium acetate, and rats of Group 2 and 3 were given weekly injections of lead acetate. Ascorbic acid was supplemented in the drinking water of rats of Group 3. At the end of six weeks, terminal sampling was done and blood obtained was used to assess the serum malondialdehyde levels and red cell parameters. RESULTS: Of the 105 rats, each group had 35(33.33%). The overall mean age was 105±15 days and the mean weight was 225±25gm. The mean malondialdehyde level was 3.2±0.39 µmol /L in Group 1, 7.8±0.48 in Group 2 and 3.8±0.34 in Group 3 (p<0.001). The mean haemoglobin level was 13.16±0.57 g/dL, 10.64±0.86 and 12.22±0.81, respectively (p<0.001). The red blood cells count was 7.63±0.33 106/µL in Group 1, 6.29±0.54 in Group 2 and 6.83±0.45 in Group 3 (p<0.001). CONCLUSIONS: Administration of ascorbic acid in drinking water significantly reduced the oxidative stress and anaemia caused by lead intoxication.

On Comparison of Series and Numerical Solutions for Flow of Eyring-Powell Fluid with Newtonian Heating And Internal Heat Generation/Absorption.

In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both series and numerical solutions. Series solution is constructed using homotopy analysis method (HAM) whereas numerical solution is presented by two different techniques namely shooting method and bvp4c. A comparison of homotopy solution with numerical solution is also tabulated. Both solutions are found in an excellent agreement. Dimensionless velocity and temperature profiles are plotted and discussed for various emerging physical parameters.

Indications for endoscopic ultrasound and diagnosis on fine-needle aspiration and cytology.

OBJECTIVE: To determine common indications for requesting Endoscopic Ultrasound (EUS) and to describe the diagnosis made after endoscopic ultrasound/Fine-Needle Aspiration and Cytology (FNAC) during two years at a tertiary gastrointestinal unit. STUDY DESIGN: Cross-sectional descriptive study. PLACE AND DURATION OF STUDY: The study was carried out in Gastrointestinal Department of Military Hospital, Rawalpindi, from March 2006 to February 2008. METHODOLOGY: One hundred and eighty nine patients who underwent EUS during study period at Military Hospital were included in the study. Patients too ill (hypoxemic/hypotensive) to undergo procedure safely and those with complete esophageal blockage at upper end by tumour not allowing scope/EUS probe to advance beyond were excluded. EUS was done with Olympus Exera EUS 160, linear or radial scope, as required. EUS findings were recorded against indications as enlarged lymph nodes, tumour, staging, normal or incomplete. Fine-Needle Aspiration (FNA) was done as per findings on EUS using 21-22 G needle. An on-site cytopathologist made the provisional cytopathological diagnosis. Final cytology/histopathology report was given after review of slides by consultant histopathologists at Armed Forces Institute of Pathology (AFIP), Rawalpindi, and were documented as tuberculosis, malignancy, chronic pancreatitis or reactive hyperplasia. Data was analyzed for documentation of patients' age, gender, common indications, findings on EUS/FNAC, using SPSS version 10. Percentages and frequencies were calculated for the presence of these above-mentioned variables. RESULTS: Of the 189 patients, 145 (77%) were male and 44 (23%) female. Age was 18-80 years (mean 49 years). Major indications for referral were lymphadenopathy in 92 (49%), suspected growth pancreas in 57 (28%), growth of stomach in 20 (11%) and a heterogeneous group included esophageal, liver, retroperitoneal masses, rectal and other pathologies. Findings on EUS included lymphadenopathy in 76, mostly in sub-carina and AP window. Mass in pancreas was seen in 36, followed by stomach tumour in 17 and esophagus in 9. FNAC was done in 142 out of 189 patients. Final diagnosis out of 67 FNAC/histopathology of lymph nodes were tuberculosis in 26 and malignant lesions in 23. These included metastatic adenocarcinoma in 8, lymphoproliferative disorder in 7, metastatic squamous cell carcinoma in 5, small cell carcinoma in 2 and anaplastic in 1. Pancreatic tumours were adenocarcinoma in 16, poorly differentiated in 3 and neuroendocrine in 2. Stomach tumours were found in 11, and included lymphomas 5, GIST 3, carcinoids 2, metastatic choriocarcinoma 1 and adenocarcinoma in 1. Therapeutically, 3 celiac blocks and one pancreatic pseudocyst drainage was done. CONCLUSION: The main indication of EUS and pathology of mediastinal and celiac nodes were metastatic malignancy and tuberculosis. Pancreatic adenocarcinoma was another common cause for asking EUS.