A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions

The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour integral, we derive a unified bound for the combined error from both sources for analytic integrands. The bound gives the Euler–Maclaurin formula in one limit and the geometric convergence of the trapezoidal rule for periodic analytic functions in another

The Remez algorithm for trigonometric approximation of periodic functions

In this paper we present an implementation of the Remez algorithm for trigonometric minimax approximation of periodic functions. There are software packages which implement the Remez algorithm for even periodic functions. However, we believe that this paper describes the first implementation for the general periodic case. Our algorithm uses Chebfun to compute with periodic functions. For each iteration of the Remez algorithm, to construct the approximation, we use the second kind barycentric trigonometric interpolation formula instead of the first kind formula. To locate the maximum of the absolute error, instead of dense sampling of the error function, we use Chebfun’s eigenvalue based root finding method applied to the Chebyshev representation of the derivative of the underlying periodic function. Our algorithm has applications for designing FIR filters with real but asymmetric frequency responses

Clinical screening for congenital heart disease in newborns at a tertiary care hospital of a developing country

Objective: To screen all newborns admitted to a tertiary care hospital to rule out congenital heart disease before discharge and to find out the utility of pulse oximetry to detect congenital heart disease. Methodology: This prospective study was done at Aga Khan University Hospital from January 2014 to December 2014 in 1,650 newborns over a period of 12 months. Pulse oximetry and clinical examination were done. Persistent oxygen saturation less than 95% was considered as positive pulse oximetry. Newborns who had positive pulse oximetry or abnormal clinical examinations findings were subjected to echocardiography. Result: Pulse oximetry was performed on 1,650 newborns, out of which 25 (1.5%) had congenital heart disease. Positive pulse oximetry cases were 16 (0.97%), out of which 10 had only positive pulse oximetry (negative clinical examination). Positive clinical examination cases were 45 (2.7%), out of which 39 cases had only positive clinical examinations (negative pulse oximetry). Six newborns had both positive pulse oximetry and positive clinical examination. Out of the 25 diagnosed cases of congenital heart disease, ventricular septal defect (VSD) was the most common congenital heart disease, followed by patent ductus arteriosus (PDA). The sensitivity, specificity, positive predictive value, and negative predictive value of pulse oximetry were 32%, 99.5%, 50%, and 98.9% respectively. Conclusion: The community setting of a developing country, a combination of pulse oximetry screening and clinical examination are better at detecting congenital heart defects than either test alon

Strontium- and Zinc-Containing Bioactive Glass and Alginates Scaffolds.

With an increasingly elderly population, there is a proportionate increase in bone injuries requiring hospitalization. Clinicians are increasingly adopting tissue-engineering methods for treatment due to limitations in the use of autogenous and autologous grafts. The aim of this study was to synthesize a novel, bioactive, porous, mechanically stable bone graft substitute/scaffold. Strontium- and zinc-containing bioactive glasses were synthesized and used with varying amounts of alginate to form scaffolds. Differential scanning calorimetric analysis (DSC), FTIR, XRD, and NMR techniques were used for the characterization of scaffolds. SEM confirmed the adequate porous structure of the scaffolds required for osteoconductivity. The incorporation of the bioactive glass with alginate has improved the compressive strength of the scaffolds. The bioactivity of the scaffolds was demonstrated by an increase in the pH of the medium after the immersion of the scaffolds in a Tris/HCl buffer and by the formation of orthophosphate precipitate on scaffolds. The scaffolds were able to release calcium, strontium and zinc ions in the Tris/HCl buffer, which would have a positive impact on osteogenesis if tested in vivo

Effect of intravenous infusion of magnesium sulphate on postoperative analgesia in patients undergoing arthroscopic knee surgeries under spinal anaesthesia

Background: Magnesium sulphate is being used for postoperative pain relief intravenously, intrathecally and epidurally. Currently, it is also gaining popularity as an adjuvant in blocks. The objective of the study was aimed at the postoperative analgesic effects of magnesium sulphate when given as intravenous infusion in patients undergoing arthroscopic knee surgeries under spinal anaesthesia and to compare the postoperative analgesic effects of magnesium sulphate infusion in a study cohort who received magnesium sulphate with the control cohort who were not given magnesium sulphate and underwent arthroscopic knee surgeries under spinal anaesthesia.Methods: After obtaining ethical committee clearance and consent from the patients, 31 patients each were placed in study cohort and control cohort. Spinal anaesthesia was administered in the lateral decubitus position through the L3–4 or L4–5 interspace. Hyperbaric bupivacaine 0.5% solution with fentanyl 20 μg was injected intrathecally. After spinal anaesthesia, patients received magnesium sulphate 50 mg/kg for 15 min and then 15 mg/kg/hr by continuous intravenous infusion until the end of surgery. The other group did not receive magnesium sulphate infusion. Postoperative pain scores and postoperative analgesic consumption were the primary end points.Results: The results of the study reveal the efficacy of perioperative intravenous infusion of magnesium sulphate in prolonging the spinal block as well as reducing the postoperative pain scores without hemodynamic variability or side effects.Conclusions: Post-operative pain and analgesic consumption was reduced with the use of intravenous magnesium following spinal anaesthesia

Effect of bypass fat on growth and body condition score of male Beetal goats during summer

The objective of the present study was to investigate the effect of feeding rumen bypass fat on the growth of male Beetal goats. Twenty-seven male kids with an average bodyweight of 34 ± 1.8 kg (mean ± SD) and aged 12 to 15 months were randomly divided into three treatment groups under a completely randomized design. The treatments consisted of : i) CON, basal diet without added fat (basal diet of chopped sorghum with 0.75 kg concentrate per animal); ii) MF, basal diet with added fat at 2.5% of dry matter in concentrate (Energizer-RP10, Scothorn Nutrition, Malaysia); and iii) HF, basal diet with added fat at 5% of dry matter in concentrate. Dry matter intake (DMI) and faecal score were recorded daily. Live bodyweight was recorded fortnightly. Linear body measurements, which included wither height (WH), heart girth (HG), body length (BL), and body condition scores (BCS), were recorded monthly. The results indicated that the addition of bypass fat in concentrate did not affect DMI linearly. However, a quadratic trend of DMI was observed in response to fat addition (P <0.1). The average daily gain was similar for CON, MF, and HF treatment groups (P >0.05). Moreover, the addition of bypass fat did not affect the BCS, WH, HG, and BL. The HF group had a higher faecal score than the CON and MF groups (P <0.05). The current findings conclude that the addition of bypass fat in diets did not improve the growth performance of yearling Beetal male goats.Keywords: average daily gain, body measurements, supplemental fat

Optical properties of diamond like carbon films prepared by DC-PECVD

Diamond-like carbon (DLC) thin films were deposited at different substrate temperatures using methane and hydrogen gas in DC-PECVD at 2x10-1Torr. From the light transmission using UV-VIS spectroscopy it was found that the optical transition had changed from allowed indirect transition to allowed direct transition as the substrate temperature increased. The Optical gap increased with temperature, highest of 3.034 eV was observed at 573 K, beyond which it dropped. Colour of the film changed from light brownish to a colourless transparent film in the higher temperature. The Urbach energy decreased from 1.25 eV to 0.75 eV with increasing substrate temperature till 573 K and a slight increase after it. This trend is attributed to change in sp3/sp2 ratio or change in structure. The cluster size decreases with temperature, resulting in larger band gap and the structure more ordered. Similar pattern is also witnessed in the emission spectrum of the photoluminescence

Extension of Chebfun to Periodic Functions

Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary differential equations. Differences from the nonperiodic Chebyshev case are highlighted