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  • Author or Editor: Elsayed Elsayed x
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In this paper we study the behavior of the difference equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x_{n + 1} = ax_{n - 2} + \frac{{bx_n x_{n - 2} }}{{cx_n + dx_{n - 3} }},n = 0,1,...$$ \end{document}
where the initial conditions x −3 , x −2 , x −1 , x 0 are arbitrary positive real numbers and a, b, c, d are positive constants. Also, we give the solution of some special cases of this equation.

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Abstract  

Comparison of Compton scattering and Compton scattering cross section with self-attenuation coefficient were explained based on the kinematic equation and Klein-Nishina formula. Naturally occurring elements, 238U (226Ra), 40K, 232Th (228Ra) and 137Cs were determined in sediments and water from Ismailia canal in Egypt which were found in the range of permissible level. Self-attenuation coefficients, K, the ratio between photopeak detection efficiency using solid and liquid standards were determined. They fit well comparing to Compton scattering, Compton scattering cross section while inversely fit to energy-absorption Compton scattering cross section based on the Klein-Nishina formula.

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We study nonlinear singular integral equation of Volterra type in Banach space of real functions defined and continuous on a bounded and closed interval. Using a suitable measure of noncompactness we prove the existence of monotonic solutions of the considered equation and its generalization. We illustrate our existence results by numerical examples.

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Summary  

The extractive first order derivative spectrophotometry is a selective method for the separation and determination of U(VI) using tri-n-butyl phosphate (TBP), which combines the roles of solvent and complexing agent. The complex is formed by extracting U(VI) from an aqueous 6M sodium nitrate solution at initial pH 3.0 into a 25% solution of TBP in kerosene. This extraction also separates U(VI) from many diverse ions that interfere. After extraction, the determination of uranium shows good accuracy and precision with relative standard deviation of 1.5% (n = 5) at 20 ppm using zero-order spectrum at lmax = 250 nm. Calibration curve was also found to obey Beer's law in the range of 10-100 ppm with 3.33 ppm detection limit. However, these accuracy and precision have been improved to give relative standard deviation of 0.7% (n = 5) at 20 ppm with a lower detection limit of 2.24 ppm using the first-derivative spectrum at l = 263 nm comparing to the normal one.

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This study was designed to establish serum cardiac troponin I (cTnI) concentrations in healthy newborn goat kids and in those with cardiac nutritional muscular dystrophy (NMD). Thirty-five single full-term newborn goat kids (20 males and 15 females; age: 6.1 ± 3.5 h; weight 3.4 ± 0.68 kg), together with their respective mothers (Group 1; G1) were enrolled consecutively. Thirty-one goat kids (age: 9.5 ± 4.3 days) with NMD, together with 20 control goat kids (age: 7.8 ± 4.3 days) were also included in this study (Group 2; G2). Blood samples were collected from G1 within 12 h of birth and from G2 on admission. Serum samples were collected and analysed for cTnI. In G1, the mean serum concentration of cTnI in goat kids was 0.290 ± 0.37 ng/mL, with no statistically significant difference between male and female kids (P = 0.61). The mean cTnI concentration in the does was 0.017 ± 0.04, ng/mL. Serum values of cTnI in the goat kids and in their respective mothers differed significantly (P = 0.0001). In G2, the mean cTnI concentration was 0.02 ± 0.05 ng/mL in the control and 11.18 ± 20.07 ng/mL in the diseased goat kids, with a statistically significant difference between diseased and control goat kids (P = 0.017). Serum concentrations of cTnI are higher in goat kids than in their respective mothers. In conclusion, the cTnI assay appears to be a sensitive and specific marker for myocardial injury in goat kids.

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Water is necessary to life so when supplied as drinking water to consumers, a satisfactory quality must be maintained. In Egypt, infectious intestinal diseases are the major cause of hospitalization in almost all regions. The purpose of this study was to evaluate the microbiological quality of treated and untreated water samples from urban and rural communities. Thirty-five samples of treated (chlorinated) water from taps, 25 samples of bottled water and 15 samples of hand pump (untreated) water collected from different cities alongside the River Nile during the winter of 2007 were bacteriologically tested for safety as drinking water. This study indicated good quality of tap water and bottled water. The untreated water samples (hand pumps) were, however, slightly contaminated by faecal coliforms, faecal enterococci, Clostridium perfringens, Salmonella and Shigella . Consequently, the consumers in the villages receiving water through hand pumps are often exposed to the risk of water-borne diseases due to inadequate treatment of the raw water. Therefore, there are guidelines necessary to protect groundwater quality. Moreover, PCR-amplified by some functional gene fragments such as dctA, dcuB, frdA, dcuS and dcuR genes of the E. coli was adapted for use as a non-cultivation-based molecular approach for detection of E. coli populations from water samples without the need for pure and identified cultures.

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In this study, two green microalgae, Dunaliella bardawil and Chlorella ellipsoidea , are exposed to different pH values. The two tested microalgae could grow in a wide range of pH (4–9 for D. bardawil and 4–10 for C. ellipsoidea ). The dry weight gain and the biochemical components of D. bardawil were greatly enhanced at pH 7.5. On the contrary, dry weight and carbohydrate content of C. ellipsoidea attained their maximum values at the alkaline pH. On the other hand, the protein content of C. ellipsoidea recorded its highest value at pH 4, while the pigment content of the same alga highly accumulated at pH 4, 6 and 7.5 and decreased as pH directed to the alkaline side. Both pH 6 and pH 9 stimulated the accumulation of vitamin E and vitamin C in D. bardawil , with the highest values of the three compounds recorded at pH 9. In case of C. ellipsoidea , β-carotene content increased at pH 6 and 10 as compared with control, but the amount of β-carotene was much higher at pH 6 than at pH 10. Contrarily, vitamin E was highly accumulated in C. ellipsoidea cells at pH 10 than at pH6. BothpH6 andpH10 caused a significant decline in vitaminCcontent in C. ellipsoidea .

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