In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.

Al-Qudis power plant was chosen, as one of the power stations of Baghdad, to investigate the effects of Cadmium that emitted from combustion of crude oil in that power plant on the workers' glutathione serum level. Air samples were taken seasonally during August 2011- July 2012 from four sites at Al- Qudis power plant which are oil treatment unit 1(site 1), oil treatment 2 (site2), pre –chimney 1(site 3) and pre-chimney 2 (site 4), to measure levels of heavy metal (cadmium) under study. Blood samples were collected from the workers to estimate the heavy metal Cadmium. Air cadmium levels during summer (August and September) were varied from 6.26 ± 0.6 μg/m3 at site 1 to 6.89 ± 0.67 μg/m3 at site 3, while in spring (end of March, and

Al-Qudis power plant was chosen, as one of the power stations of Baghdad, to investigate the effects of Cadmium that emitted from combustion of crude oil in that power plant on the workers' glutathione serum level. Air samples were taken seasonally during August 2011- July 2012 from four sites at Al- Qudis power plant which are oil treatment unit 1(site 1), oil treatment 2 (site2), pre –chimney 1(site 3) and pre-chimney 2 (site 4), to measure levels of heavy metal (cadmium) under study. Blood samples were collected from the workers to estimate the heavy metal Cadmium. Air cadmium levels during summer (August and September) were varied from 6.26 ± 0.6 μg/m3 at site 1 to 6.89 ± 0.67 μg/m3 at site 3, while in spring (end of March, and

In this article, performing and deriving the probability density function for Rayleigh distribution by using maximum likelihood estimator method and moment estimator method, then crating the crisp survival function and crisp hazard function to find the interval estimation for scale parameter by using a linear trapezoidal membership function. A new proposed procedure used to find the fuzzy numbers for the parameter by utilizing (     to find a fuzzy numbers for scale parameter of Rayleigh distribution. applying two algorithms by using ranking functions to make the fuzzy numbers as crisp numbers. Then computed the survival functions and hazard functions by utilizing the real data application.

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

The Plerion nebula is characterized by its pulsar that fills the center of the supernova remnant with radio and X-ray frequencies. In our galaxy there are nine naked plerionic systems known, of which the Crab Nebula is the best-known example. It has been studied this instance in order to investigate how the pulsar energy affect on the distribution and evolution of the remnant as well as study the pulsar kick velocity and its influence on the remnant. From the obtained results it's found that, the pulsar of the Crab Nebula injects about (2−3)𝑥 1047 erg of energy to the remnant, although this energy is small compared to the supernova explosion energy which is about 1051 erg but still plays a significant role in the distribution and the m

     This paper develop conventional Runge-Kutta methods of order four and order five to solve ordinary differential equations with oscillating solutions. The new modified Runge-Kutta methods (MRK) contain the invalidation of phase lag, phase lag’s derivatives, and amplification error. Numerical tests from their outcomes show the robustness and competence of the new methods compared to the well-known Runge-Kutta methods in the scientific literature.