Necessary and sufficient conditions for the operator equation I AXAX n  * , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

This study was carried out to investigate the effect of dietary supplementation with different levels of parsley on semen quality of local Iraqi ganders. A total of thirty-two local ganders were used in this study during the period from the beginning of February to the end of April. The ganders were allocated for 4 treatment groups containing 8 ganders each. The treatment groups were as follows: Control diet (free from parsley); T1: Control diet + 80 g/d parsley; T2: Control diet + 160 g/d parsley; T3: Control diet + 240 g/d parsley. Semen samples were collected twice a week, fortnightly, from each gander by the dorsal-abdominal message method. The first semen collection was used to evaluate semen volume, sperm concentration, live in total

Objectives: To assess the quality of life for adult patients with peptic ulcers in the city of Sulaimani.
Methodology: A descriptive study, using the assessment approach was conducted on patients with peptic ulcer
disease from January 12th, 2009 to September 30th, 2009. A purposive "non-probability" sample of (100) paƟents
(males and females) with peptic ulcers who attended Kurdistan Center for Gastroenterology and Hepatology were
selected for the study. A questionnaire was adapted from the World Health Organization quality of life questionnaire
(1998) for the purpose of the study. It is comprised of (3) parts that included sociodemographic characteristics form,
medical history form and adult peptic ulcers patients' qu

 Education is a process of learning and education at the same time. As the conditions of modern life necessitate every person to keep learning, education has become a necessity to meet life needs. The society today is concerned with the educational process and aims to live up the expectations. Since education is an integral part of education and its means, it has become as a mean to achieve its purposes. The educational environment was a traditional environment limited to specific inputs, possibilities and stimulus of both teacher and student. Due to the latest advancement, the educational environment has been expanded to become a rich, with strong connections. It has expanded to encompass the entire global environment. The current

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.

When scheduling rules become incapable to tackle the presence of a variety of unexpected disruptions frequently occurred in manufacturing systems,  it is necessary to develop a reactive schedule which can absorb the effects of such disruptions. Such responding requires efficient strategies, policies, and methods to controlling production & maintaining high shop performance. This can be achieved through rescheduling task which defined as an essential operating function to efficiently tackle and response to uncertainties and unexpected events. The framework proposed in this study consists of rescheduling approaches, strategies, policies, and techniques, which represents a guideline for most manufacturing companies operatin

Most of the water pollutants with dyes are leftovers from industries, including textiles, wool and others. There are many ways to remove dyes such as sorption, oxidation, coagulation, filtration, and biodegradation, Chlorination, ozonation, chemical precipitation, adsorption, electrochemical processes, membrane approaches, and biological treatment are among the most widely used technologies for removing colors from wastewater. Dyes are divided into two types: natural dyes and synthetic dyes.

This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some