A mathematical model is developed which predicates the performance of cylindrical ion exchange bed involving comparing of axial dispersion model for cation exchange column with different assumption, this model permits the performance to predicate the residence time within the bed with the variance, axial dispersion and Pecklet No. to indicated deviation from plug flow model.

      Two type of systems are chosen for positive ions first with divalent ions (Ca⁺²) to exchange with resin of Na⁺¹form used as application in  water softener units and second with monovalent ions (Na⁺¹) to exchange with resin of H⁺¹ form used as application in deionize water units &n

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simul

The state did not witness the emergence of independent bodies because of the nature of the ruling regimes that were characterized by political tyranny represented by the king at the time, as is the case with Greece and the Greeks and Persia and the Romans and others. As for the Islamic state, which emerged later, it saw the emergence of what looks like independent bodies that we see today, There was the so-called Diwan Al-Hesba and the Ombudsman's Office as an independent body from the Islamic State, which operated independently to support the oppressed and the equitable distribution of financial resources, even though it was headed by well-known governors of justice and honesty. A state in the modern era, many countries, especially in E

The aim of this article is to study the dynamical behavior of an eco-epidemiological model. A prey-predator model comprising infectious disease in prey species and stage structure in predator species is suggested and studied. Presumed that the prey species growing logistically in the absence of predator and the ferocity process happened by Lotka-Volterra functional response. The existence, uniqueness, and boundedness of the solution of the model are investigated. The stability constraints of all equilibrium points are determined. The constraints of persistence of the model are established. The local bifurcation near every equilibrium point is analyzed. The global dynamics of the model are investigated numerically and confronted with the obt

This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

A field study aimed at identifying the sources of mutual complaints among the Directorates of Education staff of their departments and management and run it in their daily dealings with principals in the province of Baghdad, and adopt approach. It was determined the research consists of (2357) male and female employees and 305 randomly stratified simple by the rate of (7%) from the research community as the number of sample reached (167) male and female employees, and selected sample was randomly stratified simple by the rate of (39.67%) of the research community, as the number of sample was (121) principals. It was constructed two questionnaires, the first included (28) items and the second contained (28) items. And the two researchers

The adsorption of hexavalent chromium by preparing activated carbon from date seeds with zinc chloride as chemical activator and granular date seeds was studied in a batch system. The characteristics of date seeds and prepared activated carbon (ZAC) were determined and found to have a surface area 500.01 m²/g and 1050.01  m²/g , respectively and  iodine number of 485.78 mg/g and 1012.91  mg/g, respectively. The effects of PH value (2-12), initial sorbate concentration(50-450mg/L), adsorbent weight (0.004-0.036g) and contact time (30-150 min) on the adsorption process were studied . For Cr(VI) adsorption on ZAC, at 120 min time contact, pH solution 2 and 0.02  adsorbent  weight  will ach

The study aims at knowing students’ academic assistance at the Department of Kindergarten. It further aims to know the difference of academic assistance among these students with respects to variables like (college of education for women, Baghdad, Thi-Qar). It also aims to know about the difference according to the academic level variable, in addition to its relation to some other variables. To achieve the objectives of the study, a number of university female students were selected from both Baghdad an Thi-Qar Universities in the academic year 2019-2020. The sample of the participants consisted of (400) students from the (second, third, and fourth) levels. To measure the study variable represented by the concept of academic assistance

A seemingly uncorrelated regression (SUR) model is a special case of multivariate models, in which the error terms in these equations are contemporaneously related. The method estimator (GLS) is efficient because it takes into account the covariance structure of errors, but it is also very sensitive to outliers. The robust SUR estimator can dealing outliers. We propose two robust methods for calculating the estimator, which are (S-Estimations, and FastSUR). We find that it significantly improved the quality of SUR model estimates. In addition, the results gave the FastSUR method superiority over the S method in dealing with outliers contained in the data set, as it has lower (MSE and RMSE) and higher (R-Squared and R-Square Adjus