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

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 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 non-isothermal crystallization kinetics and crystalline properties of nanocomposites poly butyleneterephthalate, [PBT] /multiwalled-carbon nanotubes (MWCNTs) were tested by differential scanning calorimetry (DSC). PBT/(MWCNTs) nanocomposite was prepared by ultrasonicated of MWCNTs (0.5, 1, 2, 4 wt %) in dichloromethane (DCM) and after that the powdered PBT polymer was added to the MWCNTs solution. The non-isothermal crystallization results show that increasing the MWCNTs contents, decreased the melting temperature (Tm) of PBT/(MWCNTs) nanocomposite as compared with pure PBT, while resulting in improving the degree of crystallinity. These results indicated that a little amount of MWCNTs can be evident strong nucleating agent in PBT na

In this paper, the generation of a chaotic carrier by Lorenz model
is theoretically studied. The encoding techniques has been used is
chaos masking of sinusoidal signal (massage), an optical chaotic
communications system for different receiver configurations is
evaluated. It is proved that chaotic carriers allow the successful
encoding and decoding of messages. Focusing on the effect of
changing the initial conditions of the states of our dynamical system
e.i changing the values (x, y, z, x1, y1, and z1).

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.