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 estimation of the regular regression model requires several assumptions to be satisfied such as "linearity". One problem occurs by partitioning the regression curve into two (or more) parts and then joining them by threshold point(s). This situation is regarded as a linearity violation of regression. Therefore, the multiphase regression model is received increasing attention as an alternative approach which describes the changing of the behavior of the phenomenon through threshold point estimation. Maximum likelihood estimator "MLE" has been used in both model and threshold point estimations. However, MLE is not resistant against violations such as outliers' existence or in case of the heavy-tailed error distribution. The main goal of t

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 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

Recently, the development and application of the hydrological models based on Geographical Information System (GIS) has increased around the world. One of the most important applications of GIS is mapping the Curve Number (CN) of a catchment. In this research, three softwares, such as an ArcView GIS 9.3 with ArcInfo, Arc Hydro Tool and Geospatial Hydrologic Modeling Extension (Hec-GeoHMS) model for ArcView GIS 9.3, were used to calculate CN of (19210 ha) Salt Creek watershed (SC) which is located in Osage County, Oklahoma, USA. Multi layers were combined and examined using the Environmental Systems Research Institute (ESRI) ArcMap 2009. These layers are soil layer (Soil Survey Geographic SSURGO), 30 m x 30 m resolution of Digital Elevati

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.

The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient b_i is random variable