The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

This research aims to numerically solve a nonlinear initial value problem presented as a system of ordinary differential equations. Our focus is on epidemiological systems in particular. The accurate numerical method that is the Runge-Kutta method of order four has been used to solve this problem that is represented in the epidemic model. The COVID-19 mathematical epidemic model in Iraq from 2020 to the next years is the application under study. Finally, the results obtained for the COVID-19 model have been discussed tabular and graphically. The spread of the COVID-19 pandemic can be observed via the behavior of the different stages of the model that approximates the behavior of actual the COVID-19 epidemic in Iraq. In our study, the COV

Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

Abstract To ensure that the distribution system has safe drinking water. It is necessary to know the residual chlorine concentrations at various points in the network. A chlorine photometer device was used to measure twenty points taken every day for a week at a selected time in the distribution system. Both pressures and flows in the network were measured using bourdon gauge and Tuf-2000H Handheld Digital ultrasonic flow meters. WaterGEMS CONNECT Edition update one software was used to simulate the flow in the network. The Baghdad water department provided the data about the network, such as the lengths of pipes, the layout of the network, and pipes diameters. The network calibrated consists of 781 pipes of different lengths and 542 juncti

     The paper shows how to estimate the three parameters of the generalized exponential Rayleigh distribution by utilizing the three estimation methods, namely, the moment employing estimation method (MEM), ordinary least squares estimation method (OLSEM),  and maximum entropy estimation method (MEEM). The simulation technique is used for all these estimation methods to find the parameters for the generalized exponential Rayleigh distribution. In order to find the best method, we use the mean squares error criterion. Finally, in order to extract the experimental results, one of object oriented programming languages visual basic. net was used

Often phenomena suffer from disturbances in their data as well as the difficulty of formulation, especially with a lack of clarity in the response, or the large number of essential differences plaguing the experimental units that have been taking this data from them. Thus emerged the need to include an estimation method implicit rating of these experimental units using the method of discrimination or create blocks for each item of these experimental units in the hope of controlling their responses and make it more homogeneous. Because of the development in the field of computers and taking the principle of the integration of sciences it has been found that modern algorithms used in the field of Computer Science genetic algorithm or ant colo

   The removal of Anit-Inflammatory drugs, namely; Acetaminophen (ACTP), from wastewater by bulk liquid membrane (BLM) process using Aliquat 336 (QCl) as a carrier was investigated. The effects of several parameters on the extraction efficiency were studied in this research, such as the initial feed phase concentration (10-50) ppm of ACTP, stripping phase (NaCl) concentration (0.3,0.5,0.7 M), temperature (30-50^oC), the volume ratio of feed phase to membrane phase (200-400ml/80ml), agitation speed of the feed phase (75-125 rpm), membrane stirring speed (0, 100, 150 rpm), carrier concentration (1, 5, 9 wt%), the pH of feed (2, 4, 6, 8, 10), and solvent type (CCl₄ and n-Heptane). The study shows that high ext

The present study aims to explore determinants of entrepreneurial behavior from perspective of social theory. It is based on model notions of (Tyler & Blader, 2003) which have focused on studying role of positively personal and social identity in motivating employees to practicing desired behavior which serves the organization in which they work. Based on these notions and previous literature, study model were built. This model explains the relationship between status judgments (perceived internal respect and perceived external prestige)  and entrepreneurial behavior. It includes three main hypotheses. The first and second hypothesis are concerning the relationship between status judgmen

The removal of COD from wastewater generated by petroleum refinery has been investigated by adopting electrocoagulation (EC) combined with adsorption using activated carbon (AC) derived from avocado seeds. The process variables influencing COD removal were studied: current density (2–10 mA/cm2), pH (4–9), and AC dosage (0.2–1 g/L). Response surface methodology (RSM) based on Box–Behnken design (BBD) was used to construct a mathematical model of the EC/AC process. Results showed that current density has the major effect on the COD removal with a percent of contribution 32.78% followed by pH while AC dosage has not a remarkable effect due to the good characteristics of AC derived from avocado seeds. Increasing current density gives be

The present investigation is concerned for the purification of impure zinc oxide (80-85 wt %) by using petroleum coke
(carbon content is 76 wt %) as reducing agent for the impure zinc oxide to provide pure zinc vapor, which will be
oxidized later by air to the pure zinc oxide.
The operating conditions of the reaction were studied in detail which are, reaction time within the range (10 to 30 min),
reaction temperature (900 to 1100 oC), air flow rate (0.2 to 1 l/min) and weight percentage of the reducing agent
(petroleum coke) in the feed (14 to 30 wt %).
The best operating conditions were (30 min) for the reaction time, (1100 oC) for the reaction temperature, (1 l/min) for
the air flow rate, and (30 wt %) of reducing