In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal method in solving these problems.
In this work, laboratory experiments were carried out to verify direct contact membrane distillation system’s performance in highly saline water desalination. The study included the investigation of various operating conditions, like feed flow rate, temperature and concentration of NaCl solution and their impact on the permeation flux were discussed. 16 cm2 of a flat sheet membrane module with commercial poly-tetra-fluoroethylene (PTFE) membrane, which has 0.22 μm pore size, 96 µm thickness and 78% average porosity, was used. A high salt rejection factor was obtained greater than 99.9%, and the permeation flux up to 17.27 kg/m2.h was achieved at 65°C for hot feed side and 20°C for cold side stream.
The effect of solution heat treatment on the mechanical properties of Aluminum-Copper alloy. (2024-T3) by the rolling process is investigated. The solution heat treatment was implemented by heating the sheets to 480 C° and quenching them by water; then forming by rolling for many passes. And then natural aging is done for one month. Mechanical properties (tensile strength and hardness) are evaluated and the results are compared with the metal without treatment during the rolling process. ANSYS analysis is used to show the stresses distribution in the sheet during the rolling process. It has been seen that good mechanical properties are evident in the alloy without heat treatment due to the strain hardening and also the mechanical
... Show MoreComplex-valued regular functions that are normalized in the open unit disk are vastly studied. The current study introduces a new fractional integrodifferential (non-linear) operator. Based on the pre-Schwarzian derivative, certain appropriate stipulations on the parameters included in this con-structed operator to be univalent and bounded are investigated and determined.
The main aim of this paper is to study how the different estimators of the two unknown parameters (shape and scale parameter) of a generalized exponential distribution behave for different sample sizes and for different parameter values. In particular,
. Maximum Likelihood, Percentile and Ordinary Least Square estimators had been implemented for different sample sizes (small, medium, and large) and assumed several contrasts initial values for the two parameters. Two indicators of performance Mean Square Error and Mean Percentile Error were used and the comparisons were carried out between different methods of estimation by using monte carlo simulation technique .. It was obse
... Show MoreUltraviolet light radiation is applied to treat Plaque Psoriasis disease by targeted phototherapy. This is available through Narrowband-UVB light radiation devices peaked at wavelength 311 nm. Ten cases were chosen as a study group, 8 males aged 22-40 years old, and 2 females aged 25 and 32 years old who were exposed to ultraviolet light radiation. Their recovery or improvement was followed weekly. Different doses were used according to the severity of the lesion and as a trial for the outcome. The dose was given two times a week, starting with 200mJ/cm2, and subsequently increased by 100 or 200 mJ/cm2 reaching a maximum dose as tolerated by each individual patient. Improvement was observed after 4 – 6 weeks. The
... Show MoreIn this paper, the Reliability Analysis with utilizing a Monte Carlo simulation (MCS) process was conducted on the equation of the collapse potential predicted by ANN to study its reliability when utilized in a situation of soil that has uncertainty in its properties. The prediction equation utilized in this study was developed previously by the authors. The probabilities of failure were then plotted against a range of uncertainties expressed in terms of coefficient of variation. As a result of reliability analysis, it was found that the collapse potential equation showed a high degree of reliability in case of uncertainty in gypseous sandy soil properties within the specified coefficient of variation (COV) for each property. When t
... Show MoreThe origin of this technique lies in the analysis of François Kenai (1694-1774), the leader of the School of Naturalists, presented in Tableau Economique. This method was developed by Karl Marx in his analysis of the Departmental Relationships and the nature of these relations in the models of " "He said. The current picture of this type of economic analysis is credited to the Russian economist Vasily Leontif. This analytical model is commonly used in developing economic plans in developing countries (p. 1, p. 86). There are several types of input and output models, such as static model, mobile model, regional models, and so on. However, this research will be confined to the open-ended model, which found areas in practical application.
... Show MoreIn the present work, a kinetic study was performed to the extraction of phosphate from Iraqi Akashat phosphate ore using organic acid. Leaching was studied using lactic acid for the separation of calcareous materials (mainly calcite). Reaction conditions were 2% by weight acid concentration and 5ml/gm of acid volume to ore weight ratio. Reaction time was taken in the range 2 to 30 minutes (step 2 minutes) to determine the reaction rate constant k based on the change in calcite concentration. To determine value of activation energy when reaction temperature is varied from 25 to 65 , another investigation was accomplished. Through the kinetic data, it was found that selective leaching was controlled by
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