The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.
The use of biopolymer material Chitosan impregnated granular activated carbon CHGAC as adsorbent in the removal of lead ions pb.2+ from aqueous solution was studied using batch adsorption mode. The prepared CHGAC was characterized by Scanning Electronic Microscopy (SEM) and atomic-absorption pectrophotometer. The adsorption of lead ions onto Chitosan-impregnated granular activated carbon was examined as a function of adsorbent weight, pH and
contact time in Batch system. Langmuir and Freundlich models were employed to analyze the resulting experimental data demonstrated that better fitted by Langmuir isotherm model than Freundlich model, with good correlation coefficient. The maximum adsorption capacity calculated f
The ability of Cr (VI) removal from aqueous solution using date palm fibers (leef) was investigated .The effects of pH, contact time, sorbets concentration and initial metal ions concentration on the biosorption were investigated.
The residual concentration of Cr (VI) in solution was determined colorimetrically using spectrophotometer at wave length 540 nm .The biosorption was pH-dependent, the optimum pH was 7 and adsorption isotherms obtained fitted well with Langmuir isotherms .The Langmuir equation obtained was Ce/Cs = 79.99 Ce-77.39, the correlation factor was 0.908.These results indicate that date palm fibers (leef) has a potential effect for the uptake of Cr (VI) from industrial waste water.
Background: It was stated in scientific literatures that the entire craniofacial complex is influenced by the growth of the cranial base structures. Nevertheless, many times this is not the case, and this point is subject to great controversy so the aim of this study is to evaluate the possible differences in cranial base shape and flexure between different skeletal classes for both genders and to investigate any possible correlation between cranial base variables and other skeletal base variables. Materials and Methods: The sample include 75 lateral cephalometric radiographs of Iraqi adults aged between 18-25 years (39 males, 36 females), collected from patients and undergraduate students in the orthodontic department of College of Dentist
... Show MoreThe aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.
Abstract
A two electrode immersion electrostatic lens used in the design
of an electron gun, with small aberration, has been designed using
the finite element method (FEM). By choosing the appropriate
geometrical shape of there electrodes the potential V(r,z) and the
axial potential distribution have been computed using the FEM to
solve Laplace's equation.
The trajectory of the electron beam and the optical properties of
this lens combination of electrodes have been computed under
different magnification conditions (Zero and infinite magnification
conditions) from studying the properties of the designed electron
gun can be supplied with Abeam current of 5.7*10-6 A , electron
gun with half acceptance
This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.
In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.
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A field experiment was conducted at Abu-Ghrib during 2013- 2014 season to study the effect of harrowing systems on the decomposition and fermentation on organic matter(OM) when added and mixed with the soil under special technology, as well as its effect on the growth parameters and productivity of (Zea mays L. 5018). The experiment was laid out using factorial randomized complete block design (RCBD) in split-split design with three replications in SCL bare soil with a percent of moisture ranged from 16 – 18 %. The main plots were designated to the two systems of harrowing (Rotary Harrowand Disc Harrow ). The sub main plots were specified for two organic matters ( Sheep manure ,cow manure ) . Data were statistically analyzed, and
... Show MoreThe techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of
... Show MoreIn the past years, the Algerian Economy has witnessed various monetary developments characterized by different monetary and banking reforms aimed by monetary authorities to achieve monetary stability and driving overall growth. It should be noted that there is evidence to initiate fundamental changes on the basis of which new monetary, financing and banking policy mechanisms must be formulated in Algeria by enhancing the pursuit of reforming the monetary system, in order to improve monetary and economic indicators.
The study a
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