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.

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is

Excessive intake of fluoride, mainly through drinking water is a serious health hazard affecting humans worldwide. In this study, the defluoridation capacities of locally available raw waste beef bones have been estimated. Several experimental parameters including contact time, pH, bone dose, fluoride initial concentration, bone grains size, agitation rate, and the effect of co-existence of anions in actual samples of wastewater were studied for fluoride removal from aqueous solutions. Results indicated excellent fluoride removal effeciency up to 99.7% at fluoride initial concentration of 10 mg F/L and 120 min contact time. Maximum fluoride uptake was obtained at neutral pH range 6-7. Fluoride removal kinetic was well described by the ps

There are serious environmental problems in all countries of the world, due to the waste material such as crushed clay bricks (CCB) and in huge quantities resulting from the demolition of buildings. In order to reduce the effects of this problem as well as to preserve natural resources, it is possible to work on recycling (CCB) and to use it in the manufacture of environmentally friendly loaded building units by replacing percentages in coarse aggregate by volume. It can be used as a powder and replacing of percentages in cement by weight and study the effect on the physical and mechanical properties of the concrete and the masonry unit. Evaluation of its performance through workability, dry density, compressive strength, thermal conduct

Several million tons of solid waste are produced each year as a result of construction and demolition activities around the world, and brick waste is one of the most widely wastes. Recently, there has been growing number in studies that conducted on using of recycling brick waste (RBW) to produce environmentally friendly concrete. The use of brick waste (BW) as potential partial cement or aggregate replacement materials is summarized in this review where the performance is discussed in the form of the mechanical strength and properties that related to durability of  concrete. It was found that, because the pozzolanic activity of clay brick powder, it can be utilized as substitute for cement in replacement level up t

Several million tons of solid waste are produced each year as a result of construction and demolition activities around the world, and brick waste is one of the most widely wastes. Recently, there has been growing number in studies that conducted on using of recycling brick waste (RBW) to produce environmentally friendly concrete. The use of brick waste (BW) as potential partial cement or aggregate replacement materials is summarized in this review where the performance is discussed in the form of the mechanical strength and properties that related to durability of  concrete. It was found that, because the pozzolanic activity of clay brick powder, it can be utilized as substitute for cement in replacement level up to 10%. Whereas,

Experimental programs based test results has been used as a means to find out the response of individual elements of structure. In the present study involves investigated behavior of five reinforced concrete deep beams of dimension (length 1200 x height 300 x width150mm) under two points concentrated load with shear span to depth ratio of (1.52), four of these beams with hallow core and
retrofit with carbon fiber reinforced polymer CFRP (with single or double or sides Strips). Two shapes of hallow are investigated (circle and square section) to evaluated the response of beams in case experimental behavior. Test on simply supported beam was performed in the laboratory & loaddeflection, strain of concrete data and crack pattern of