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 produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.
words of God the Quranic text , is genera words have many faces and connotations a ccording to references, cutures and Ages.That the Quranic text is fixed , But the connotations are moveable the scientists agreed about the miracle of the Qurantic text , But they differd of the Position of miracLe including the muatazala and Al- Ashaira who have adopted the idea of sytem and miracle of linguistic . Most of them were lingustics, grammerians and writers as: AL- Jahith, AL- Faraa Abivbeida , Ibn kutaba , AL -Rumani , AL -katabi , AL- Bakilaai , AL- Gargani and Others.
They also differed in what the words of Allaah mean . Is the Quranic text creature or updated ,it is the issue that exhausted the effort.of muslim scientists though its imbo
The idea of a homomorphism of a cubic set of a KU-semigroup is studied and the concept of the product between two cubic sets is defined. And then, a new cubic bipolar fuzzy set in this structure is discussed, and some important results are achieved. Also, the product of cubic subsets is discussed and some theorems are proved.
he dairy industry is one of the industrial activities classified within the food industries in all phases of the dairy industry, which leads to an increase in the amount of wastewater discharged from this industry. The study was conducted in the Abu Ghraib dairy factory, classified as one of the central factories in Iraq, located in the west of Baghdad governorate, with a design capacity of 22,815 tons of dairy products. The characteristics of the liquid waste generated from the factory were determined for the following parameters biological oxygen demand (BOD5), Chemical oxygen demand (COD), total suspended solids (TSS), pH, nitrate, phosphate, chloride, and sulfate with an average value of (1079, 1945, 323, 9.2, 24, 2
... Show MoreThermal conductivity of compacted bentonite is one of the most important properties where this type of clay is proposed for use as a buffer material. In this study, Lee's disc method was used to measure the thermal conductivity of compacted bentonite specimens. The experimental results have been analyzed to observe the three major factors affecting the thermal conductivity of bentonite buffer material. While the clay density reaches to a target value, the measurement is taken to evaluate the thermal conductivity. By repeating this procedure, a relationship between clay dry density and thermal conductivity has been established in specimens after adjusting the water contents of the bentonite by placing its specimens in a drying oven for diffe
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