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.
We have chosen the subject of the research (the letters at Ibn Jinnie in the lexicon of the tongue of the Arabs) in order to know the opinion of Ibn Jinnie in this range of words and compare them with the opinions of scientists who preceded him to know the personality of this linguistic world.
The current study included the anatomical structure of the metatarsal bone in sheep in terms of the traditional structural description of the bone, as it was found that the metatarsal bone in the fore and hind limbs of adult sheep had no visible differences between it and animals, especially ruminants. The metacarpal \tarsal bone No. 3 was cylindrical in shape, with the presence of the metacarpal \tarsal bones 2 and 4 declines, articulated from the proximal end with the metacarpal and metatarsal bones whereas from the distal part with the fetlock joint and the first phalanx bone. The aim of the study is to determine whether the environment and its changes in Iraq have affected the animals and their bones in terms of length, thicknes
... Show MoreIdioms are a very important part of the English language: you are told that if you want to go far (succeed) you should pull your socks up (make a serious effort to improve your behaviour, the quality of your work, etc.) and use your grey matter (brain).1 Learning and translating idioms have always been very difficult for foreign language learners. The present paper explores some of the reasons why English idiomatic expressions are difficult to learn and translate. It is not the aim of this paper to attempt a comprehensive survey of the vast amount of material that has appeared on idioms in Adams and Kuder (1984), Alexander (1984), Dixon (1983), Kirkpatrick (2001), Langlotz (2006), McCarthy and O'Dell (2002), and Wray (2002), among others
... Show MoreThe 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 MoreThe artistic concepts differ in their expressive and semantic relations, among these concepts are the artistic values, as there are points of view, social concepts and historical values interacted from one generation to another over the time. These values represent symbols and indications reflect reality, which has passed through the time to reach us with environmental forms saved by the history at the Natural History Museum, has an impact on the receives mind with its formal and sensory dimensions and connecting with that history as an environment that lacks to the current reality which has immortal means particularly in the cognitive thinking , and the reflection of that in the Iraqi culture and with the associated concepts of interior
... Show MoreThis paper presents a new approach to discover the effect of depth water for underwater visible light communications (UVLC). The quality of the optical link was investigated with varying water depth under coastal water types. The performance of the UVLC with multiple input–multiple output (MIMO) techniques was examined in terms of bit error rate (BER) and data rate. The theoretical result explains that there is a good performance for UVLC system under coastal water.