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.
The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal's triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely develo
... Show MoreBackground: clinically significant macular edema (CSME) is the commonest cause of visual loss in patients with diabetes mellitus and laser focal photocoagulation is the golden standard for treating it. Patients and Methods: A frequency doubled Nd: YAG laser was used to treat all eyes included in this study with diabetic maculopathy. Thirty eyes of three insulin dependent and twenty six non insulin dependent diabetic Iraqi patients were included. The study involved twenty six males, three females and followed for one year. Their ages were ranging between 36- 59 years, all of them from patients attending ophthalmic out-patient department in the medical city in the period between January 2005 and June 2006. Eyes divided in to two groups (fifte
... Show MoreThis paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.
In the present study, the effect of new cross-section fin geometries on overall thermal/fluid performance had been investigated. The cross-section included the base original geometry of (triangular, square, circular, and elliptical pin fins) by adding exterior extra fins along the sides of the origin fins. The present extra fins include rectangular extra fin of 2 mm (height) and 4 mm (width) and triangular extra fin of 2 mm (base) 4 mm (height). The use of entropy generation minimization method (EGM) allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by con
... Show MoreThe integration of gender in urban studies is considered a goal and objective to build a society characterized by justice and equality. It further allows all its residents to enjoy the opportunities to live in a safe urban life. Based on the that, the limitations of the research and its field of interest related to the relationship between gender and urban studies have become clear. The insufficient knowledge in this regard considers gender as a concept that does not exist in itself, but rather overlaps and intersects with several concepts and studies, including urban studies. Thus, it has become necessary to adopt a descriptive methodology that helps reach a theoretical framework to explain the beginnings of such an interaction and inte
... Show MoreIron oxide (Fe3O4) nanoparticles were synthesized via an eco-friendly green approach by adding Phoenix dactylifera extract to the aqueous solution of ferric chloride. The effect of annealing temperature (Ta) (100-150) °C on particle size was studied. X-ray diffraction (XRD), UV-visible spectroscopy, atomic force microscopy (AFM), and field emission scanning electron microscopy (FESEM) were used to evaluate the produced nanoparticles. According to XRD spectra, the crystallite size of the samples was determined using the Scherrer formula. AFM and FE-SEM were used to determine surface morphology. A UV-Vis optical spectroscopic examination was carried out to determine the band gap energy of the iron oxide nanoparticles. It was found th
... Show MoreSubmerged arc welding (SAW) process is an essential metal joining processes in industry. The quality of weld is a very important working aspect for the manufacturing and construction industries, the challenges are made optimal process environment. Design of experimental using Taguchi method (L9 orthogonal array (OA)) considering three SAW parameter are (welding current, arc voltage and welding speed) and three levels (300-350-400 Amp. , 32-36-40 V and 26-28-30 cm/min). The study was done on SAW process parameters on the mechanical properties of steel type comply with (ASTM A516 grade 70). Signal to Noise ratio (S/N) was computed to calculate the optimal process parameters. Percentage contributions of each parameter are validated by using an
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