The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very

The proposed design of neural network in this article is based on new accurate approach for training by unconstrained optimization, especially update quasi-Newton methods are perhaps the most popular general-purpose algorithms. A limited memory BFGS algorithm is presented for solving large-scale symmetric nonlinear equations, where a line search technique without derivative information is used. On each iteration, the updated approximations of Hessian matrix satisfy the quasi-Newton form, which traditionally served as the basis for quasi-Newton methods. On the basis of the quadratic model used in this article, we add a new update of quasi-Newton form. One innovative features of this form's is its ability to estimate the energy functio

The current study showed that the plants were collected from 23 geographical locations in Brenaj, Wasit, Iraq. The region was characterized by a great diversity of wild plants spread densely in this region. The results were as follows: 32 families, 149 species. Asteraceae was the most widespread with 29 species from the group of dicotyledons, followed by the Fabaceae family (19) species, but there are 13 plant families, with one plant species recorded for each plant family. in Brenaj, Wasit included: Aizoaceae, Capparaceae, Convolvulaceae, Frankeniaceae, Molluginaceae, Papaveraceae, Phyllanthaceae, Primulaceae, Rutaceae, Rubiaceae, Verbenaceae, Zygophyllaceae, Urticaceae, while the plant family Poaceae was most widespread in genera and spec

In this research the specifications of Iraqi drinking bottled water brands are investigated throughout the comparison between local brands, Saudi Arabia and the World Health Organization (WHO) for bottled water standard specifications. These specifications were also compared to that of Iraqi Tap Water standards. To reveal variations in the specifications for Iraqi bottled water,  and above mentioned standards some quality control tools are conducted for more than 33% of different bottled water brands (of different origins such as spring, purified,..etc) in Iraq by investigating the  selected quality parameters registered on their marketing labels. Results employing Minitab software (ver. 16) to generate X bar,

This study investigated the ability of using crushed glass solid wastes in water filtration by using a pilot plant, constructed in Al-Wathba water treatment plant in Baghdad. Different depths and different grain sizes of crushed glass were used as mono and dual media with sand and porcelaniate in the filtration process. The mathematical model by Tufenkji and Elimelech was used to evaluate the initial collection efficiency η of these filters. The results indicated that the collection efficiency varied inversely with the filtration rate. For the mono media filters the theoretical ηth values were more than the practical values ηprac calculated from
the experimental work. In the glass filter ηprac was obtained by multiplying ηth by a

Many image processing and machine learning applications require sufficient image feature selection and representation. This can be achieved by imitating human ability to process visual information. One such ability is that human eyes are much more sensitive to changes in the intensity (luminance) than the color information. In this paper, we present how to exploit luminance information, organized in a pyramid structure, to transfer properties between two images. Two applications are presented to demonstrate the results of using luminance channel in the similarity metric of two images. These are image generation; where a target image is to be generated from a source one, and image colorization; where color information is to be browsed from o