The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

In this paper, new brain tumour detection method is discovered whereby the normal slices are disassembled from the abnormal ones. Three main phases are deployed including the extraction of the cerebral tissue, the detection of abnormal block and the mechanism of fine-tuning and finally the detection of abnormal slice according to the detected abnormal blocks. Through experimental tests, progress made by the suggested means is assessed and verified. As a result, in terms of qualitative assessment, it is found that the performance of proposed method is satisfactory and may contribute to the development of reliable MRI brain tumour diagnosis and treatments.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

Co-composting process can be acquired by combining organic fraction of municipal solid waste (OFMSW) with sewage sludge (SS) and mature compost (MC) as enhancement and bulking agent to overcome the problems of municipal solid waste and wastewater treatment plants besides the finally produced fertilizer usage for agriculture and horticulture. The effects of different mixture ratios of (OFMSW), (SS) and (MC) on the performance of composting process were investigated in this study. Piles of about 10 kg were prepared by mixing OFMSW, SS and MC in three different ratios (w/w) [OFMSW: SS: MC= 3:1:1, 3:2:1, and 3:3:1]. Results showed that the pile [3:1:1] was most beneficial to composting. The final compost products contained a

Impressed current cathodic protection controlled by computer gives the ideal solution to the changes in environmental factors and long term coating degradation. The protection potential distribution achieved and the current demand on the anode can be regulated to protection criteria, to achieve the effective protection for the system.

In this paper, cathodic protection problem of above ground steel storage tank was investigated by an impressed current of cathodic protection with controlled potential of electrical system to manage the variation in soil resistivity. Corrosion controller has been implemented for above ground tank in LabView where tank's bottom potential to soil was manipulated to the desired set poi