This paper devoted to the analysis of regular singular boundary value problems for ordinary differential equations with a singularity of the different kind , we propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the regular singular points and its numerical approximation. Many examples are presented to demonstrate the applicability and efficiency of the methods. Finally , we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

In this paper, Min-Max composition fuzzy relation equation are studied. This study is a generalization of the works of Ohsato and Sekigushi. The conditions for the existence of solutions are studied, then the resolution of equations is discussed.

The study aims to investigate the antimicrobial activity of propolis obtained from different regions of Iraq compared with that of propolis obtained from Iran. Samples were investigated for their antimicrobial activity against Staphylococcus aureus, Pseudomonas aeruginosa, Eschericha coli, Klebsiella pneumoniae, Bacillus cereus , Staphylococcus epidermidis and Candida albicans using standard antimicrobial assays. Marked variations in the antimicrobial activity of the different propolis samples were observed, the method of extraction selected gives the highest antimicrobial activity and the best alcohol concentration using in the extraction of propolis , then the crude extract of propolis showed synergistic effect with some antibiotics in

In this article, we define and study a family of modified Baskakov type operators based on a parameter . This family is a generalization of the classical Baskakov sequence. First, we prove that it converges to the function being approximated. Then, we find a Voronovsky-type formula and obtain that the order of approximation of this family is . This order is better than the order of the classical Baskakov sequence  whenever . Finally, we apply our sequence to approximate two test functions and analyze the numerical results obtained.

Cohesive soils present difficulties in construction projects because it usually contains expansive clay minerals. However, the engineering properties of cohesive soils can be stabilized by using various techniques. The research aims to elaborate on the influences of using hydrated lime on the consistency, compaction, and shear strength properties of clayey soil samples from Sulaimnai city, northern Iraq. The proportions of added hydrated lime are 0%, 2.5%, 5%, 7.5% and 10% to the natural soil sample. The results yielded considerable effects of hydrated lime on the engineering properties of the treated soil sample and enhancement its strength. The soil's liquid limit, plasticity index, and optimum moisture content were de

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.

Features is the description of the image contents which could be corner, blob or edge. Corners are one of the most important feature to describe image, therefore there are many algorithms to detect corners such as Harris, FAST, SUSAN, etc. Harris is a method for corner detection and it is an efficient and accurate feature detection method. Harris corner detection is rotation invariant but it isn’t scale invariant. This paper presents an efficient harris corner detector invariant to scale, this improvement done by using gaussian function with different scales. The experimental results illustrate that it is very useful to use Gaussian linear equation to deal with harris weakness.

Milling Machining is a widely accepted nontraditional machining technique used to produce parts with complex shapes and configurations. The material is removed in two stages roughing and finishing, the flat end cutter removed the unwanted part of material, then finished by end mill cutter. In milling technique, the role of machining factors such as cutting depth, spindle speed and feed has been studied using Taguchi technique to find its effectiveness on surface roughness.  Practical procedure is done by Taguchi Standard matrix. CNC milling is the most conventional process which is used for removing of material from workpiece to perform the needed shapes. The results and relations indicate that the rate of feed is v

As a result of the growth of economic, demographic and building activities in Iraq, that necessitates carrying out geotechnical investigations for the dune sand to study behavior of footings resting on these soils. To determine these properties and to assess the suitability of these materials for resting shallow foundation on it, an extensive laboratory testing program was carried out. Chemical tests were carried out to evaluate any possible effects of the mineralogical composition of the soil on behavior of foundation rested on dune sands.
Collapse tests were also conducted to trace any collapse potential. Loading tests were carried out for optimum water content and different shapes of footing. Loading test recommends manufacturing o