In this study, the effect of design parameters such as pipe diameter, pipe wall thickness, pipe material and the effect of fluid velocity on the natural frequency of fluid-structure interaction in straight pipe conveying fully developed turbulent flow were investigate numerically,analytically and experimentally. Also the effect of support conditions, simply-simply and clamped-clamped was investigated. Experimentally, pipe vibrations were characterized by accelerometer mounted on the pipe wall. The natural frequencies of vibration were analyzed by using Fast Fourier Transformer (FFT). Five test sections of two different pipe diameters of 76.2
mm and 50.8 mm with two pipe thicknesses of 3.7 mm and 2.4 mm and two pipe materials,stainles

At a time when the general rules in the different legal systems require the presence of two parties to the contract, one of which is issued the first expression of the will and is called the offer, and the other is issued from the other and is called the acceptance. A special type of contracts emerged in the beginning of the last century called the “unilateral contracts”. The side sparked a major jurisprudential dispute, as well as the issuance of several contradictory judicial rulings on it. Hence, this research came to highlight this special type of contract. Key words: the definition of a unilateral contract, its distinction from other legal situations, and its effects.

This research aims primarily to highlight personal tax exemptions A comparative study with some Arab and European regulations. And by conducting both theoretical comparative analyses. Most important findings of the study is the need to grant personal and family exemptions that differ according to the civil status of the taxpayer (single or married). In other words, the exemption increases as the number of family members depend on its social sense. Also taking into account some incomes that require a certain effort and looking at the tax rates, it is unreasonable for wages to be subject to the same rates applied to commercial profits.      

 Computer theoretical study has been carried out on the design of five electrode immersion electrostatic lens used in electron gun application. The finite element method (FEM) is used in the solution of the Poisson's equation fro determine axial potential distribution, the electron trajectory under Zero magnification condition .      The optical  properties : focal length ,spherical and chromatic aberrations are calculated,From studying the properties of the designed electron gun. we have good futures for these  electron gun where are abeam current 4*10-4A    can be supplied by using cathode tip of radius 100 nm.

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

     In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm).  And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr

     The goal of the research is to develop a sustainable rating system for roadway projects in Iraq for all of the life cycle stages of the projects which are (planning, design, construction and operation and maintenance). This paper investigates the criteria and its weightings of the suggested roadway rating system depending on sustainable planning activities. The methodology started in suggesting a group of sustainable criteria for planning stage and then suggesting weights from (1-5) points for each one of it. After that data were collected by using a closed questionnaire directed to the roadway experts group in order to verify the criteria weightings based on the relative importance of the roadway related impacts

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.