In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.

In this work, linear and nonlinear optical properties of two types of Iraqi heavy crude oil extracted from fields in southern Iraq were determined. The nonlinear optical properties were measured utilizing Z-scan technology with He-Ne laser at 632.8 nm. It was found that nonlinear refractive index (NLR) values for the Basra and Kut heavy crude oil samples are 6.34381×10^-4  and 8.25108×10^-4  cm²/mW, respectively, while those for the nonlinear absorption coefficient (NLA) are 2.68942×10^-5  and 2.58874×10^-5 , respectively. These results showed that the two samples with linear and nonlinear optical properties can be used in optics field applications as

In a hybrid cooling solar thermal systems , a solar collector is used to convert solar energy into heat energy in order to super heat the refrigerant leaving the compressor, and this process helps in the transformation of refrigerant state from gaseous state to the liquid state in upper two-thirds of the condenser instead of the lower two-thirds such as in the traditional air-conditioning systems and this will reduce the energy needed to run the process of cooling .In this research two systems with a capacity of 2 tons each were used, a hybrid air-conditioning system with an evacuated tubes solar collector and a traditional air-conditioning system . The refrigerant of each type was R22.The comparison was in the amou

This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabi

A laboratory investigation of six different tests were conducted on silty clay soil spiked with lead in concentrations of 1500 mg/kg. A constant DC voltage gradient of 1 V/cm was applied for all these tests with duration of 7 days remediation process for each test. Different purging solutions and addition configurations, i.e. injection wells, were investigated experimentally to enhance the removal of lead from Iraqi soil during electro-kinetic remediation process. The experimental results showed that the overall removal efficiency of lead for tests conducted with distilled water, 0.1 M acetic acid, 0.2 M EDTA and 1 M  ammonium citrate as the purging solutions were equal to 18 %, 37 %, 42 %, and 29 %, respectively. H

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function i

In this paper, we study the effect of group homomorphism on the chain of level subgroups of fuzzy groups. We prove a necessary and sufficient conditions under which the chains of level subgroups of homomorphic images of an a arbitrary fuzzy group can be obtained from that of the fuzzy groups . Also, we find the chains of level subgroups of homomorphic images and pre-images of arbitrary fuzzy groups

Purpose: The study aims to investigate the extent to which material and non-material requirements are available in applying budgeting programs and performance in Iraqi governmental companies that are not aimed at achieving profits. whose activities are limited to providing services of public interest. This is done by studying the extent to which the requirements of each stage of preparing the programs and performance budget can be met.   Theoretical framework: The process of evaluating financial performance is the main objective of all economic units, whether they are governmental or private economic units. Budgets contribute to the evaluation process by analyzing deviations in the application. The study includes an analytical pres

      A 3D velocity model was created by using stacking velocity of 9 seismic lines and average velocity of 6 wells drilled in Iraq. The model was achieved by creating a time model to 25 surfaces with an interval time between each two successive surfaces of about 100 msec.  The summation time of all surfaces reached about 2400 msec, that was adopted according to West Kifl-1 well, which penetrated to a depth of 6000 m, representing the deepest well in the study area. The seismic lines and well data were converted to build a 3D cube time model and the velocity was spread on the model. The seismic inversion modeling of the elastic properties of the horizon and well data was applied to achieve a corrected veloci