In this thesis, we study the topological structure in graph theory and various related results. Chapter one, contains fundamental concept of topology and basic definitions about near open sets and give an account of uncertainty rough sets theories also, we introduce the concepts of graph theory. Chapter two, deals with main concepts concerning topological structures using mixed degree systems in graph theory, which is M-space by using the mixed degree systems. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are defined and studied. In chapter three we study supra-approximation spaces using mixed degree systems and primary object in this chapter are two topological spaces, namely o-space and i-space. In chapter four we introduce two new approximation operators using mixed degree systems and comparing of them and we find the accuracy of the second new approximation operator is more thin the first new approximation operator. For reason we study in detail the properties of the second new operator. Finally, in chapter five we introduce new generalization of rough set theory using a finite number of graphs by using the second new approximation operators in the preiow chapter. Several characterizations and properties of these concepts are obtained.
Schiff bases are versatile compounds synthesized from the condensation of primary amino compounds with aldehydes or ketones. The high thermal of many Schiff base and their complexes were useful attributes for their application as catalysts in reactions involving at high temperatures. This thermal behavior of Schiff bases and their complexes was evaluated by TGA/DTG and DTA curves with 10 mass losses related to dehydration and decomposition. This review summarizes the developments in the last decade for thermal analysis of Schiff bases. Therefore, synthesis of Schiff bases and their complexes are reviewe
To assess the use of miniaturized percutaneous nephrolithotomy (mini-PCNL) for renal stones in children, as well as its safety and efficacy. Seventy-seven patients with more than 15 mm renal stones whose age was less than 15 years were enrolled in this prospective case-controlled study at Al-Ramadi Teaching Hospital, Ar Razi Private Hospital, and Ghazi Al-Hariri Hospital for Surgical Specialties, Anbar and Baghdad, Iraq. The study was conducted from January 2020 to January 2024. The group mentioned above served as group A, and it was compared to the control group (group B), which consisted of 70 adult patients aged 18–60 years. Patients in both groups underwent mini-PCNL. Gender, stone size and location, time of operation, stone-free rate
... Show MoreThe Tigris River is a major source of Iraq’s drinking and agricultural water supply. An increase in pollution by heavy metals can be a great threat to human and aquatic life. In this study, the pollution index (PI) and metal index (MI) were used to evaluate the status of the Tigris River in Baghdad City. Five stations were chosen to conduct the study. Five heavy metals were analyzed: iron (Fe), lead (Pb), nickel (Ni), zinc (Zn), and chromium (Cr). The result of PI was ranked between “No effect to moderately affected for Fe; Slightly Affected to Seriously Affected for Pb; no effect to moderately affected for Ni, and no effect to strongly affected for Cr; only Zn was in the No effec
Motives: The research deals with the issue of urban sprawl on agricultural lands. It is an urban problem caused by rapid urbanization and poor planning. It is considered one problem that threatens cities with environmental and health disasters. It also threatens agricultural life and the green belt surrounding cities. Changes in urban sprawl on agricultural land are associated with complex processes that lead to multiple social, economic, political, and environmental risks and thus pose a threat and an obstacle to the sustainability of cities. Aim: The research aims to study and evaluate the reality of the city of Baghdad and the extent of its ability and flexibility to withstand the disaster of urban sprawl on agricultural lands. T
... Show MoreThis paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th
... Show MoreINTRODUCTION: A range of tools and technologies are at disposal for the purpose of defect detection. These include but are not limited to sensors, Statistical Process Control (SPC) software, Artificial Intelligence (AI) and machine learning (ML) algorithms, X-ray systems, ultrasound systems, and eddy current systems. OBJECTIVES: The determination of the suitable instrument or combination of instruments is contingent upon the precise production procedure and the category of flaw being identified. In certain cases, defects may necessitate real-time monitoring and analysis through the use of sensors and SPC software, whereas more comprehensive analysis may be required for other defects through the utilization of X-ray or ultrasound sy
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