For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptional of I (I the identity conjugacy class), when n=5+4k , k>=0.
HTH Ali Tarik Abdulwahid , Ahmed Dheyaa Al-Obaidi , Mustafa Najah Al-Obaidi, eNeurologicalSci, 2023
Most researchers concentrate their studies on the design, stress and pressure distributions of the prosthetic socket. A little attention is considered for the stiffness of the various materials of the prosthetic sockets. Prosthetic laminated sockets in Iraq are costly to be manufactured while polypropylene socket is relatively cheap in comparing with the laminates.
Experimental study is conducted to compare the stiffness of five prosthetic sockets made of different materials. Compression, three point flexural and tensile tests are implemented by the Testometric machine. The laminate sockets give better results in compression than polypropylene. Polypropylene gives good results in bending compared with the laminate sockets. When t
... Show MoreSpraying pesticides is one of the most common procedures that is conducted to control pests. However, excessive use of these chemicals inversely affects the surrounding environments including the soil, plants, animals, and the operator itself. Therefore, researchers have been encouraged to...
Notwithstanding the importance of international cooperation as the other facet of international interactions, a strategy of conflict resolution, a maintainer of international peace and security, its provision in the United Nations conventions, as an objective of the United Nations after the international peace and security, however, the recognition of international cooperation has not been underlined by global, intellectual think tanks. While realism emphasized on the state's role in achieving international cooperation to ensure mutual and multilateral interests, liberalism focused on the role of international organizations in building such cooperation. Additionally, constructivist approaches developed other sub-variables to contribute to t
... Show MoreIn the last years of the twentieth century, scholars solidly focused on paradiplomacy as a study subject, linking it to federalism and decentralised systems. In the Arab world, which has 22 countries, a few states have adopted federalism or decentralisation. Only five countries, i.e., 22.7%, have adopted federalism and decentralised experience. Therefore, limited research and academic work has been conducted regarding paradiplomacy. This paper aims to research the relationship between federalism and paradiplomacy conceptually and practically and then analyse the Arab experiences in federalism and whether they applied paradiplomacy and succeeded in doing so. To explore that, the paper studies and compares the related articles of constitution
... Show MoreThe aim of this paper is to design a PID controller based on an on-line tuning bat optimization algorithm for the step-down DC/DC buck converter system which is used in the battery operation of the mobile applications. In this paper, the bat optimization algorithm has been utilized to obtain the optimal parameters of the PID controller as a simple and fast on-line tuning technique to get the best control action for the system. The simulation results using (Matlab Package) show the robustness and the effectiveness of the proposed control system in terms of obtaining a suitable voltage control action as a smooth and unsaturated state of the buck converter input voltage of ( ) volt that will stabilize the buck converter sys
... Show MoreThe inhibitory behavior of L-Cysteine (Cys) and its derivatives towards iron corrosion through density functional theory (DFT) was investigated. The current research study undertakes a rigorous evaluation of global as well as local reactivity descriptors of the Cys in protonated as well as neutral forms and the changes in reactivity after the combination of Cys into di- and tripeptides. The inhibitory effect of di- and tri-peptides increases since, in the molecular structure, the number of reaction centers increase. We computed the adsorption energies (Eads) and low energy complexes with most stability for the adsorption of small peptides and Cys amino acids onto the surfaces of Fe (1 1 1). We found that the adsorption of tri-peptides onto
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