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.
The In this experimental study, natural stone powder was utilized to improve a cohesive soil’s compaction and strength properties. According to the significant availability of limestone in the globe, it has been chosen for the purpose of the study, in addition to considering the existing rock industry massive waste. Stone powder was used in percentages of 4, 8, 12, 16% replaced from the soil weight in dry state. Some of cohesive soil’s consistency, shear, and compaction properties were depicted after improvement. The outcomes yielded in significant amendments in the experimented geotechnical properties after stone powder addition considering 60 days curing period. Cohesion and friction angle were notably increased by
... Show MoreThis study deals with segmenting the industrial market as an independent variable and targeting the industrial market as a dependent variable. Since the industrial sector represents one of the most important fundamental pillars to build the economies of countries and their development , the Iraqi industrial sector was chosen as a population for the study . Based on measuring the study variables , identifying them and testing the correlation and effect on each other , the study reached a group of findings:
1- Increasing the level of availability of study variables inside the companies “The study sample”.
2- There is a correlation between the independent v
... Show MoreThis study evaluated the extent to which obturation materials bypass fractured endodontic instruments positioned in the middle and apical thirds of severely curved simulated root canals using different obturation techniques. Sixty resin blocks with simulated root canals were used, each with a 50° curvature, a 6.5 mm radius of curvature, and a length of 16.5 mm, prepared to an ISO #15 diameter and taper. Canals were shaped using ProTaper Universal files (Dentsply Maillefer) attached to an X-smart Plus endo motor (Dentsply), set at 3.5 Ncm torque and 250 rpm, up to size S2 at working length. To simulate fractures, F2 and F3 files were weakened 3 mm from the tip, then twisted to break in the apical and middle sections of the canal, re
... Show MoreFiber‐reinforced elastic laminated composites are extensively used in several domains owing to their high specific stiffness and strength and low specific density. Several studies were performed to ascertain the factors that affect the composite plates’ dynamic properties. This study aims to derive a mathematical model for the dynamic response of the processed composite material in the form of an annular circular shape made of polyester/E‐glass composite. The mathematical model was developed based on modified classical annular circular plate theory under dynamic loading, and all its formulas were solved using MATLAB 2023. The mathematical model was also verified with real experimental work involving the vibration test of the f
... Show MoreThis research explores the intricate relationship between environmental sustainability and urban design in Al-Jumhuriya Neighborhood, Baghdad, reflecting urban development challenges and opportunities. It highlights the need to balance growth, functionality, and quality of life with environmental responsibility in urban areas worldwide. The research includes a literature review on environmental sustainability in urban design and the utilization of multifunctional land in contemporary cities. The research employs a mixed-methods approach, combining quantitative and qualitative data collection methods. Survey results show a diverse range of perspectives, indicating concerns about air quality and local regulations but also positive views on co
... Show MoreThis research studies the Saudi women participation in the visual arts, presents descriptive and analytical overview on their artworks and assess development through their participation in the said exhibition, frequency of participation, and aims to understand the most important stages and changes of the subjects addressed, artistic styles and the factors affecting these results in view of female artist's attitude pertaining to several aspects such as administrative organization, judging committees etc.
Interviews were held with a sample of female artists, 17 artists from different regions and generations out of 182 participants and reviewed relevant exhibition literature during the period 1979-2018. The research problem is to id
... Show MoreThis study investigates the corrosion inhibition performance of a newly synthesized quinazolinone derivative, AMQ, on mild steel in a hydrochloric acid medium. The inhibition efficiency was evaluated using potentiodynamic polarization at varying inhibitor concentrations (100–250 ppm) and temperatures (303– 333 K). The results showed that AMQ exhibited effective corrosion inhibition, with the highest efficiency of 74% observed at 250 ppm and 323 K. Density Functional Theory (DFT) calculations were conducted to study the electronic properties of AMQ and its adsorption behavior. The thermodynamic parameters, including activation energy, enthalpy, and Gibbs free energy, were calculated, indicating spontaneous adsorption of AMQ onto the meta
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