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Commuting Involution Graphs for Certain Exceptional Groups of Lie Type
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Abstract<p>Suppose that <italic>G</italic> is a finite group and <italic>X</italic> is a <italic>G</italic>-conjugacy classes of involutions. The commuting involution graph <inline-formula><alternatives><tex-math>$${\mathcal {C}}(G,X)$$</tex-math><math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>C</mi> <mo>(</mo> <mi>G</mi> <mo>,</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></alternatives></inline-formula> is the graph whose vertex set is <italic>X</italic> with <inline-formula><alternatives><tex-math>$$x, y \in X$$</tex-math><math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>∈</mo> <mi>X</mi> </mrow> </math></alternatives></inline-formula> being joined if <inline-formula><alternatives><tex-math>$$x \ne y$$</tex-math><math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>x</mi> <mo>≠</mo> <mi>y</mi> </mrow> </math></alternatives></inline-formula> and <inline-formula><alternatives><tex-math>$$xy = yx$$</tex-math><math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>x</mi> <mi>y</mi> <mo>=</mo> <mi>y</mi> <mi>x</mi> </mrow> </math></alternatives></inline-formula>. Here for various exceptional Lie type groups of characteristic two we investigate their commuting involution graphs.</p>
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Publication Date
Tue Nov 03 2020
Journal Name
Modern Sport
Effect of using flat hierarchical method on some aspects of muscular strength and straight serve skill for nascent tennis players
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The researcher focused on the importance of the physical abilities of the tennis game, as this game is one of the games that are characterized by its specificity in performance as this game is characterized by continuous movement and dealing with different elements, so this game requires the development of muscle strength, which plays an important role in Performance skills in the game of tennis. There are several methods to develop strength, including flat hierarchical technique, which is one of the most common forms of training in the development of muscle strength.     As for the research problem, the researcher found a method that has an effect on the development of force. Therefore, the researcher tried to diversify a

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Publication Date
Mon Jul 01 2024
Journal Name
Ecological Engineering &amp; Environmental Technology
Use of Nano Co-Ni-Mn Composite and Aluminum for Removal of Artificial Anionic Dye Congo Red by Combined System
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The removal of congo red (CR) is a critical issue in contemporary textile industry wastewater treatment. The current study introduces a combined electrochemical process of electrocoagulation (EC) and electro-oxidation (EO) to address the elimination of this dye. Moreover, it discusses the formation of a triple composite of Co, Mn, and Ni oxides by depositing fixed salt ratios (1:1:1) of these oxides in an electrolysis cell at a constant current density of 25 mA/cm2. The deposition ended within 3 hours at room temperature. X-ray diffractometer (XRD), field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), and energy dispersive X-ray (EDX) characterized the structural and surface morphology of the multi-oxide sedim

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Publication Date
Fri Dec 15 2017
Journal Name
Journal Of The College Of Education For Women
The Effect of Using Authentic Materials on ESP Students’ Achievement at College of Physical Education and Sciences Sport for Women
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Authentic materials are the most important tools that the teacher could use in class in order to make teaching go smoothly and effectively in transmitting the necessary knowledge to all students. This research has investigated experimentally the effect of using authentic materials in teaching English as a foreign Language, because a number of studies point out that the use of authentic materials is regarded a useful means to motivate learners, arouse their interest and expose them to the real language they will face in real life situations.

It is hypothesis that there is no statistical significance difference between the experimental group who taught English as a foreign language by using the authentic materials with those  

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Publication Date
Thu Jul 01 2021
Journal Name
Chemical Methodologies
Novel Synthesis of Some N-Hydroxy Phthalimide Derivatives with Investigation of Its Corrosion Inhibition for Carbon Steel in HCl Solution
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In the current study, new derivatives were synthesized by reaction of N-hydroxyphthalimide with chloro acetyl chloride in the presence of Et3N as a base to form 1,3-dioxoisoindolin-2-yl 2-chloroacetate (B1), which in turn enters several reactions with different amines where it interacts with primary amines to give 1,3-dioxoisoindolin-2-yl acetate derivatives (B2-B4) in basic medium, in the same way it interacts with these amines but with adding KNCS to form thiourea derivatives (B5-B7). It also reacts with diamines to give bis(azanediyl) derivatives (compounds B8-B10). The prepared derivatives were diagnosed using infrared FTIR and 1HNMR,13CNMR for some derivatives. Compounds B4, B5 and B9 were measured as corrosion inhibitors the inhibitio

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Publication Date
Fri Jun 30 2023
Journal Name
Iraqi National Journal Of Nursing Specialties
Effectiveness of Cardiac Rehabilitation Instructional Program on Health-related Quality of Life for Patients Undergone Coronary Artery Bypass Graft Surgery
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Objective(s): evaluation of effectiveness of cardiac rehabilitation instructional program on health-related quality of life and to find out the relationship between health-related quality of life and patient’s socio-demographic and clinical characteristics. 

Methodology: A descriptive study design was carried out from 8th August, 2022 to 10th January, 2023.

A non-probability purposive sample of (50) patients undergone coronary artery bypass graft surgery at Iraqi center for heart diseases using pre-experimental design. The data were collected by direct interview with sample using questionnaire composed of three parts: part (1) Socio-demographic and clinical ch

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Publication Date
Fri Jun 20 2025
Journal Name
Journal Of Kufa For Chemical Sciences
Synthesis, Characterization, Antimicrobial Activity of New Schiff Base Complexes and Thermodynamic Study for Adsorption of Pt(IV) Complex Using Bentonite
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Publication Date
Fri Jan 01 2021
Journal Name
Annals Of Maxillofacial Surgery
The use of screw retained hybrid arch bar for maxillomandibular fixation in the treatment of mandibular fractures: A comparative study
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Introduction: The use of screw-retained hybrid arch bars (HABs) is a relatively recent development in the treatment of mandibular fractures. The purpose of this study is to compare the clinical outcome between HAB and the conventional Erich arch bar (EAB) in the closed treatment of mandibular fractures. Materials and methods: This study included 18 patients who were treated for mandibular fractures with maxillomandibular fixation (MMF), patients were randomly assigned into a control group (n = 10) in which EAB was used and study group (n = 8) in which HAB was used. The outcome variables were time required for application and removal, gingival inflammation scores, postoperative complications, and incidence of wire-stick injury or gloves perf

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Publication Date
Thu Dec 01 2022
Journal Name
Al-kut University College Of Humanities
The values ​​of environmental sustainability among the student-teacher at the College of Education for Pure Sciences, Ibn al-Haytham
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Publication Date
Tue Nov 03 2020
Journal Name
Modern Sport
Effect of using flat hierarchical method on some aspects of muscular strength and straight serve skill for nascent tennis players
...Show More Authors

The researcher focused on the importance of the physical abilities of the tennis game, as this game is one of the games that are characterized by its specificity in performance as this game is characterized by continuous movement and dealing with different elements, so this game requires the development of muscle strength, which plays an important role in Performance skills in the game of tennis. There are several methods to develop strength, including flat hierarchical technique, which is one of the most common forms of training in the development of muscle strength.     As for the research problem, the researcher found a method that has an effect on the development of force. Therefore, the researcher tried to diversify a

... Show More
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Publication Date
Sat Nov 22 2025
Journal Name
Journal Of Baghdad College Of Dentistry
Validity of 3D Reconstructed Computed Tomographic Image in Using Craniometrical Measurements of the Skull for Sex Differentiation (An Iraqi Study)
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Background: The skull offers a high resistance of adverse environmental conditions over time, resulting in the greater stability of the dimorphic features as compared to other skeletal bony pieces. Sex determination of human skeletal considered an initial step in its identification. The present study is undertaken to evaluate the validity of 3D reconstructed computed tomographic images in sex differentiation by using craniometrical measurements at various parts of the skull. Materials and Method: 3D reconstructed computed tomographic scanning of 100 Iraqi subject, (50 males and 50 females) were analyzed with their age range from20-70 years old. Craniometrical linear measurements were located and marked on both side of the 3D skull images.

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