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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
Thu Oct 01 2009
Journal Name
Journal Of The College Of Languages (jcl)
Computer-assisted Programme for the Teaching of the English Syllable in RP Allophonic Pronunciation
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Native speakers of English from different parts of the world have different accents,but the differences of accents are mainly the result of differences in the sound of  vowels  and consonants . The actual use of all these sounds in combination leads the speaker to produce a number of segments which only appear on the production level and realized on the perceptual  one . RP pronunciation represents the teachable variety in all Iraqi universities because it is the most acceptable and understandable accent all over the world and not only in South East London ..The structure of the English syllable in RP  pronunciation is influenced by the appearance of certain allophones especially aspiration and glottalization which ch

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Publication Date
Mon Dec 29 2025
Journal Name
Journal Of Applied Engineering And Technological Science (jaets)
Using Fuzzy Cognitive Maps For Modeling Environmental Aspect of Sustainable Development in Construction Projects
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The pillars of sustainable development are representing the interface between environmental, economic, and social sustainability. Sustainable development is a method of planning and managing construction projects to reduce the effect of the construction process on the environment so that there is a balance between environmental capabilities and the human needs of present and future generations. Usually, Environmental sustainability is most important and effective in construction projects. The environment suffers from significant negative impacts as a result of the implementation of construction projects; therefore, this study aims to identify the effecting factors on environmentally sustainable development. The methodology of this s

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Publication Date
Wed Nov 02 2022
Journal Name
Clinical Oral Investigations
Development of a remineralizing calcium phosphate nanoparticle-containing self-etching system for orthodontic bonding
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Abstract<sec> <title>Objectives

This study aimed to incorporate hydroxyapatite nanoparticles (nHA) or amorphous calcium phosphate nanoparticles (nACP) into a self-etch primer (SEP) to develop a simplified orthodontic bonding system with remineralizing and enamel preserving properties.

Materials and Methods

nHA and nACP were incorporated into a commercial SEP (Transbond™ plus) in 7% weight ratio and compared with the plain SEP as a control. Shear bond strengths (SBS), enamel damage, and adhesive remnant index (ARI) scores were evaluated at 24 h

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Publication Date
Mon Mar 18 2019
Journal Name
Al-khwarizmi Engineering Journal
Effect of optimal shot peening time on fatigue life for aluminum alloy 6061-T651
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The compressive residual stresses generated by shot peening, is increased in a direct proportional way with shot peening time (SPT). For each metal, there is an optimum shot peening time (O.S.T) which gives the optimum fatigue life. This paper experimentally studied to optimize shot peening time of aluminium alloy 6061-T651 as well as using of and analysis of variance (ANOVA).

Two types of fatigue test specimens’ configuration were used, one without notch (smooth) and the other with a notch radius (1,25mm), each type was shot peened at different time. The (O.S.T) was experimentally estimated  to be 8 minutes reaching the surface stresses at maximum peak of -184.94 MPa.

A response surface methodology (RSM) is presen

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Publication Date
Wed Jan 01 2025
Journal Name
Journal Of Advanced Pharmacy Education And Research
Ultra HPLC method development and validation for the determination of meclizine in pharmaceutical formulation
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Publication Date
Wed Nov 27 2019
Journal Name
Environmental Science And Pollution Research
Application of emulsion and Pickering emulsion liquid membrane technique for wastewater treatment: an overview
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Publication Date
Thu Apr 01 2021
Journal Name
Applied Soft Computing
Evolutionary multi-objective set cover problem for task allocation in the Internet of Things
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Publication Date
Sat Mar 01 2025
Journal Name
Journal Of Ecological Engineering
Synthesis of sulfated zirconia-HY zeolite catalysts doped by platinum metal for hydroisomerization reaction
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Publication Date
Tue Aug 01 2023
Journal Name
Journal Of Engineering
Comparative Analysis of H2 and H∞ Robust Control Design Approaches for Dynamic Control Systems
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This paper discusses using H2 and H∞ robust control approaches for designing control systems. These approaches are applied to elementary control system designs, and their respective implementation and pros and cons are introduced. The H∞ control synthesis mainly enforces closed-loop stability, covering some physical constraints and limitations. While noise rejection and disturbance attenuation are more naturally expressed in performance optimization, which can represent the H2 control synthesis problem. The paper also applies these two methodologies to multi-plant systems to study the stability and performance of the designed controllers. Simulation results show that the H2 controller tracks a desirable cl

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Publication Date
Wed Mar 05 2025
Journal Name
Full Text Book Of Rimarcongress04
Natural and Artificial Radioactivity Estimation for Different types of Pasta Samples in Baghdad City
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