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the coincidence lefschetz number for self-maps of lie groups
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Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g EC and a differ-entiable map F: G G , write GA to denote the tangent space of G at g [4,p.10] , and denote by d x F the linear map rig F :Tx0 T, (x)G induced by F , it is called the differential of Fat g [4,p.22]. Let LA, Rx :0 G be respec-tively the left translation Lx(i)=4..(g,e) , and the right translation Rx(1)./..(gcg). Then there is a natural homomorphism Ad ,the adjoin representation, from G to GL(G•), (the group of nonsingular linear transformations of Qdefined as follows:- Ad(g)= deRe, od,Lx. Note that d xRc, ad.; =d(4,( Lx(e)))0 de; =d.(4, 04)=4(40 Re) = d(4(4, (e)))0 (44, =d ar, o (44, . Since G is connected , the image of Ad belongs to the connected component of G(G)containing the identity,i.e. for each g E 0, detAd(g) > 0 . By Exercise Al • Dr.-Prof.-Department of Mathematics- College of Science- University of Baghdad. •• Dr.-Department of Mathematics- College of Science for Woman- University of Baghdad.

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Publication Date
Mon Jun 01 2020
Journal Name
Iraqi Journal Of Physics
Optimum diameter for laser beam and effect of temperature rise on the optical bistability hysteresis loops
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 In this research, analytical study for simulating a Fabry-Perot bistable etalon (F-P cavity) filled with a dispersive optimized nonlinear optical material (Kerr type) such as semiconductors Indium Antimonide (InSb). An optimization procedure using reflective (~85%) InSb etalon (~50µm) thick is described. For this etalon with a (50 µm) spot diameter beam, the minimum switching power is (~0.078 mW) and switching time is (~150 ns), leading to a switching energy of (~11.77 pJ) for this device. Also, the main role played by the temperature to change the etalon characteristic from nonlinear to linear dynamics.

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Publication Date
Tue Feb 01 2022
Journal Name
Baghdad Science Journal
Flow Injection Analysis with Turbidity Detection for the Quantitative Determination of Mebeverine Hydrochloride in Pharmaceutical Formulations
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The main objective of this paper is to develop and validate flow injection method, a precise, accurate, simple, economic, low cost and specific turbidimetric method for the quantitative determination of mebeverine hydrochloride (MbH) in pharmaceutical preparations.  A homemade NAG Dual & Solo (0-180º) analyser which contains two identical detections units (cell 1 and 2) was applied for turbidity measurements. The developed method was optimized for different chemical and physical parameters such as perception reagent concentrations, aqueous salts solutions, flow rate, the intensity of the sources light, sample volume, mixing coil and purge time. The correlation coefficients (r) of the developed method were 0.9980 and 0.9986 for cell

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Publication Date
Wed Aug 18 2021
Journal Name
Chemical Papers
Analytical methods for the identification of micro/nano metals in e-cigarette emission samples: a review
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Publication Date
Mon Feb 28 2022
Journal Name
Journal Of Educational And Psychological Researches
Psychological Security and Its Relation to Motivation for Achievement of Social Researchers Working in the Courts
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The research aims to measure the psychological security of social working in the courts, to measure the motivation of achievement for social researchers working in the courts. In addition to, identify the Psychological security and its relation to the motivation of achievement for social researchers working in the courts. To achieve these aims, the researcher adopted two scales: Maslow scale for Psychological security, which was translated to Arabic by Dwany and Dirany 1983 consisted of (75) items. The second scale is Othman scale for achievement motivation 2014 consisted of (24) items. The two scales had been applied to a sample consisted of (100) social researchers working in the courts of Baghdad with its two branches Al-karkh and Al-

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Publication Date
Thu Jan 27 2022
Journal Name
Eurasian Chemical Communications
Equilibrium and kinetic modeling studies for the adsorption-desorption of methyl violet 10B onto leather waste
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In this study, vegetable tanned leather waste of cow (VTLW-C) is used as adsorbent for removing methyl violet 10B dye from aqueous solution. The VTLW-C adsorbent was characterized by FTIR and SEM in order to evaluate its surface properties before using in adsorption experiments. Batch adsorption method was applied to study the effect of different factors such as weight of leather waste, time of shaking, and starting concentration of methyl violet 10B dye. Different isothermal models such as Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (D–R) were used to analyze the experimental data. Kinetic study proceeds using (PFO) kinetic model and (PSO) kinetic model. The results showed better agreement with the Freundlich model; this means

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Publication Date
Fri Dec 23 2022
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Sensitive Cloud Point Extraction Method for the Determination of Isoxsuprine Hydrochloride in Pharmaceutical forms using Spectrophotometry
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      A simple and highly sensitive cloud point extraction process was suggested for preconcentration of micrograms amount of isoxsuprine hydrochloride (ISX) in pure and pharmaceutical samples. After diazotization coupling of ISX with diazotized sulfadimidine in alkaline medium, the azo-dye product quantitatively extracted into the Triton X-114 rich phase, dissolved in ethanol and determined spectrophotometrically at 490 nm. The suggested reaction was studied with and without extraction and simple comparison between the batch and CPE methods was achieved. Analytical variables including concentrations of reagent, Triton X-114 and base, incubated temperature, and time were carefully studied. Under the selected optimum conditions,

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Publication Date
Tue Apr 01 2025
Journal Name
Journal Of Engineering
Comparative Analysis of The Combined Model (Spatial and Temporal) and Regression Models for Predicting Murder Crime
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This research dealt with the analysis of murder crime data in Iraq in its temporal and spatial dimensions, then it focused on building a new model with an algorithm that combines the characteristics associated with time and spatial series so that this model can predict more accurately than other models by comparing them with this model, which we called the Combined Regression model (CR), which consists of merging two models, the time series regression model with the spatial regression model, and making them one model that can analyze data in its temporal and spatial dimensions. Several models were used for comparison with the integrated model, namely Multiple Linear Regression (MLR), Decision Tree Regression (DTR), Random Forest Reg

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Publication Date
Mon May 27 2024
Journal Name
Eureka: Physics And Engineering
Systematic development of an autonomous robotic car for fire-fighting based on the interactive design approach
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Fire incidences are classed as catastrophic events, which mean that persons may experience mental distress and trauma. The development of a robotic vehicle specifically designed for fire extinguishing purposes has significant implications, as it not only addresses the issue of fire but also aims to safeguard human lives and minimize the extent of damage caused by indoor fire occurrences. The primary goal of the AFRC is to undergo a metamorphosis, allowing it to operate autonomously as a specialized support vehicle designed exclusively for the task of identifying and extinguishing fires. Researchers have undertaken the tasks of constructing an autonomous vehicle with robotic capabilities, devising a universal algorithm to be employed

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Publication Date
Tue Aug 15 2023
Journal Name
Al-academy
Formal questioning and its representations in the design of contemporary residential rooms for children with autism
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The formal investigation of the interior spaces of the residential bedrooms for children with autism is one of the basic tasks that should be known by the interior designer. Achieving an atmosphere compatible with his health condition, which contributes to generating a sense of spatial intimacy through the design dimension provided by the interior designer and his tireless endeavor to meet the needs of the child in an internal environment that achieves the functional dimension and spiritual approaches that enhance the child’s sense of spatial belonging and contribute to improving his mood and this positively reflects on his behavior and social integration. The current research has reached the most important design criteria that must be

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Publication Date
Wed Feb 04 2026
Journal Name
Al–bahith Al–a'alami
HUMAN MODELING IN THE IRAQI PRESS: (A Survey of Human Modeling for March And April 2011)
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This research deals with what so called concept of The Human Model and how Iraqi Media concerns of this concept practically as it plays a key role in attracting readers, on the first hand. On the second, it is important to shed light on the scientific desire of the Iraqi Media and how it deals with this contemporary trend especially in editorial media.

The importance of the research stems from the fact that it alerts to a new stream of modern trends in journalistic writing, according to many modern Arab and foreign media studies; and to the importance of employing human modeling in dealing with facts, events, issues and problems in various editorial arts within their effective influence in concilia

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