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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
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
Extraction and estimation of curcumin compounds from turmeric (Curcuma longa) rhizomes by using different variables (solvent, time and temperature).
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The study aimed to investigate the effect of different times as follows 0.5, 1.00, 2.00 and 3.00 hrs, type of solvent (acetone, methanol and ethanol) and temperature (~ 25 and 50)ºc on curcumin percentage yield from turmeric rhizomes. The results showed significant differences (p? 0.05) in all variables. The curcumin content which were determined spectrophotometrically ranged between (0.55-2.90) %. The maximum yield was obtained when temperature, time and solvent were 50ºC, 3 hrs and acetone, respectively.

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Publication Date
Mon Mar 04 2024
Journal Name
Journal Of Emergency Medicine, Trauma And Acute Care
Cone beam computed tomography (CBCT) evaluation of ridge shape and bone density in Iraqi sample pre-dental implant insertion
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One of the critical factors for dental implant success is accurate clinical and radiological assessment. Cone-beam computed tomography systems (CBCT) allow surgeons to determine the quality and quantity before surgery, aiding in treatment planning. This study highlights the importance of such an assessment Materials and Methods A total of 40 patients were referred to CBCT scanning for pre-dental implant assessment in the Oral and Maxillofacial Radiology department at Al-Shaheed Gazi Al Hariri Hospital from 2021 to 2022. The patients were between 18 and 50 years old. All data were analyzed with on-demand 3D software (Kavo OP 3D: Cone Beam 3D imaging Germany). Results: Regarding the ridge shape: In the upper anterior and posterior regions, th

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Publication Date
Wed Jan 01 2020
Journal Name
Annals Of Tropical Medicine And Public Health
Determination of hepcidin (25) level in hemodialysis Iraqi male patients and its relation with erythropoietin and some biochemical parameters
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Background: Anemia is a common finding in patients with renal failure disease and it is, primarily, due to reduced production of iron and erythropoietin. Therefore, the aim of current study was to evaluate the relationship between serum level of hepcidin 25, on the one hand, and levels of serum iron, total iron-binding capacity, serum erythropoietin and transferrin saturation% in Iraqi male patients undrgoning haemodialysis.. Methods: Serum from75 males in the end stage of hemodialysis, as group one, and 25 Iraqi healthy malecontrols, as group two, were recruited in this study. Results: Data from current study showed significant increase in hepcidin 25 and significant decrease in serum iron, total iron-binding capacity, transferrin saturati

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Publication Date
Fri Apr 29 2022
Journal Name
Iraqi Journal Of Agricultural Sciences
STABL ISOTOPES AND HYDROCHEMICAL PARAMETER AS INDICATORS OF AL-RAZZAZA LAKE WATER INTERACTION WITH GROUNDWATER SURROUNDING / KARBALA GOVERNORATE- IRAQ.
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This research was aimed to study the exposure of Razzazah Lake  to major hydrological changes in recent years as a result of natural climatic changes  and  drought, high evaporation in lake due to stop discharge from Habbaniyah Lake  by Al- majera channel. During 2019, we collected surface water samples at three locations, and three samples from groundwater, in addition one samples from each location Imam Ali Drop and Sewage water  of Karbala. The Results  show that the heavy isotopes in lake and groundwater well are enriched during the warm period, and depleted during the cold period. Chemically, The dominant cations and anions in Al-Razzaza lake water are mainly of in Order  Ca > Na > Mg and  Cl>SO4 and the water

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Publication Date
Wed Mar 13 2019
Journal Name
Al-khwarizmi Engineering Journal
Investigation Microwave Furnace Effects on Mechanical Properties and Fatigue Life of AA 7075-T73 with Dry and Acid Treatments
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Microwave heating is caused by the ability of the materials to absorb microwave energy and convert it to heat. The aim of this study is to know the difference that will occur when heat treating the high strength aluminum alloys AA7075-T73 in a microwave furnace within different mediums (dry and acidic solution) at different times (30 and 60) minutes, on mechanical properties and fatigue life. The experimental results of microwave furnace heat energy showed that there were variations in the mechanical properties (ultimate stress, yielding stress, fatigue strength, fatigue life and hardness) with the variation in mediums and duration times when compared with samples without treatment. The ultimate stress, yielding stress and fatigue streng

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Publication Date
Wed Nov 01 2023
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Protective Effects of Citronellol Against Rhabdomyolysis-Induced Acute Kidney Injury in Mice by Inhibiting NF-κB and IL-1β
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Objectives: acute kidney injury (AKI) is a serious pathophysiology side effect of rhabdomyolysis. Inflammatory mechanisms play a role in the development of rhabdomyolysis-induced AKI. Citronellol (CT) is a naturally occurring monoterpene alcohol (3,7-Dimethyl-6-often-1-ol) found in aromatic plant species' essential oils. In this study, we explored the protective effects of Citronellol on glycerol-induced AKI.

Methods: Four groups of eight mice each (n=8) were formed by randomly dividing the animals into the groups, glycerol-induced AKI model group, low-dose CT-treated group (50mg/kg), high-dose CT-treated group (100mg/kg), and control group. The renal functions of mice from all groups were evalua

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Publication Date
Sat Jun 28 2025
Journal Name
Journal Of Baghdad College Of Dentistry
Elevation in surface temperature of root canals obturated with different thermoplasticized gutta-percha obturation techniques-an in vitro study
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Background: Many studies have been conducted to evaluate the effect of using a hot material in the root canal and its potential for causing damage to the tooth supporting structure. Materials and methods: thirty permanent premolars were obturated with thermoplasticized Gutta-Percha using three different obturation techniques: soft core, Thermafil, and obtura to evaluate the rise in temperature on the root surface using a multipurpose digital thermometer. Results: temperature increases was significantly greater for Obtura versus Soft core (p<0.003), not significant for Thermafil versus Soft core (p<0.087), and Thermafil versus Obtura (p<0.125). Conclusions: temperatures rise on the root surface were below the critical level and, therefore, s

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Publication Date
Sat Jun 28 2025
Journal Name
Journal Of Baghdad College Of Dentistry
Periodontal health status of heavy and light smokers and its correlation with salivary superoxide dismutase enzyme (A comparative study)
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Background: Periodontal disease is a chronic bacterial infection that affects the gingiva and bone supporting the teeth. Smoking, which is an important risk factor for periodontitis, induce oxidative stress in the body and cause an imbalance between reactive oxygen species (ROS) and antioxidants, such as superoxide dismutase (SOD). This study aimed to evaluate the influence of smoking on periodontal health status by estimating the levels of salivary SOD level in non-smokers (controls) and light and heavy smokers and to test the correlation between the SOD enzyme level and the clinical periodontal parameters in each group. Materials and Methods: The study sample consisted of 75 male, with age ranged from 35 to 50 years. Clinically, the perio

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Publication Date
Sun Sep 07 2008
Journal Name
Baghdad Science Journal
Effects of sulpher foam and mycorrhizal fungi on Eggplant infested with Nematode(Meloidogyne javanica) at seed or seedling stage
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Arbuscular mycorrhizal fungi and sulphur foam added either at direct seeding or at transplanting decreased the effects of nematode (Meloidogyne javanica) on eggplant growth, and improved plant health. Experiments were conducted to study the possible interactions between the Mycorrhizal fungi (Glomus mossae and Gigaspora spp.) and sulphur foam to control M. javanica on eggplant at seed or seedling stage. Experiment at seed stage treated with Mycorrhiza or sulphur foam alone or together stimulated the growth and reduced Nematode infestation significantly. Treated plant at seedling stage increased plant growth and reduced the number of galls /gm of root system. The interaction between Mycorrhiza and sulpher foam treatments was not significant

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Publication Date
Tue Dec 01 2015
Journal Name
Journal Of Engineering
Civilizations and Environmental Particulars of Place in Islamic Holy Thresholds in Iraq (Alkadhumain Holy Threshold as a case study)
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Islamic shrines architecture is one of the Islamic Architectural building types. It is called (Thresholds); (Atabat) in Arabic. Thoroughbred throughout the Islamic world from the east to west. In addition, it carries the style features and peculiarities of uniqueness from the rest of the types of Islamic architecture. By virtue of the particularity of its function as tomb for important person in Islamic history. Islamic shrines architecture has grown and evolved in started from the small shrines, and then taken to widen with the evolution of time in line with the value of the event and the rituals associated with it. Some of them to became centers of large cities of the largest in many parts of the Islamic world.

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