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.
The current research aims to identify the extent to which cognitive economics skills are included in the content of the chemistry textbook for the third intermediate grade, and the research sample was represented in the chemistry textbook for the third intermediate grade. A list of knowledge economy skills was prepared (6) main skills (basic skills, communication skills, thinking skills, work skills Group, information-gathering skill, behavioral skills (and (20) sub-skills) (reading, writing, operations, computer skills and employability, oral expression and written communication, dialogue, persuasion, influence and arousal, analysis, problem-solving, decision-making, suggestions and hypotheses and employing them. Controlling, directing
... Show MoreSustainable development is launched through the interaction between the economy and natural resources and preserving them from exhaustion as well as the efficient management of natural and social resources and includes a diversified economic condition and thus is the focus of attention to the development of economic structures, which is intended to improve the level of human well-being by increasing its share in the necessary goods and services and their relationship With economic growth, which is the most important driver of economic transformation, because it reflects the ability of society and increasing its productive capabilities and investing in the optimal way Although the Iraqi economy is considered one of the diversified
... Show MoreThe problem of rebellion is considered one of the features of rapid changes that a society undergoes in all spheres and directions of life, especially in the realm of social relations, customs, traditions, values, and principles. Rebellion may manifest itself in rebellion against oneself, against values or traditions, or against social or governmental authority. One may find that submission plays a vital role in all of these interactions. This study deals with the problem of rebellion in the works of two renowned authors: The French Gustave Flaubert and the Israeli Amos Oz, through two main characters who share similar qualities and traits. Emma Bovary and Henna Konin demonstrate this through their rebellion against themselves, their relati
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The research aims to identify tax exemptions, their objectives and types, as well as to shed light on the concept of sustainable development, its objectives, dimensions and indicators (economic, social and environmental), as well as to analyze the relationship between tax exemptions and economic development, in addition to measuring and analyzing the impact of tax exemptions on economic development in Iraq for the period ( 2015 - 2021) using the NARDL model. The research problem centers on the fact that failure to employ financial policy tools correctly led to a weakness in achieving economic justice, which leads to a failure to improve social welfar
... Show MoreThe present analysis targets to recognize the influence of the separate teaching approach on the accomplishment of grammar for scholars of the College of Islamic Sciences. The target of attaining this target led the investigations developing the subsequent null theories: 1. No statistically substantial variance is happened at the consequence level of 0.05 between the mean scores of the scholars in the investigational category who learnt consistent with the separate learning approach and the mean scores of the scholars in the control category who learnt in the conventional method in the accomplishment test. 2. No statistically substantial variance has been observed at the consequence level of 0.05 in the mean differences between the
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A novel mixed natural coagulant has been developed to remove sewage pollutants and heavy metals from Qanat- al- Jayesh by using low cost adsorbent natural materials. In these materials, significant interaction contains Arabic gum mixed with extracted silica from rice husk ash (natural coagulants) by the Batch device approach, using two variables, pH values ranging from 5-8 and contact times between 0.25-5 hrs. All wastewater samples were collected after treatment by adsorbents and examined for determination of residual heavy metal concentrations: Pb, Ni, Zn and Cu by atomic absorption spectroscopy (AAS), turbidity, pH, total dissolved salts (TDS), electrical conductivity (EC) and total salinity (TS). The results obtained indicate Th
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The operation and management of water resources projects have direct and significant effects on the optimum use of water. Artificial intelligence techniques are a new tool used to help in making optimized decisions, based on knowledge bases in the planning, implementation, operation and management of projects as well as controlling flowing water quantities to prevent flooding and storage of excess water and use it during drought.
In this research, an Expert System was designed for operating and managing the system of AthTharthar Lake (ESSTAR). It was applied for all expected conditions of flow, including the cases of drought, normal flow, and during floods. Moreover, the cases of hypothetical op
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Five serological methods for detection of Brucella were compaired in this study, Four of the methods are commonely used in the detections:- 1-Rose-Bengal: as primary screening test which depends on detecting antibodies in the blood serum. 2-IFAT: which detects IgG and IgM antibodies in the serum. 3-ELISA test: which detects IgG antibodies in the serum. 4-2ME test: which detects IgG antibodies The fifth methods. It was developed by a reasercher in one of the health centers in Baghdad. It was given the name of spot Immune Assay (SIA). Results declares that among (100) samples of patients blood, 76, 49, 49, 37, and 28. samples were positive to Rose Bengal, ELISA, SIA, 2ME and IFAT tests, respectively. When efficiency, sensitivity and specific
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A novel mixed natural coagulant has been developed to remove sewage pollutants and heavy metals from Qanat- al- Jayesh by using low cost adsorbent natural materials. In these materials, significant interaction contains Arabic gum mixed with extracted silica from rice husk ash (natural coagulants) by the Batch device approach, using two variables, pH values ranging from 5-8 and contact times between 0.25-5 hrs. All wastewater samples were collected after treatment by adsorbents and examined for determination of residual heavy metal concentrations: Pb, Ni, Zn and Cu by atomic absorption spectroscopy (AAS), turbidity, pH, total dissolved salts (TDS), electrical conductivity (EC) and total salinity (TS). The results obtained indicate Th
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