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.
This research includes the principles of the democracy، and to which extent it can contribute in establishing these principles. Democracy is not only to hold parliamentary or presidential elections but also the result of these elections wills it lead to the emergence of an integrated regime that can actually expresses the citizen's rights and to which extent those citizens can contribute in that regime and control it. Since 2005، when the first elections took place in Iraq after the US occupation of Iraq 2003، Iraqi people are looking to a rule that represented them and achieve their interests after getting rid of the totalitarian regimes and establishing an institutional regime that work by democratic means in order to achieve the so
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The current research deals with the dialectical relationship resulting from the conflict in the violent combination and construction of the living ( the actor)and the dead (the item) in the structure of the Sinography construction and the emergence of the theatrical play space , which can be summed up by the following question: what is the nature of the dialectical relationship between the living (the actor) and the dead( the item) in the Sinography creation, which limited the research in a central objective : to identify the controversy of the living (actor) and the dead (item) in the performance unit of the theatrical scene . The research, in its objective limits set forth in its methodological framework, analyzes this controversy in o
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phenomenon in the Arab women's contemporary literature, but it is rare in Iraqi women's
literature and falls short to the level of the phenomenon until now. Perhaps this is one of the
main reasons that caused the reluctance of researchers to study it, and this is probably the first
academic research in this field.
This research followed the discourse of Autobiography of women in Iraq, depending on the
two factors of charter and reference of the elements of Philippe Lejeune’s definition of the
genre of Autobiography, without focusing on narrative method, so it handled notes,
memories, diaries and biography of the other and counted all under the genre of the
Biography.
It came in three sections, the first follo
Rapid, reproducible and accurate method has been developed for the assay for of mebendazol (MBZ) residual assay. The method is based on alkaline hydrolysis of MBZ with sodium hydroxide then oxidation with N-bromosuccinimide (NBS) followed by coupling with 4-Bromoaniline (4-BA) to yield a highly colored product absorbed at maximum 434 nm. Regression analysis of linearity range was found (0.6-2.8) µg.ml-1. The optimum conditions that affect the oxidation were studied. The developed method was found to be precise with mean value of relative standard deviation (1.153- 1.303) and accurate with relative error (-0.5940-1.7821) .The calculated molar absorptivity and sandal sensitivity values of (29825 L.mol-1.cm
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An enzyme linked immunosorbent assay (ELISA) for the detection and quantitation of human immunoglobulin G (IgG) antibodies against vero- cytotoxine (VT) producing Escherichia coli serogroup O157:H7 was produced. E. coli O157: H7 lipopolysaccharide was extracted from locally isolated strains by using hot phenol- water method, followed by partial purification using gel filtration chromatography by sepharose- 4B. The purity of the lipopolysaccharide was checked by measuring the protein and nucleic acid content and then used as antigen. Four isolates of vero- cytotoxin producing E. coli serogroup O157:H7 was obtained by culturing 350 stool samples from children suffering from bloody diarrhea. These isolates were identified on bacteriological, s
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EFFECT OF SPRAYING IRON AND ZINC CONCENTRATIONS IN GRAIN AND LEAF CONTENT FOR TWO VARIETIES OF WHEAT CROP
The past decades have witnessed a development in the concept of corporate governance and the transformation of a concept that is limited to large companies listed in capital markets in major economies to an issue that concerns all business activities in the public and private sectors in both large and small countries. The aim of this research is to propose a guide to the mechanisms and rules of governance in the municipal institutions that contributes to the activation of the internal control system to reduce the fraud and manipulation of this activity. Institutions. The research was based on the hypothesis that the implementation of the principles and rules of governance in municipal institutions lead to the contribution of the activati
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Background: the early identification of developmental disabilities allows intervention at the earliest possible point to
improve the developmental potential.
Objective: Identify the scope of knowledge of nurses toward signs of gross motor delay for children and its relation to
their demographic characteristics.
Methodology: A descriptive study design was conducted at (18) primary health care centers in first of the primary
health care sector of Alhawija District in Kirkuk Governorate. This study started from September 2010 to the end of
January 2011, in order to identify the level of nurses' knowledge toward signs of gross motor delay for children in
primary health care centers. Non probability (purposive) sample of
The present study investigates the characterization of silver nanoparticles (AgNPs) synthesized using Fusarium solani and their impact on tomato seed germination, plant growth, and disease resistance. A visible color change from yellow to dark smoky indicated the formation of AgNPs, while UV-visible spectrophotometry revealed an absorbance peak at 437 nm, confirming their presence. Atomic force microscopy analysis showed that the AgNPs ranged from 0 to 39.27 nm in size, with an average height of 5.772 nm, while scanning electron microscopy highlighted their diverse surface morphology. The application of AgNPs and mycorrhizal fungi significantly improved tomato seed germination rates, plant height, and dry weight compared to untreate
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