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 main objective of present work is to describe the feasibility of friction stir welding (FSW) for
joining of low carbon steel with dimensions (3 mm X 80 mm X 150 mm). A matrix (3×3) of welding
parameters (welding speed and tool rotational speed) was used to see influence of each parameter on
properties of welded joint .Series of (FSW) experiments were conducted using CNC milling machine
utilizing the wide range of rotational speed and transverse speed of the machine. Effect of welding
parameters on mechanical properties of weld joints were investigated using different mechanical tests
including (tensile and microhardness tests ). Micro structural change during (FSW) process was
studied and different welding zones
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Polycystic ovarian syndrome, additionally called PCOS is the most widespread endocrine illness amongst women. The aetiology of PCOS is attributed to a multi-factorial interplay among environmental and genetic effects. The overarching goal evaluates the correlation among blood concentrations of total testosterone, sex-hormone-binding globulin (SHBG), estradiol (E2), follicle-stimulating hormone (FSH) and luteinizing hormone (LH) in ladies with PCOS and the impact of obesity, age, marital popularity on the obtained results. This study was conducted at the National Center for Educational Laborites /Medical City/ Baghdad. The study comprised of a sample of 83 women, elderly between 17 -45 years, who had been selected in a random manner
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Gypseous soil is considered as a problematic soil for embankment construction, however, implementation of emulsified asphalt as a stabilization agent could be a proper solution for enhancing its properties as a subgrade soil. In this work, the sustainability of asphalt stabilized soil has been assessed in terms of its resistance to cyclic (freezing-thawing) and (heating-cooling) processes. Specimens have been prepared at optimum fluid content (moisture and emulsion) and tested under direct shear stresses while subjected to 30 cycles of (freezing-thawing) and (heating-cooling). Both of dry and soaked testing conditions have been implemented. Data have been observed after each 10 cycles, and compared with that of reference mix. It was conclud
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This research aims to identify the role of Psychological Capital (PsyCap) in the Spirituality at the Workplace (SAW) for a sample of the teaching staff of the four Colleges of the University of Kufa reached (200) out of (470) teaching, and to achieve the objective of this research and through access to research and studies of foreign adopted researchers standards scales of research variables, since it relied on the model (Luthans, Youssef, et al., 2007) to represent the components of Psychological Capital (self-efficacy, and hope, and optimism, and resilience), and given the attention organizations in the human element because of it
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The general budget is usually linked to the role of the state in public life and economic activity, whether this role is neutral or interventionist and thus reflects the general objectives that the state seeks to achieve.
for importance of the public budget in clarifying the image of the political state philosophy and its objectives it seeks to achieve on the one hand and clarifying the degree and rank it occupies in the ladder of development among the other countries. This study is intended to highlight the concepts of the general budget and how its concept has evolved since the Middle Ages. Of the importance of the general budget in Iraq was not based on scientific and objective and then the study
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Monetary sterilization policies are one of the modern trends of monetary policy in rentier countries, specifically to confront the positive shocks in foreign assets flowing into the national economy and the impact of these shocks on monetary and real variables. And that the Central Bank contains these emergency increases in foreign exchange with the aim of avoiding the impact of this increase on the official local currency through its three main monetary tools, which are the rediscount rate, the legal reserve, and open market operations. As well as the relationship between the central bank and the objective of external balance, which is reflected in the balance of payments balance, the central bank resorts to managing the exchange rate
... Show MoreAgricultural lands have great importance in people's lives, and their exploitation has a great impact on strengthening the national economy. Therefore, countries have given great importance to this sector, and because of the importance of this sector, the state has given large areas of these lands to the farmers to invest in agriculture, and among these farmers are those who died and left behind children who took up crafts. Agriculture, for fear that these agricultural lands would be abandoned and turned into waste lands, a land system was introduced called (regular distribu- tion), which corresponds to (legitimate inheritance). Under this system, these lands were trans- ferred to the children of farmers who died so that the process of inve
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