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.
Abstract: Israel formulated its security theory, which it established on the "pretext of war", meaning converting any Arab action that Israel deems a threat to its security, into a pretext to ignite the fuse of war, considering this a violation of an existing situation, and then it initiates preventive and pre-emptive attacks, then immediately turns into transfer the war to the enemy's land, to achieve a quick solution by (destroying the enemy), occupying its lands, and benefiting of the advantage of working on (internal lines against an enemy) working on external lines, and ending the war quickly, before the major powers intervene to impose a ceasefire
In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.
Research included the preparation of medicinal substances ( propyl thiouracil). Which is the rule thiourea and related compounds a fundamental rule in preparation fall within the range of drugs of anti-thyroid activity (Antithyroid Drug ) , this drug prevents the thyroid hormone production against excessive activity of the thyroid gland .That the formation of iodine is important for their impact on hormone secretion thyroid , the two types, thyroxin or T4 is the main hormone ,Triiodothyronine or T3, and these hormones released by hormone regulator called (TSH) . Article attend thiourea treatment with an alcohol- soluble sodium and added to the interaction rule b- oxo ester after adjusting the PH=4 output ( propylthiouracil ) the
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A revolution called information revolution has recently invaded the world. It is Currently considered one of the most important properties of development to the countries of the world The criteria provided by computers such as accuracy, speed, time saving Storage and restore have led them to be widely used in economy, industry, agriculture, communications, etc., as well as being the major finder of reengineering the operations of innovation. The use of computers in the preparation of budgets will lead to achieve accuracy. Since, the operation draws upon the statistic and quantity estimations about budget items, the computerized balance sheet may save time and effort of preparing mathematical equations annually. According to the problem o
... Show MoreAO Dr. Ali Jihad, Journal of Physical Education, 2021
Abstract
The objective of the research is to identify the role of innovative leadership in achieving the dimensions of administrative empowerment in the company for the public of food industries. The various variables have shown the importance of innovative leadership to achieve the dimensions of administrative empowerment in both international and local companies. Administrative Empowerment "In order to answer this question, a virtual model was developed to reflect the relationship and impact between innovative leadership and administrative empowerment. The research was based on the analytical descriptive approach. the research community, The company represented the general company for food industries, retrie
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Abstract
The human mind knew the philosophy and logic in the ancient times, and the history afterwards, while the semiotics concept appeared in the modern time, and became a new knowledge field like the other knowledge fields. It deals, in its different concepts and references, with the processes that lead to and reveals the meaning through what is hidden in addition to what is disclosed. It is the result of human activity in its pragmatic and cognitive dimensions together. The semiotic token concept became a knowledge key to access all the study, research, and investigation fields, due to its ability of description, explanation, and dismantling. The paper is divided into two sections preceded by a the
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