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.
A mathematical model has been introduced to investigate the effect of nuclear reaction constant ( A ), probability of the BEC ground state occupation Ω i, nD is the number density of deuteron (d) and the overall number of nuclei ND on the total nuclear d-d fusion rate (R). Under steady-state of the condensates of Bose-Einstein, the postulate of quantum theory and Bose-Einstein theory were applied to evaluate the total nuclear (d-d) fusion rate trapping in Nickel-metal The total nuclear fusion rate trapping predicts a strong relationship between astrophysical S-factor and masses of Nickel. The reaction rate trapping model was tested on three reaction d(d,p)T, d(d, n)3He and d(d, 4He)Q = 23.8MeV respectively. The reaction rate has described
... Show MoreCompanies need to educate people about the facts that characterize the business. This is the mission of promotion, it is an important marketing activity, promotion communicates with others and seeks to provide customers with a new business process experience.
Advertising is the most important methods of promotion and the best way to reach an audience. Once the organization advertises its products and services, it can operate in a competitive environment. Marketing competition requires knowledge of humanity that must be affected and convinced. Advertising should create Desires and need for satisfaction. This research comes in the study of visual representations of this psychological incident and how to use it communicatively to create
(Sepak takraw) is a game that mixes football and volleyball, it is played on a court similar to a badminton court, in which players have the right to play the ball with any part of the body except the arm and hand. The object of the game is to return the ball to the opponent's court and score a point. Since it is a newly emerging game, all aspects related to it must be studied and covered in order to reach the highest levels, and it is known that each game or sporting activity has its own physical and motor capabilities, which is important to determine the level of technical performance, as the game's abilities contribute to mastering the skills. The importance of research in determining standard levels of physical and motor abilities for y
... Show MoreThe research aims at identifying the extent to which the top management in the organization is interested in managing the talents of its employees, through which it can face the competing organizations, as well as the great challenges faced by all organizations in recent years. The task of attracting and maintaining talented human resources is one of the biggest challenges facing Organizations
... Show More
A faunistic review of the genus Chaitophorus Koch, 1854, including four species in Iraq is given; the distribution data of each species and their hosts have been recorded. In this investigation the poplar leaf aphid Ch. populialbae (Boyer de Fonscolombe, 1841) is recorded here for the first time in Iraq on popular trees Populus euphratica Oliv. during the period from November 2016 to April 2017 in Baghdad province.
A brief description for apterous viviparous female of this species is given; and a key to the species of the genus Chaitophorus is constricted.
The ground state proton, neutron, and matter density distributions and corresponding root-mean-square radii (rms) of the unstable neutron-rich
22C exotic nucleus are investigated by two-frequency shell model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO)
potential are used with two oscillator parameters bcore and bhalo. According to this model, the core nucleons of 20C are assumed to move in the model
space of spsdpf. Shell model calculations are performed with (0+2)hw truncations using Warburton-Brown psd-shell (WBP) interaction. The outer (halo) two neutrons in 22C are assumed to move in HASP (H. Hasper) model space (2s1/2, 1d3/2, 2p3/2, and 1f7/2 orbits) using the HASP interaction. The halo st
تم استخدام خرائط ضبط الجودة الإحصائية لتقييم جودة الخدمة التعليمية في جامعة الباحة، ويهدف هذا البحث إلى استخدام خرائط ضبط الجودة الإحصائية لقياس مستوى الجودة وفجوة الجودة بين توقعات الطلبة وإدراكاتهم لمستوى الخدمة الذي تقدمه جامعة الباحة. حيث تم اختيار عينة من 200 طالب وطالبة عشوائيا باستخدام العشوائية العنقودية من 4 كليات خلال الفترة 01 – 30/2015م، وجمعت البيانات من خلال استبيان جودة الخدمة الذي يقيس ت
... Show MoreBanks face many of the various risks: which are of dangerous phenomena that cause the state achieved a waste of money and a threat to future development plans to be applied to reach the goals set by: prompting banks and departments to find appropriate solutions and fast: and it was within these solutions rely on Banking risk management and effective role in defining and identifying: measuring and monitoring risk and trying to control and take risks is expected to occur in order to encircle and make it in within acceptable limits: and try to avoid them in the future to reduce the losses that are likely to be exposed to the bank: and it began to emerge and dominate a lot of legislation that seeks to structure the year risk management and t
... Show More
This paper analyses the relationship between selected macroeconomic variables and gross domestic product (GDP) in Saudi Arabia for the period 1993-2019. Specifically, it measures the effects of interest rate, oil price, inflation rate, budget deficit and money supply on the GDP of Saudi Arabia. The method employs in this paper is based on a descriptive analysis approach and ARDL model through the Bounds testing approach to cointegration. The results of the research reveal that the budget deficit, oil price and money supply have positive significant effects on GDP, while other variables have no effects on GDP and turned out to be insignificant. The findings suggest that both fiscal and monetary policies should be fo
... Show More