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.
To promote sustainable steel-concrete composite structures, it is essential to develop special shear connectors that facilitate accelerated construction and deconstruction. A lockbolt demountable shear connector (LBDSC) was recently proposed. While the LBDSC has been evaluated using horizontal and vertical (standard) push-out tests, it is essential to further assess the disassembly mechanism and the positive flexural performance of prefabricated demountable composite beams (PDCBs) under both serviceability and ultimate limit states. Two full-scale test specimens of PDCBs with LBDSC were designed with partial shear connections and assessed using a three or four-point load beam setup under both cyclic and static monotonic loading conditions.
... Show More
(1)
In recent years, there has been a significant increase in research demonstrating the new and diverse uses of non-thermal food processing technologies, including more efficient mixing and blending processes, faster energy and mass transfer, lower temperature and selective extraction, reduced thermal and concentration gradients, reduced equipment size, faster response to extraction control, faster start-up, increased production, and a reduction in the number of steps in preparation and processing. Applications of ultrasound technology have indicated that this technology has a promising and significant future in the food industry and preservation, and there is a wide scope for its use due to the higher purity of final products and the
... Show More
The study aimed at identifying the role of the Faculty of Education in the community service in light of vision of the Kingdom 2030 from the faculty members’ point of view at the University of Jeddah. The study used a descriptive method through a questionnaire administered to a sample of the faculty members.It concluded that the role of the College in serving the community is the development of the right habits in the family and the importance of establishing bridges of cooperation between the Faculty of Education and the surrounding environment and teaching special education teachers how to apply some methods of measurement to determine the needs of students with disabilities. The results also pointed out that there are no statistical
... Show MoreWith the growth of democratic thought in our country, widened the trading term
citizenship to the magnitude of the meanings of participation in political life, economic, social
and cultural rights, as the recipe ( citizen ) does not mean only affiliation to the homeland and
link him as a child , but is as such an actor in various fields has his being independent , and
own convictions and the right to freely express his views and personal choices and play a
positive role in public life . Do not correct the democratic structure of any state without the
manifestation of the spirit of citizenship in the relations of each individual citizen to state
institutions.
The current research aims to Pfhom definition of citizen
(19)
(16)
Objective: The approximate life span of a silicone maxillofacial prosthesis is as short as1.5–2 years of clinical service, then a new prosthesis should be fabricated. The most common reasonfor re-making the prosthesis is silicone mechanical properties degradation. The aim of this studywas to assess some mechanical properties of VST-30 silicone for maxillofacial prostheses after addi-tion of intrinsic pigments.Methods: Two types of intrinsic pigments (rayon flocking and burnt sienna); each of them wasincorporated into silicone. One hundred and twenty samples were prepared and split into 4 groupsaccording to the conducted tests (tear strength, hardness, surface roughness, and tensile strengthand elongation percentage) with 30 samples for ea
... Show More
(19)
(18)
A field experiment was carried out during winter season of 2019-2020 at Al-Mhanawyah Research Station - Agriculture Research Directorate - Babylon Governorate / Iraqi, to study the gene expression of Sgr gene responsible for controlling the duration of staying green in varieties of wheat under effect of plant growth regulator during the two growth stages (vegetative and reproductive) by using quantitative reverse transcription-PCR (RT-qPCR) technique and achieving the highest grain yield for a number of wheat varieties. Randomized complete block design (RCBD) arranged according to split plots used with three replicates. The experiment included twelve wheat varieties (Saberbic, Al-Rasheed, Iraq, Tamoz-3, Al-Adnaniya, Babel, IPA-99, Al-Latife
... Show More
(9)
Objective: To find out any gender differences in health promoting behaviors for a sample of students attending Institute of Technology/ Baquba. Methodology: An analytical, cross-sectional study conducted randomly for a sample of students attending Technical Institute/ Baquba, during the period from 10th November 2015 to 10th April 2016. A questionnaire used to collecting data, this questionnaire was consisted from two domains related to health promoting behaviors including (Dietary domain and domain of some daily life activities like sleep duration, rise time, bedtime and walking period per week). The
This work aims to enhance acoustic and thermal insulation properties for polymeric composite by adding nanoclay and rock wool as reinforcement materials with different rations. A polymer blend of (epoxy+ polyester) as matrix materials was used. The Hand lay-up technique was used to manufacture the castings. Epoxy and polyester were mixed at different weight ratios involving (50:50, 60:40, 70:30, 80:20, and 90:10) wt. % of (epoxy: polyester) wt. % respectively. Impact tests for optimum sample (OMR), caustic and thermal insulation tests were performed. Nano clay (Kaolinite) with ratios ( 5 and 7.5% ) wt.% , also hybrid reinforcement materials involving (Kaolite 5 & 7.5 % wt.% + 10% volume fraction of rockwool ) were added as reinforcem
... Show More
(5)
(4)