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.
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The compressive residual stresses generated by shot peening, is increased in a direct proportional way with shot peening time (SPT). For each metal, there is an optimum shot peening time (O.S.T) which gives the optimum fatigue life. This paper experimentally studied to optimize shot peening time of aluminium alloy 6061-T651 as well as using of and analysis of variance (ANOVA).
Two types of fatigue test specimens’ configuration were used, one without notch (smooth) and the other with a notch radius (1,25mm), each type was shot peened at different time. The (O.S.T) was experimentally estimated to be 8 minutes reaching the surface stresses at maximum peak of -184.94 MPa.
A response surface methodology (RSM) is presen
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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.
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