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.
This research considers a proposed mechanism relying on frictional interactions between the grasped object and the gripper, thus attaining a case of self-locking condition for a tendon type robotic gripper. A mathematical model was derived for this proposed mechanism, upon which a special purpose apparatus was fabricated and tested. Both results, theoretically and experimentally, are in good agreement, showing that the weight of the grasped object played a major role in attaining the self-locking condition.
The practice of self medication is continuously increasing worldwide due to its important roles in curing minor conditions or symptoms. This study was conducted to evaluate the factors associated with self medication practice of Iraqi respondents residing in Baghdad City. This study was designed as cross sectional study in which data was collected via direct interviews with respondents using a previously prepared questionnaire. This study investigated 348 respondents from different age groups. The majority of respondents were male aged between 30-60 years, married with secondary or academic level of education and employed with accepted monthly income. The main reason for practicing self medication was previous experience with the same condi
... Show MoreSurface water flow samples were collected with distances downstream over Saqlawiya main drain whose stretch of about 24.5 km. The drain travels through different land use pattern, before, flowing into Tigris River. Eight sampling points were carefully
selected downstream the channel during dry season. The examined water parameters were pH, NH3, NO3, PO= 4, BOD5, COD, TDS, S.S, Cl-, SO= 4, Na+ , Ca+2, Mg+2, and Oil and Grease. Descriptive and inferential methods through finding the best curve fit correlation were employed in the study to test the strength of the association between water chemical characteristics and distance downstream the channel. A comparison of the values of chemical parameters at the Al-Saqlawiya Drain-Tigris Riv
The disposal of the waste material is the main goal of this investigation by transformation to high-fineness powder and producing self-consolidation concrete (SCC) with less cost and more eco-friendly by reducing the cement weight, taking into consideration the fresh and strength properties. The reference mix design was prepared by adopting the European guide. Five waste materials (clay brick, ceramic, granite tiles, marble tiles, and thermostone blocks) were converted to high-fine particle size distribution and then used as 5, 10, and 15% weight replacements of cement. The improvement in strength properties is more significant when using clay bricks compared to other activated waste
The disposal of the waste material is the main goal of this investigation by transformation to high-fineness powder and producing self-consolidation concrete (SCC) with less cost and more eco-friendly by reducing the cement weight, taking into consideration the fresh and strength properties. The reference mix design was prepared by adopting the European guide. Five waste materials (clay brick, ceramic, granite tiles, marble tiles, and thermostone blocks) were converted to high-fine particle size distribution and then used as 5, 10, and 15% weight replacements of cement. The improvement in strength properties is more significant when using clay bricks compared to other activated waste
This paper performance for preparation and identification of six new complexes of a number of transition metals Cr (lII), Mn (I1), Fe (l), Co (II), Ni (I1), Cu (Il) with: N - (3,4,5-Trimethoxy phenyl-N - benzoyl Thiourea (TMPBT) as a bidentet ligand. The prepared complexes have been characterized, identified on the basis of elemental analysis (C.H.N), atomic absorption, molar conductivity, molar-ratio ,pH effect study, I. Rand UV spectra studies. The complexes have the structural formula ML2X3 for Cr (III), Fe (III), and ML2X2 for Mn (II), Ni (II), and MLX2 for Co (Il) , Cu (Il).
Various activities taking place within the city of Baghdad have significantly contributed to organic pollution in Rivers Tigris and Diyala. The present study aimed to assess some physical, chemical and biological aspects of six sites on Rivers Tigris and Diyala as they flow through the city of Baghdad. Monthly samples were collected for the period January to December, 2005. Marked differences in the physical and chemical characteristics of water were noted between the two rivers’ sites. Average values during the study period of dissolved oxygen, biochemical oxygen demand, particulate organic matter, nitrate, phosphate and total dissolved solids for Tigris and Diyala were 7.8,4.7; 2.4,10.4; 350.1,921.4;7.8,13.9;1.2,4.8;814,2176 mg / l re
... Show MoreA novel series of liquid crystalline compounds containing 2,4-thiazolidinedione units with varying terminal alkyl chain lengths was successfully synthesized and characterized. The chemical structures of the synthesized compounds were confirmed by FT-IR, ¹H-NMR, and mass spectrometry. The mesomorphic behavior was investigated using polarized optical microscopy (POM) and differential scanning calorimetry (DSC). Compounds [V]₄, [V]₅, and [V]₆ exhibited enantiotropic nematic phases, while compound [V]₈ displayed a smectic A (SmA) phase. No liquid crystalline behavior was observed for compound [V]₃. The liquid crystalline properties were found to depend on the terminal-to-lateral chain length ratio, molecular geometry, and the nature
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This study aims at investigating the relationship between mindfulness and academic self-efficacy among Northern Border University students. To achieve this objective, the researcher adopted the correlative survey method for (97) students. For data collection, the researcher developed a mindfulness scale consisting of (42) items divided into seven topics, each one consisting of six items. The researcher developed an academic self-efficacy scale consisting of (20) items, adopting a five-point Likert scale. The results showed that there is a high level of mindfulness among students at the level of the seven units which formed the mindfulness scale; the conscious thinking unit showed the highest mean value o
... Show Moret-Self-Compacting Concrete (SCC) reduces environmental noise and has more workability. This research presents an investigation of the behavior of SCC under mechanical loading (impact loading). Two types of cement have been used to produce SCC mixtures, Ordinary Portland Cement (OPC) and Portland Limestone Cement (PLC), which reduces the emission of carbon dioxide during the manufacturing process. The mixes were reinforced with Carbon Fiber Reinforced Polymer (CFRP) which is usually used to improve the seismic performance of masonry walls, to replace lost steel reinforcements, or to increase column strength and ductility. Workability tests were carried out for fresh SCC. Prepared concrete slabs of 500×500×50mm were tested for lo
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