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.
In this work, porous silicon (PS) are fabricated using electrochemical etching (ECE) process for p-type crystalline silicon (c-Si) wafers of (100) orientation. The structural, morphological and electrical properties of PS synthesized at etching current density of (10, 20, 30) mA/cm2 at constant etching time 10 min are studied. From X-ray diffraction (XRD) measurement, the value of FWHM is in general decreases with increasing current density for p-type porous silicon (p-PS). Atomic force microscope (AFM) showed that for p-PS the average pore diameter decreases at 20 mA. Porous silicon which formed on silicon will be a junction so I-V characteristics have been studied in the dark to calculate ideality factor (n), and saturation current (Is
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The road transportation system is considered as major component of the infrastructure in any country, it affects the developments in economy and social activities. The Asphalt Concrete which is considered as the major pavement material for the road transportation system in Baghdad is subjected to continuous deterioration with time due to traffic loading and environmental conditions, it was felt that implementing a comprehensive pavement maintenance management system (PMMS), which should be capable for preserving the functional and structural conditions of pavement layers, is essential. This work presents the development of PMMS with Visual inspection technique for evaluating the Asphalt Concrete pavement surface condition; common types o
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The possibility of using zero-valent iron as permeable reactive barrier in removing lead from a contaminated groundwater was investigated. In the batch tests, the effects of many parameters such as contact time between adsorbate and adsorbent (0-240 min), initial pH of the solution (4-8), sorbent dosage (1-12 g/100 mL), initial metal concentration (50-250 mg/L), and agitation speed
(0-250 rpm) were studied. The results proved that the best values of these parameters achieve the maximum removal efficiency of Pb+2 (=97%) were 2 hr, 5, 5 g/100 mL, 50 mg/L and 200 rpm respectively. The sorption data of Pb+2 ions on the zero-valent iron have been performed well by Langmuir isotherm model in compared with Freundlich model under the studied
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The applications of Multilevel Converter (MLC) are increased because of the huge demand for clean power; especially these types of converters are compatible with the renewable energy sources. In addition, these new types of converters have the capability of high voltage and high power operation. A Nine-level converter in three modes of implementation; Diode Clamped-MLC (DC-MLC), Capacitor Clamped-MLC (CC-MLC), and the Modular Structured-MLC (MS-MLC) are analyzed and simulated in this paper. Various types of Multicarrier Modulation Techniques (MMTs) (Level shifted (LS), and Phase shifted (PS)) are used for operating the proposed Nine level - MLCs. Matlab/Simulink environment is used for the simulation, extracting, and ana
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Iraqi siliceous rocks were chosen to be used as raw materials in this study which is concern with the linear shrinkage and their related parameters. They are porcelinite from Safra area (western desert) and Kaolin Duekla, their powders were mixed in certain percentage, to shape compacts and sintered. The study followed with thermal and chemical treatments, which are calcination and acid washing. The effects on final compact properties such as linear shrinkage were studied. Linear shrinkage was calculated for sintered compacts to study the effects of calcination processes, chemical washing, weight percentage, sintering processes, loading moment were studied on this property where the compacts for groups is insulating materials.
Linear
The aim of this research work is to study the effect of stabilizing gypseous soil, which covers
vast areas in the middle, west and south parts of Iraq, using liquid asphalt on its strength properties
to be used as a base course layer replacing the traditional materials of coarse aggregate and broken
stones which are scarce at economical prices and hauling distances.
Gypseous soil brought from Al-Ramadi City, west of Iraq, with gypsum content of 66.65%,
medium curing cutback asphalt (MC-30), and hydrated lime are used in this study.
The conducted tests on untreated and treated gypseous soil with different percentages of medium
curing cutback asphalt (MC-30), water, and lime were: unconfined compression strength, and o
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Identifying breast cancer utilizing artificial intelligence technologies is valuable and has a great influence on the early detection of diseases. It also can save humanity by giving them a better chance to be treated in the earlier stages of cancer. During the last decade, deep neural networks (DNN) and machine learning (ML) systems have been widely used by almost every segment in medical centers due to their accurate identification and recognition of diseases, especially when trained using many datasets/samples. in this paper, a proposed two hidden layers DNN with a reduction in the number of additions and multiplications in each neuron. The number of bits and binary points of inputs and weights can be changed using the mask configuration
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End of the twentieth century witnessed by the technological evolution Convergences between the visual arts aesthetic value and objective representation of the image in the composition of the design of the fabric of new insights and unconventional potential in atypical employment. It is through access to the designs of modern fabrics that address the employment picture footage included several scenes footage from the film, which focuses on research and analytical as a study to demonstrate the elements of the picture and the organization of its rules and how to functioning in the design of fabrics, Thus, it has identified the problem by asking the following: What are the elements of the picture footage and how the functioning of the struct
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In this modern Internet era and the transition to IPv6, routing protocols must adjust to assist this transformation. RIPng, EIGRPv6 and OSPFv3 are the dominant IPv6 IGRP (Interior Gateway Routing Protocols). Selecting the best routing protocol among the available is a critical task, which depends upon the network requirement and performance parameters of different real time applications. The primary motivation of this paper is to estimate the performance of these protocols in real time applications. The evaluation is based on a number of criteria including: network convergence duration, Http Page Response Time, DB Query Response Time, IPv6 traffic dropped, video packet delay variation and video packet end to end de
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