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.
The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s
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A geographic information system (GIS) is a very effective management and analysis tool. Geographic locations rely on data. The use of artificial neural networks (ANNs) for the interpretation of natural resource data has been shown to be beneficial. Back-propagation neural networks are one of the most widespread and prevalent designs. The combination of geographic information systems with artificial neural networks provides a method for decreasing the cost of landscape change studies by shortening the time required to evaluate data. Numerous designs and kinds of ANNs have been created; the majority of them are PC-based service domains. Using the ArcGIS Network Analyst add-on, you can locate service regions around any network
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The experimental proton resonance data for the reaction P+48Ti have been used to calculate and evaluate the level density by employed the Gaussian Orthogonal Ensemble, GOE version of RMT, Constant Temperature, CT and Back Shifted Fermi Gas, BSFG models at certain spin-parity and at different proton energies. The results of GOE model are found in agreement with other, while the level density calculated using the BSFG Model showed less values with spin dependence more than parity, due the limitation in the parameters (level density parameter, a, Energy shift parameter, E1and spin cut off parameter, σc). Also, in the CT Model the level density results depend mainly on two parameters (T and ground state back shift energy, E0), which are app
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The research aimed at finding out the effect of functional rotation on the tax performance of the employees of the General Authority for Taxes through the five-meter questionnaire prepared according to the required data. The data obtained from the research sample were analyzed. The results showed a significant effect of recycling In the tax performance, and this is evident from the proportion of his contribution to the interpretation of the total variation, which is a good indicator of the impact of functional rotation in the performance of the body sample research.
This research presents a new algorithm for classification the
shadow and water bodies for high-resolution satellite images (4-
meter) of Baghdad city, have been modulated the equations of the
color space components C1-C2-C3. Have been using the color space
component C3 (blue) for discriminating the shadow, and has been
used C1 (red) to detect the water bodies (river). The new technique
was successfully tested on many images of the Google earth and
Ikonos. Experimental results show that this algorithm effective to
detect all the types of the shadows with color, and also detects the
water bodies in another color. The benefit of this new technique to
discriminate between the shadows and water in fast Matlab pro
Criteria to be met in selecting the obtimal areas for generating alternative electric energy from wind
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In this work, a fiber-optic biomedical sensor was manufactured to detect hemoglobin percentages in the blood. SPR-based coreless optical fibers were developed and implemented using single and multiple optical fibers. It was also used to calculate refractive indices and concentrations of hemoglobin in blood samples. An optical fiber, with a thickness of 40 nanometers, was deposited on gold metal for the sensing area to increase the sensitivity of the sensor. The optical fiber used in this work has a diameter of 125μm, no core, and is made up of a pure silica glass rod and an acrylate coating. The length of the fiber was 4cm removed buffer and the splicing process was done. It is found in practice that when the sensitive refractive i
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This paper presents an enhancement technique for tracking and regulating the blood glucose level for diabetic patients using an intelligent auto-tuning Proportional-Integral-Derivative PID controller. The proposed controller aims to generate the best insulin control action responsible for regulating the blood glucose level precisely, accurately, and quickly. The tuning control algorithm used the Dolphin Echolocation Optimization (DEO) algorithm for obtaining the near-optimal PID controller parameters with a proposed time domain specification performance index. The MATLAB simulation results for three different patients showed that the effectiveness and the robustness of the proposed control algorithm in terms of fast gene
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Lower neck pain is one of the problems facing all ages, especially the elderly, as it revolves around the causes of this pain from many diverse factors. The aim of the research is to use special intense exercise accompanied by intermittent electrical stimulation to get rid of lower neck pain among professors of the College of Science - University of Baghdad for ages. (40-60) years and to identify the extent of the effect. The research assumed the presence of statistically significant differences. The research sample represented professors at the University of Baghdad - College of Science who suffer from continuous pain for the period between (10/15/2023) and (1/15/) 2024) and their number is (5), The researchers used the experimenta
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