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.
Nowadays, the mobile communication networks have become a consistent part of our everyday life by transforming huge amount of data through communicating devices, that leads to new challenges. According to the Cisco Networking Index, more than 29.3 billion networked devices will be connected to the network during the year 2023. It is obvious that the existing infrastructures in current networks will not be able to support all the generated data due to the bandwidth limits, processing and transmission overhead. To cope with these issues, future mobile communication networks must achieve high requirements to reduce the amount of transferred data, decrease latency and computation costs. One of the essential challenging tasks in this subject
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This study aimed to incorporate hydroxyapatite nanoparticles (nHA) or amorphous calcium phosphate nanoparticles (nACP) into a self-etch primer (SEP) to develop a simplified orthodontic bonding system with remineralizing and enamel preserving properties.
nHA and nACP were incorporated into a commercial SEP (Transbond™ plus) in 7% weight ratio and compared with the plain SEP as a control. Shear bond strengths (SBS), enamel damage, and adhesive remnant index (ARI) scores were evaluated at 24 h
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In the last years, the self-balancing platform has become one of the most common candidates to use in many applications such as flight, biomedical fields, industry. This paper introduced the simulated model of a proposed self-balancing platform that described the self–balancing attitude in (X-axis, Y-axis, or both axis) under the influence of road disturbance. To simulate the self-balanced platform's performance during the tilt, an integration between Solidworks, Simscape, and Simulink toolboxes in MATLAB was used. The platform's dynamic model was drawn in SolidWorks and exported as a STEP file used in the Simscape Multibody environment. The system is controlled using the proportional-integral-derivative (PID) co
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The main objective of the research is to identify the role of strategic training and its effect on enhancing the self-growth of the individual. Stratigic training represents a contemporary tendency. that is adopted by business organizations in carrying out their activities and tasks.
It is worth to mention, that self-growth of the individual is one of the indictors used to determine the ability of organization to a achieve its goals.
The problem of the research has pointed out to the minimum awareness of the important role played by training strategy in enhancing the self-growth of the individual. The researcher has adopted an analytical approach, in collecting and analyses
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In the last years, the self-balancing platform has become one of the most common candidates to use in many applications such as flight, biomedical fields, industry. This paper introduced the simulated model of a proposed self-balancing platform that described the self–balancing attitude in (X-axis, Y-axis, or both axis) under the influence of road disturbance. To simulate the self-balanced platform's performance during the tilt, an integration between Solidworks, Simscape, and Simulink toolboxes in MATLAB was used. The platform's dynamic model was drawn in SolidWorks and exported as a STEP file used in the Simscape Multibody environment. The system is controlled using the proportional-integral-deriva
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Art education is one among the fundamental subjects for elementary school students, because it contributes to assembling learners’ personalities and developing their technical skills. For this reason, this research comes, which aims to understand the effect of the task groups’ strategy in developing the performance of elementary school students in art education. to realize the goal of the research, the researcher put the subsequent hypotheses:
-There is not any statistically significant difference at the amount (5%) between the typical many students between the experimental group that studied consistent with the strategy of task groups and therefore the control group that studied in keeping with the same old method that they obt
In this paper normal self-injective hyperrings are introduced and studied. Some new relations between this concept and essential hyperideal, dense hyperideal, and divisible hyperring are studied.
Cryptography is a method used to mask text based on any encryption method, and the authorized user only can decrypt and read this message. An intruder tried to attack in many manners to access the communication channel, like impersonating, non-repudiation, denial of services, modification of data, threatening confidentiality and breaking availability of services. The high electronic communications between people need to ensure that transactions remain confidential. Cryptography methods give the best solution to this problem. This paper proposed a new cryptography method based on Arabic words; this method is done based on two steps. Where the first step is binary encoding generation used t
... Show MoreThis study aims at identifying the reality of alternative assessment for teachers of the first cycle of the basic education in the Sultanate of Oman with respect to the degree of teachers' use of alternative assessment strategies, level of self-efficacy for alternative assessment strategies, and attitude towards alternative assessment, and their relationship with other variables. To achieve the aims of the study, a descriptive research approach was utilized. A 5-point self-rated questionnaire was developed. It consists of three sections: Actual use of alternative assessment strategies (21 items), self-efficacy for alternative assessment strategies (21 items), and attitude towards alternative assessment (27 items). The psychometric proper
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