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

An experimental study was conducted to determine the performance of a solar electric refrigeration system. The system contained flat photovoltaic solar panel which absorbs the solar energy and convert it to electrical energy, used to run the refrigeration cycle. Two refrigeration cycles with electrical solar panel were used over a period of 12 months, the first one with classical parts known in refrigeration cycle, while the second one introduced heat exchanger which improves the coefficient of performance by saving the consumed energy. The coefficient of performance of these refrigeration cycles with compressor efficiency 85% are 2.102 and 2.57 respectively. The overall efficiency of the two systems are 18.9% and 23.13%.

Economic units can benefit from the cleaner production strategy, which aims to reduce the environmental impact of economic activities while improving efficiency and profitability. Accordingly, the aim of the research was to clarify the knowledge foundations of cleaner production costs and to indicate their role in reducing the costs of poor quality (the costs of failure). A set of conclusions has been reached, the most important of which is that cleaner production has achieved a reduction in the costs of external failure, represented by the costs of guarantee, by an amount of 12,339,000 dinars. Contributes to reducing the costs of failure, and based on the conclusions, a set of recommendations were presented, the most important of w

Flow of water under concrete dams generates uplift pressure under the dam, which may cause the dam to function improperly, in addition to the exit gradient that may cause piping if exceeded a safe value. Cutoff walls usually used to minimize the effect of flow under dams. It is required to
1)minimize the flow quantity to conserve water in the reservoir, it is also required to
2)minimize the uplift pressure under the dam to maintain stability of the dam, and it is required to

3) minimize the exit gradient to prevent quick condition to occur at the toe of the dam where piping may occur and may cause erosion of the soil. Varying the angle of cutoff walls affects its influence on the factors aforementioned that are required to

The type of groundwater in the studied area is slightly brackish. In general, the dominant water type is calcium-sulfate. The reasons behind these different chemical groundwater types can be referred to the active ion exchange between the groundwater of the Dammam aquifer and Rus Formation. The groundwater of the Dammam unconfined aquifer is not suitable for human drinking in all the parameters properties. The groundwater class is fair in the Qasir Al-Ukhaider area, while the Shebcha area and Al-Salman area are poor class except the eastern part of Al-Salman area is very poor.

This research aims at investigating pupils’ ability in using discourse markers which are identified in the English textbooks of secondary schools. Four texts are chosen from third intermediate class. The four texts are short stories of different topics.                                                  

        This research hypothesizes that there are no statistical significant differences among Iraqi intermediate pupils’ ability in using textual

Digital forensics has become a fundamental requirement for law enforcement due to the growing volume of cyber and computer-assisted crime. Whilst existing commercial tools have traditionally focused upon string-based analyses (e.g., regular expressions, keywords), less effort has been placed towards the development of multimedia-based analyses. Within the research community, more focus has been attributed to the analysis of multimedia content; they tend to focus upon highly specialised specific scenarios such as tattoo identification, number plate recognition, suspect face recognition and manual annotation of images. Given the ever-increasing volume of multimedia content, it is essential that a holistic Multimedia-Forensic Analysis Tool (M-

Background: zirconium (Zr) implants are known for having an aesthetically pleasing tooth-like colour Unlike the grey cervical collar that develops over time when titanium (Ti) implants are used in thin gingival biotypes. However, the surface qualities of Zr implants can be further improved. This present study examined using thermal vapour deposition (TVD) to coat Zr implants with germanium (Ge) to improve its physical and chemical characteristics and enhance soft and hard tissue responses. Materials and methods: Zr discs were divided into two groups; the uncoated (control) group was only grit-blasted with alumina particles while the coated (experimental) group was grit-blasted then coated with Ge via TVD. Field emission scanning ele

The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one

        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