Search results for: Raouf Ahmed Mohamed Hassan

Authors: Ibrahim Ali, Adamu Danlami Ahmed

Abstract:

This study examines the impact of depreciation on taxable income and financial performance of consumer goods companies quoted on the Nigerian stock exchange. The study adopts ex-post factor research design. Data were collected using a secondary source. The findings of the study suggest that, method of depreciation adopted in any organization influence the taxable profit. Depreciation techniques can either be: depressive, accelerative and linear depreciation. It was also recommended that consumer goods should adjust their method of depreciation to make sure an appropriate method is adopted. This will go a long way to revitalize their taxable profit.

Keywords: accelerated, linear, depressive, depreciation

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Authors: Kaouther Selmi, Alaeddine Sridi, Mohamed Bouallegue, Kais Bouallegue

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Neurons are the fundamental units of the brain and the nervous system. The variable structure model of neurons consists of a system of differential equations with various parameters. By optimizing these parameters, we can create a unique model that describes the dynamic behavior of a single neuron. We introduce a neural network based on neurons with multiple dendrites employing an activation function with a variable structure. In this paper, we present a model for heart behavior. Finally, we showcase our successful simulation of the heart's ECG diagram using our Variable Structure Neuron Model (VSMN). This result could provide valuable insights into cardiology.

Keywords: neural networks, neuron, dendrites, heart behavior, ECG

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Authors: Aries Nawel, Bentarzi Mohamed

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This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model (PINMA_{S}(q)). The closed forms of the mean, the second moment and the periodic autocovariance function are obtained. Furthermore, the time reversibility of the model is discussed in details. Moreover, the estimation of the underlying parameters are obtained by the Yule-Walker method, the Conditional Least Square method (CLS) and the Weighted Conditional Least Square method (WCLS). A simulation study is carried out to evaluate the performance of the estimation method. Moreover, an application on real data set is provided.

Keywords: periodic integer-valued moving average, periodically correlated process, time reversibility, count data

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Authors: Saman Javadi, Mohammad Hassan Mahmoudi, Fatemeh Jafari, Aminreza Neshat

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Urmia Lake’s water level has been dropped during the past decade. Although the most common reason in studies was declared climate change, but observation of adjacent lake (like Van in Turkey) is not the same as the common reason. Most of studies were focused on climate and land use change, but groundwater resource as one of the most important element is negligible. Due to population and agriculture activities growth, exploration of groundwater resource has been increased. In as much as continued decline of water levels can lead to saltwater intrusion, reduce stream discharge near outcrop regions and threaten groundwater quality, aquifers of this region were affected by saltwater intrusion of Urmia Lake. In this research comparison of saltwater intrusion into eastern and western coastal aquifer was studied. In conclusion eastern aquifers are in a critical situation; vice versa the western ones are in a better situation. Thus applying management of groundwater operation would be necessary for eastern aquifers.

Keywords: coastal aquifer, groundwater over-exploration, saltwater intrusion, Urmia Lake

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Authors: Abdelaziz Rabhi, Mohamed Amrani, Abderrazek Ziane, Nabil Belkadi, Abdelraouf Hocini

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In this paper, a bedimensional simulation program of the electric characteristics of reverse biased lateral polysilicon PIN diode is presented. In this case we have numerically solved the system of partial differential equations formed by Poisson's equation and both continuity equations that take into account the effect of impact ionization. Therefore we will obtain the current-voltage characteristics (I-V) of the reverse-biased structure which may include the effect of breakdown.The geometrical model assumes that the polysilicon layer is composed by a succession of defined mean grain size crystallites, separated by lateral grain boundaries which are parallel to the metallurgic junction.

Keywords: breakdown, polycrystalline silicon, PIN, grain, impact ionization

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Authors: A. Benhadji, M. Taleb Ahmed

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Among the various methods of treatment, advanced oxidation processes (AOP) are the most promising ones. In this study, Peroxi Electrocoagulation Process (PEP) was investigated for the treatment of detergent wastewater. The process was compared with electrooxidation treatment. The results showed that chemical oxygen demand (COD) was high 7584 mgO₂.L^-1, while the biochemical oxygen demand was low (250 mgO₂.L^-1). This wastewater was hardly biodegradable. Electrochemical process was carried out for the removal of detergent using a glass reactor with a volume of 1 L and fitted with three electrodes. A direct current (DC) supply was used. Samples were taken at various current density (0.0227 A/cm² to 0.0378 A/cm²) and reaction time (1-2-3-4 and 5 hour). Finally, the COD was determined. The results indicated that COD removal efficiency of PEP was observed to increase with current intensity and reached to 77% after 5 h. The highest removal efficiency was observed after 5 h of treatment.

Keywords: AOP, COD, detergent, PEP, wastewater

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Authors: Ahmed Shaban Abdel Hay Gabr

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Water hyacinth (W-H) has an adverse effect on Nile river in Egypt, it absorbs high quantities of water, it needs to serve these quantities especially at this time, so by burning W-H, it can be used in concrete mix to reduce the permeability of concrete and increase both the compressive and splitting strength. The effect of W-H on non-structural concrete properties was studied, but there is a lack of studies about the behavior of structural concrete containing W-H. Therefore, in the present study, the behavior of 15 RC beams with 100 x 150 mm cross section, 1250 mm span, different reinforcement ratios and different W-H ratios were studied by testing the beams under two-point bending test. The test results showed that Water Hyacinth is compatible with RC which yields promising results.

Keywords: beams, reinforcement ratio, reinforced concrete, water hyacinth

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Authors: Chun-Qing Li, Hassan Baji, Wei Yang

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Corrosion of steel in reinforced concrete structures is a major problem worldwide. The volume expansion of corrosion products causes concrete cover cracking, which could lead to delamination of concrete cover. The time to cover cracking plays a key role to the assessment of serviceability of reinforced concrete structures subjected to corrosion. Many analytical, numerical, and empirical models have been developed to predict the time to cracking initiation due to corrosion. In this study, a numerical model based on finite element modeling of corrosion-induced cracking process is used. In order to predict the service life based on time to cover initiation, the numerical approach is coupled with a probabilistic procedure. In this procedure, all the influential factors affecting time to cover cracking are modeled as random variables. The results show that the time to cover cracking is highly variables. It is also shown that rust product expansion ratio and the size of more porous concrete zone around the rebar are the most influential factors in predicting service life of corrosion-affected structures.

Keywords: corrosion, crack width, probabilistic, service life

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Authors: Aaminah Hassan

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Advertisements carry a great potential to influence our lives because they are crafted to meet particular ends. Stereotypical representation in advertisements is capable of forming unconscious attitudes among people towards any gender and their abilities. This study focuses on gender representation in Pakistani prime time advertisements. For this purpose, 13 advertisements were selected from three different categories of foods and beverages, cosmetics, cell phones and cellular networks from the prime time slots of one of the leading Pakistani entertainment channel, ‘Urdu 1’. Both quantitative and qualitative analyses are carried out for range of variables like gender, age, roles, activities, setting, appearance and voice overs. The results revealed that gender representation in advertisements is stereotypical. Moreover, in few instances, the portrayal of women is not only culturally inappropriate but is demeaning to the image of women as well. Their bodily charm is used to promote products. Comparing different entertainment channels for their prime time advertisements and broadening the scope of this research will yield greater implications for the researchers who want to carry out the similar research. It is hoped that the current study would help in the promotion of media literacy among the viewers and media authorities in Pakistan.

Keywords: Advertisements, Content Analysis, Gender, Prime time

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Authors: Ahmed H. Elkholy

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Aircraft gas turbine engines are subject to damage by airborne foreign objects such as birds and garbage dumps. In order to assess their effect on engine performance, a complete foreign object damage (FOD) test was carried out and a component failure analysis was used to verify airworthiness standards (AWS) requirements for engine certification as set by international regulations. Ingestion damage due to 1.8 Kg (4 lb.) bird strike on an engine is presented in some detail. Based on the observed damage, improvements to the engine design were suggested in two different locations: the front bearing housing and the low compressor shaft. When these improvements were implemented, the engine showed an acceptable containment capability that meets AWS requirements.

Keywords: aircraft engine, airworthiness standards, bird ingestion, foreign object damage

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Authors: Hadj Mohamed Nacera, Boutaleb Abdelhak

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The Hercynian granite in Western Algeria, has a typical high-K calc-alkaline evolution, with peraluminous trend U-Pb zircon geochronology yielded the minimum emplacement age of 297 ± 1 Ma. It shows dark microgranular enclaves, veins of pegmatite, aplite, tourmaline and quartz. The granite plutons selected for this study are formed during the late Variscian phase and intrudes the Lower Silurian metasediments which were affected by the major Hercynian folding phases. An important Quartz vein field cross-cutting metasedimentary and granitic rocks. Invisible gold occurs in a very small arsenopyrite minerals. The purpose of this study is to highlight the relationship between the gold mineralisation and the intrusion by combining petrographic and geochemic studies.

Keywords: Algeria, basement, geochemestry, granite

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Authors: Carole A. El Raheb, Hassan K. Abdel-Salam, Ingi Elcherif

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An architect carrying the design process alone is the main reason for the deterioration of the quality of the architectural product as the complexity of the projects makes it a multi-disciplinary work; then, the Integrative Design Process (IDP) must be applied in the architectural firm especially from the early design phases to improve the product’s quality and to eliminate the ignorance of the principles of design causing the occurrence of low-grade buildings. The research explores the Integrative Design (ID) principles that fit in the architectural practice. Constraints facing this application are presented with strategies and solutions to overcome them. A survey questionnaire was conducted to collect data from a number of recognized Egyptian Architecture, Engineering and Construction (AEC) firms that explores their opinions on using the IDP. This survey emphasizes the importance of the IDP in firms and presents the reasons preventing the firms from applying the IDP. The aim here is to investigate the potentials of integrating this approach into architectural firms emphasizing the importance of this application which ensures the realization of the project’s goal and eliminates the reduction in the project’s quality.

Keywords: application, architectural firms, integrative design principles, integrative design process, the project quality

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Authors: Ali Musbah Mohamed Elwahishi

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Democracy is demand for the majority of people in the whole world, Specifically in the regions that are still outside the democratic life such as Libya and other Arab countries. Although democracy has spread across the world through three waves of democratization, Libya is still outside the democratic process, even recently its regime has changed. The challenges of democracy in Libya are not new, they represent accumulations over time that impeded to achieve this goal. This paper concludes that the absence of democracy in Libya because of set of factors that include: colonial legacy, oil wealth, the lack of institutions, the lack of political parties, tribal factor and recently the spread of the armed groups. These factors prevented Libya to be democratic state whether during King Idris’, Qaddafi’s or even after Qaddafi rule.

Keywords: the failure of democracy, political transition, the lack of institutions, Libya, Arab countries

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Authors: Cristina Rodriguez, Abed Alaswad, Zaki El-Hassan, Abdul G. Olabi

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This study investigates the effect on methane production from the waste paper when co-digested with macroalgal biomass as a source of nitrogen. Both feedstocks were previously mechanically pretreated in order to reduce their particle size. Methane potential assays were carried out at laboratory scale in batch mode for 28 days. The study was planned according to two factors: the feedstock to inoculum (F/I) ratio and the waste paper to macroalgae (WP/MA) ratio. The F/I ratios checked were 0.2, 0.3 and 0.4 and the WP/MA ratios were 0:100, 25:75, 50:50, 75:25 and 100:0. The highest methane yield (608 ml/g of volatile solids (VS)) was achieved at an F/I ratio of 0.2 and a WP/MA ratio of 50:50. The methane yield at a ratio WP/MA of 50:50 is higher than for single compound, while for ratios WP/MA of 25:75 and 75:25 the methane yield decreases compared to biomass mono-digestion. This behavior is observed for the three levels of F/I ratio being more noticeable at F/I ratio of 0.3. A synergistic effect was found for the WP/MA ratio of 50:50 and all F/I ratios and for WP/MA=50:50 and F/I=0.2. A maximum increase of methane yield of 49.58% was found for a co-digestion ratio of 50:50 and an F/I ratio of 0.4. It was concluded that methane production from waste paper improves significantly when co-digested with macroalgae biomass. The methane yields from co-digestion were also found higher that from macroalgae mono-digestion.

Keywords: anaerobic co-digestion, biogas, macroalgae, waste paper

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Authors: Djehich Mohamed Yousri

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In this research paper, the future of international relations is believed to have an important place on the theoretical and applied levels because policy makers in the world are in dire need of such analyzes that are useful in drawing up the foreign policies of their countries, and protecting their national security from potential future threats, and in this context, The topic raised a lot of scientific controversy and intellectual debate, especially in terms of the extent of the effectiveness, accuracy, and ability of foresight methods to identify potential futures, and this is what attributed the controversy to the scientific foundations for foreseeing international relations. An arena for intellectual discussion between different thinkers in international relations belonging to different theoretical schools, which confirms to us the conceptual and implied development of prediction in order to reach the scientific level.

Keywords: foresight, forecasting, international relations, international relations theory, concept of international relations

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Authors: Syed Hassan Amjad

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In today’s competitive environment, in order for a company to exist, it must continually improve its Performance by reducing cost, improving quality and productivity, and easy access to market.The purpose of this thesis is to check the firm financial growth and performance and which type of factors affect the firm financial performance. This paper examines the key determinants of firm financial performance. We will differentiate between financial and non financial drivers of the firm financial performance. For the measurement of the firm financial performance there are many ways but all the measure had been taken in aggregation, such as debt, tax rate, operating expenses, earning per share and economic conditions. This study has also been done in developed countries but these researches show that foreign companies face many difficulties inimproving the firm financial performance. In findings we found that marketing expenditures and international diversification had a positive impact on firm valuation. In research also found that a firm's ownership composition, particularly the level of equity ownership by Domestic Financial Institutions and Dispersed Public Shareholders, and the leverage of the firm, tax rate and economic conditions were important factors affecting its financial performance.

Keywords: debt, tax rate, firm financial performance, operating expenses, dividend per share, economic conditions

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Authors: Noha E. Hassan

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Little is known regarding the influence of lymphatic microvessel density (LMVD) on prognosis in endometrial cancer. Prospective study was done in tertiary education and research hospital (Shatby Alexandria university hospital) on sixty patients presented with endometrial carcinoma underwent complete surgical staging. Our aim was to assess the intratumoral and peritumoral Lymphatic microvessel density (LMVD) of endometrial carcinomas identified by immunohistochemical staining using an antibody against podoplanin and to investigate their association with classical clinicopathological factors and prognosis. The result shows that high LMVD was associated with endometroid type of tumors, lesser myometrial, adnexal, cervical and peritoneal infiltration, lower tumor grade and stage and lesser recurrent cases. There is lower lymph node involvement among cases with high intratumoral LMVD and cases of high peritumoral LMVD; that reach statistical significance only among cases of high intratumoral LMVD. No association was seen between LMVD and lymphovascular space invasion. On the other hand, low LMVD was associated with poor outcome. Finally, we can conclude that increased LMVD is associated with favorable prognosis in endometrial cancer patients.

Keywords: endometrial carcinoma, lymphatic microvessel, microvessel density, prognosis

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Authors: Hossein Alimohammadi, Kristina Vassiljeva, Hassan HosseinNia, Eduard Petlenkov

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This research article discusses the mechanisms for bandgap tuning of beam-type resonators to achieve ‎broadband vibration suppression through adjustable stiffness. The method involves changing the center of ‎mass of the cantilever-type resonator to achieve piezo-free tuning of stiffness. The study investigates the ‎effect of the center of masses variation (δ) of attached masses on the bandgap and vibration suppression ‎performance of a non-uniform beam-type resonator within a phononic structure. The results suggest that the ‎cantilever-type resonator beam can be used to achieve tunability and real-time control and indicate that ‎varying δ significantly impacts the bandgap and transmittance response. Additionally, the research explores ‎the use of the first and second modes of resonators for tunability and real-time control. These findings examine ‎the feasibility of this approach, demonstrate the potential for improving resonator performance, and provide ‎insights into the design and optimization of metamaterial beams for vibration suppression applications.

Keywords: bandgap, adjustable stiffness, spatial variation, tunability

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Authors: Boukhatem Mohamed Belkaid, Lahdi Mourad

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In this paper, we propose a new encryption system for security issues medical images. The hybrid encryption scheme is based on AES and RSA algorithms to validate the three security services are authentication, integrity, and confidentiality. Privacy is ensured by AES, authenticity is ensured by the RSA algorithm. Integrity is assured by the basic function of the correlation between adjacent pixels. Our system generates a unique password every new session of encryption, that will be used to encrypt each frame of the medical image basis to strengthen and ensure his safety. Several metrics have been used for various tests of our analysis. For the integrity test, we noticed the efficiencies of our system and how the imprint cryptographic changes at reception if a change affects the image in the transmission channel.

Keywords: AES, RSA, integrity, confidentiality, authentication, medical images, encryption, decryption, key, correlation

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Authors: Mohamed El-Sayed Mosaad

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An analytic approach is obtained for the steady heat transfer problem of two fluid systems, in thermal communication via heat conduction across a solid wall separating them. The two free convection layers created on wall sides are assumed to be in parallel flow. Fluid-solid interface temperature on wall sides is not prescribed in analysis in advance; rather, determined from conjugate solution among other unknown parameters. The analysis highlights the main conjugation parameters controlling thermal interaction process of involved heat transfer modes. Heat transfer results of engineering importance are obtained.

Keywords: conjugate heat transfer, boundary layer, convection, thermal systems

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Authors: Mohamed Derbeli, Maissa Farhat, Oscar Barambones, Lassaad Sbita

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Conventional controller (PI) applied to a DC/DC boost converter for the improvement and optimization of the Proton Exchange Membrane Fuel Cell (PEMFC) system efficiency, cannot attain a good performance effect. Thus, due to its advantages comparatively with the PI controller, this paper interest is focused on the use of the sliding mode controller (SMC), Stability of the closed loop system is analytically proved using Lyapunov approach for the proposed controller. The model and the controllers are implemented in the MATLAB and SIMULINK environment. A comparison of results indicates that the suggested approach has considerable advantages compared to the traditional controller.

Keywords: DC/DC boost converter, PEMFC, PI controller, sliding mode controller

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Authors: Hassan Gana Abdullahi, Michael A. Fullen, David Oloke

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Drought poses an enormous global threat to sustainable development and is expected to increase with global climate change. Drought and desertification are major problems in Yobe State (north-east Nigeria). This investigation aims to develop a workable framework and management tool for drought mitigation in Yobe State. Mixed methods were employed during the study and additional qualitative information was gathered through Focus Group Discussions (FGD). Data on socio-economic impacts of drought were thus collected via both questionnaire surveys and FGD. In all, 1,040 questionnaires were distributed to farmers in the State and 721 were completed, representing a return rate of 69.3%. Data analysis showed that 97.9% of respondents considered themselves to be drought victims, whilst 69.3% of the respondents were unemployed and had no other means of income, except through rain-fed farming. Developing a viable and holistic approach to drought mitigation is crucial, to arrest and hopefully reverse environment degradation. Analysed data will be used to develop an integrated framework for drought mitigation and management in Yobe State. This paper introduces the socio-economic and environmental effects of drought in Yobe State.

Keywords: drought, climate change, mitigation, management, Yobe State

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Authors: Iman Ali Ahmed Al-Rashed

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This paper directs attention to the limitations of the teacher-centered strategy in teaching. The aim of this study is to draw more educational attention to learner-centered strategy in order to shift the emphasis from the traditional concept of teaching to a new concept in teaching. To begin bridging the traditional concept of teaching and the new concept, the study will explore the new concept of teaching to support teaching in Arab World generally and in Iraq specifically. A qualitative case study orientation was used to collect data in the form of classroom observations, interviews and field notes. The teaching practices used by three university instructors are investigated and according to the findings, some explanations and recommendations are made.

Keywords: case study, learner-centered strategy, qualitative study, teacher-centered strategy, traditional teaching

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Authors: N. Ibrahim-Rassoul, A. Kessi, E. K. Si-Ahmed, N. Djilali, J. Legrand

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The static and dynamic formation of liquid water bridges is analyzed using a combination of visualization experiments in a microchannel with a mathematical model. This paper presents experimental and theoretical findings of water plug/capillary bridge formation in a 250 μm squared microchannel. The approach combines mathematical and numerical modeling with experimental visualization and measurements. The generality of the model is also illustrated for flow conditions encountered in manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The predictions of the model agree favorably the observations as well as with the experimental recordings.

Keywords: green energy, mathematical modeling, fuel cell, water plug, gas diffusion layer, surface of revolution

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Authors: Mohamed El-Bady

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The Northern Egyptian Lagoons are (from east to west) Bardawil Lagoon, Manzala Lagoon, Burullus Lagoon, Edku Lagoons and Mariute Lagoon. These lagoons have been received the bulk of drainage water from the lands of Delta and from the other coastal areas. Where, the heavy metals can occur in Lagoons environments through a variety of sources, including industries, wastewaters and domestic effluents. The potential ecological risk index (RI) calculation of the bottom sediments of the northern lagoons depends on contamination factor (CF), potential ecological risk factor and proposed toxic response factor (Tr). Each lagoon with special indices according to its conditions.

Keywords: Northern Lagoons, Nile Delta, ecological risk index, contamination factor

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Authors: Mohamed Amine Ben Abdallah, Imed Khemili, Nizar Aifaoui

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This work denotes an insight into dynamic synthesis of multibody systems. A set of mechanism parameters design variable are synthetized based on a desired mechanism response, such as, velocity, acceleration and bodies deformations. Moreover, knowing the work space, for a robot, and mechanism response allow defining optimal parameters mechanism handling with the desired target response. To this end, evolutionary genetic algorithm has been deployed. A demonstrative example for imperfect mechanism has been treated, mainly, a slider crank mechanism with a flexible connecting rod. The transversal deflection of the connecting rod has been chosen as response to identify the mechanism design parameters.

Keywords: dynamic response, evolutionary genetic algorithm, flexible bodies, optimization

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Authors: Yehya Abdellatif, Ahmed Alsalaymeh, Iyad Muslih, Ali Alshduifat

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Photovoltaic (PV) power generation systems, mainly small scale, are rapidly being deployed in Jordan. The impact of these systems on the grid has not been studied or analyzed. These systems can cause many technical problems such as reverse power flows and voltage rises in distribution feeders, and real and reactive power transients that affect the operation of the transmission system. To fully understand and address these problems, extensive research, simulation, and case studies are required. To this end, this paper studies the cloud shadow effect on the power generation of a ground mounted PV system installed at the test field of the Renewable Energy Center at the Applied Science University.

Keywords: photovoltaic, cloud effect, MPPT, power transients

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Authors: Hala A. Hassan, Vasiliki K. Tsiouri, Konstantinos E. Konstantinos

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Fugitive particulate matter (PM) is a major source of airborne pollution in the Middle East countries. The meteorological conditions and topography of the area make it highly susceptible to wind-blown particles which raise many air quality concerns. Air quality tools such as field monitoring, emission factors, and dispersion modeling have been used in previous research studies to analyze the release and impacts of fugitive PM in the region. However, these tools have been originally developed based on experiments made for European and North American regions. In this work, an experimental campaign was conducted on April-May 2014 in a construction site in Doha city, Qatar. The ultimate goal is to evaluate the applicability of the existing emission factors for construction sites in dry and arid areas like the Middle East. This publication was made possible by a NPRP award [NPRP 7-649-2-241] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Keywords: particulate matter, emissions, fugitive, construction, air pollution

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Authors: Souhila Bendenia, Chahrazed Bendenia, Hanaa Merad-Dib, Sarra Merabet, Samia Moulebhar, Sid Ahmed Khantar

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Today, environmental pollution is a major concernworldwide, threateninghumanhealth. Various techniques have been used, includingdegradation, filtration, advancedoxidationprocesses, ion exchange, membrane processes, and adsorption. The latter is one of the mostsuitablemethods, usinghighly efficient materials. In this study, NaX zeolite was modified with Cu or Ni at various rates. Following ion exchange, the samples were characterized by XRD, BET and SEM/EDX. After characterization, the exchanged zeolites were used for adsorption of various pollutants as CO2. Different thermodynamic parameters were studied such as Qst. XRD results show that the most intense peaks characteristic of 13X persist after the exchange reaction for all samples. The SEM images of our samples have uniform and regular crystal shapes. The results show that ion exhange with Cu or Ni affect the textural properties of X zeolites and prove that the exchange zeolites can be used as an adsorbent for depollution.

Keywords: X zeolites (NaX), ion exchange, characterization, adsorption

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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