Search results for: Manal Hassan Abdel Aziz

Authors: Abdel-Samad M. Ali

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Given the motivation of maps impact in enhancing the perception of the quality of life in a region, this work examines the use of spatial analytical techniques in exploring the role of space in shaping human development patterns in Assiut governorate. Variations of human development index (HDI) of the governorate-s villages, districts and cities are mapped using geographic information systems (GIS). Global and local spatial autocorrelation measures are employed to assess the levels of spatial dependency in the data and to map clusters of human development. Results show prominent disparities in HDI between regions of Assiut. Strong patterns of spatial association were found proving the presence of clusters on the distribution of HDI. Finally, the study indicates several "hot-spots" in the governorate to be area of more investigations to explore the attributes of such levels of human development. This is very important for accomplishing the development plan of poorest regions currently adopted in Egypt.

Keywords: Human development, Egypt, GIS, Spatial analysis.

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Authors: Hassan Saberi-Nik, Mahin Golchaman

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This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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Authors: M. R. Gad El- Kareem, A. M. K. Abdel Aal, A. Y. Mohamed

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During 2011 and 2012 seasons, Zaghloul date palms received four sprays of silicon (Si) at 0.05 to 0.1% and selenium (Se) at 0.01 to 0.02%. Growth, nutritional status, yield as well as physical and chemical characteristics of the fruits in response to application of silicon and selenium were investigated. Single and combined applications of silicon at 0.05 to 0.1% and selenium at 0.01 to 0.02% was very effective in enhancing the leaf area, total chlorophylls, percentages of N, P and K in the leaves, yield, bunch weight as well as physical and chemical characteristics of the fruits in relative to the check treatment. Silicon was superior to selenium in this respect. Combined application was favorable than using each alone in this connection. Treating Zaghloul date palms four times with a mixture of silicon at 0.05% + selenium at 0.01% resulted in an economical yield and producing better fruit quality.

Keywords: Date Palms, Zaghloul, Silicon, Selenium, leaf area.

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Authors: Najam Aziz, Nasru Minallah, Ahmad Junaid, Kashaf Gul

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Landcover classification using automated classification techniques, while employing remotely sensed multi-spectral imagery, is one of the promising areas of research. Different land conditions at different time are captured through satellite and monitored by applying different classification algorithms in specific environment. In this paper, a SPOT-5 image provided by SUPARCO has been studied and classified in Environment for Visual Interpretation (ENVI), a tool widely used in remote sensing. Then, Artificial Neural Network (ANN) classification technique is used to detect the land cover changes in Abbottabad district. Obtained results are compared with a pixel based Distance classifier. The results show that ANN gives the better overall accuracy of 99.20% and Kappa coefficient value of 0.98 over the Mahalanobis Distance Classifier.

Keywords: Landcover classification, artificial neural network, remote sensing, SPOT-5.

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Authors: Sima Sh. Alian, Abdul Aziz Omar, Ali F. Alta'ee, Irzie Hani

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In this work, the precipitation of asphaltene from a Malaysian light oil reservoir was studies. A series of experiments were designed and carried out to examine the effect of CO2 injection on asphaltene precipitation. Different pressures of injections were used in Dynamic flooding experiment in order to investigate the effect of pressure versus injection pore volume of CO2. These dynamic displacement tests simulate reservoir condition. Results show that by increasing the pore volume of injected gas asphaltene precipitation will increases, also rise in injection pressure causes less precipitation. Sandstone core plug was used to represent reservoir formation during displacement test; therefore it made it possible to study the effect of present of asphaltene on formation. It is found out that the precipitated asphaltene can reduce permeability and porosity which is not favorable during oil production.

Keywords: Asphaltene, asphaltene precipitation, enhanced oil recovery.

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Authors: Abdel Majid Kassir, Joël Sonnard, Ludovic Roulin, Martine Baudin, Gilles Courret, Wolfram Manuel Brück

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Motivated by the current COVID-19 pandemic and the need to find alternative methods to contain and battle it, the purpose of this innovative project is to conceive a disinfection module equipped with a cold atmospheric plasma source. Such a plasma source was developed for a potential integration into pulsed air hand dryers. This type of plasma is known for its ability to generate reactive oxygen and nitrogen species that initiate bio-molecular reactions involved in bacterial and viral deactivation mechanisms. This study shows how additive manufacturing helped accelerate the prototyping of a nozzle allowing the preservation of the plasma flow from circulation cells and external interferences in the discharge’s surrounding.

Keywords: Cold atmospheric plasma, hand disinfection, hand sanitization, bacterial and viral deactivation, plasma chemistry.

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Authors: Tallal Abdel Karim Bouzir, Nourdinne Zemmouri, Djihed Berkouk

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In this research, a quantitative assessment of the urban sound environment of the city of Biskra, Algeria, was conducted. To determine the quality of the soundscape based on in-situ measurement, using a Landtek SL5868P sound level meter in 47 points, which have been identified to represent the whole city. The result shows that the urban noise level varies from 55.3 dB to 75.8 dB during the weekdays and from 51.7 dB to 74.3 dB during the weekend. On the other hand, we can also note that 70.20% of the results of the weekday measurements and 55.30% of the results of the weekend measurements have levels of sound intensity that exceed the levels allowed by Algerian law and the recommendations of the World Health Organization. These very high urban noise levels affect the quality of life, the acoustic comfort and may even pose multiple risks to people's health.

Keywords: Noise pollution, road traffic, sound intensity, public health, noise monitoring.

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Authors: M. M. Shahidul Hassan, Omiya Hassan

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Bangladesh has set its goal to reach upper middle-income country status by 2024. To attain this status, the country must satisfy the World Bank requirement of achieving minimum Gross National Income (GNI). Number of youth job seekers in the country is increasing. University graduates are looking for decent jobs. So, the vital issue of this country is to understand how the GNI and jobs can be increased. The objective of this paper is to address these issues and find ways to create more job opportunities for youths at home and abroad which will increase the country’s GNI. The paper studies proportion of different goods Bangladesh exported, and also the percentage of employment in different sectors. The data used here for the purpose of analysis have been collected from the available literature. These data are then plotted and analyzed. Through these studies, it is concluded that growth in sectors like agricultural, ready-made garments (RMG), jute industries and fisheries are declining and the business community is not interested in setting up capital-intensive industries. Under this situation, the country needs to explore other business opportunities for a higher economic growth rate. Knowledge can substitute the physical resource. Since the country consists of the large youth population, higher education will play a key role in economic development. It now needs graduates with higher-order skills with innovative quality. Such dispositions demand changes in a university’s curriculum, teaching and assessment method which will function young generations as active learners and creators. By bringing these changes in higher education, a knowledge-based society can be created. The application of such knowledge and creativity will then become the commodity of Bangladesh which will help to reach its goal as an upper middle-income country.

Keywords: Bangladesh, economic sectors, economic growth, higher education, knowledge-based economy, massifcation of higher education, teaching and learning, universities’ role in society.

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

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Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: Azza. A. Al-Ghamdi, Abir. A. Abdel-Naby

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The construction of Nitro -N-amino phenyl maleimide branches onto Cellulose acetate (CA) substrate by free radical graft copolymerization using benzoyl peroxide as initiator led to formation of highly thermal stable copolymers as shown from the results of gravimetric analysis (TGA). CA-g-2,4-dinitro amino phenyl maleimide exhibited higher thermal stability than the CA-g-4-nitro amino phenyl maleimide as shown from the initial decomposition temperature (T_o). This is due to the ability of nitro group to form hydrogen bonding with hydroxyl group of the glucopyranose ring which increases the crystallinity of polymeric matrix. The crystalline shapes representing the graft part are clearly distinct in the Emission scanning electron microscope (ESEM) morphology of the copolymer. A suggested reaction mechanism for the grafting process was also discussed.

Keywords: Cellulose acetate, crystallinity, graft copolymerization, thermal properties.

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Authors: Mohamed Abdel Fattah, Fuji Ren

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This work proposes an approach to address automatic text summarization. This approach is a trainable summarizer, which takes into account several features, including sentence position, positive keyword, negative keyword, sentence centrality, sentence resemblance to the title, sentence inclusion of name entity, sentence inclusion of numerical data, sentence relative length, Bushy path of the sentence and aggregated similarity for each sentence to generate summaries. First we investigate the effect of each sentence feature on the summarization task. Then we use all features score function to train genetic algorithm (GA) and mathematical regression (MR) models to obtain a suitable combination of feature weights. The proposed approach performance is measured at several compression rates on a data corpus composed of 100 English religious articles. The results of the proposed approach are promising.

Keywords: Automatic Summarization, Genetic Algorithm, Mathematical Regression, Text Features.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

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A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: Meryem Lamrani, Younès El Amrani, Aziz Ettouhami

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The ability of UML to handle the modeling process of complex industrial software applications has increased its popularity to the extent of becoming the de-facto language in serving the design purpose. Although, its rich graphical notation naturally oriented towards the object-oriented concept, facilitates the understandability, it hardly successes to report all domainspecific aspects in a satisfactory way. OCL, as the standard language for expressing additional constraints on UML models, has great potential to help improve expressiveness. Unfortunately, it suffers from a weak formalism due to its poor semantic resulting in many obstacles towards the build of tools support and thus its application in the industry field. For this reason, many researches were established to formalize OCL expressions using a more rigorous approach. Our contribution join this work in a complementary way since it focuses specifically on OCL predefined properties which constitute an important part in the construction of OCL expressions. Using formal methods, we mainly succeed in expressing rigorously OCL predefined functions.

Keywords: Formal methods, Z, OCL, predefined properties, metamodel types.

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Authors: André Smith, Amr Abdel-Dayem

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The stereo matching problem, while having been present for several decades, continues to be an active area of research. The goal of this research is to find correspondences between elements found in a set of stereoscopic images. With these pairings, it is possible to infer the distance of objects within a scene, relative to the observer. Advancements in this field have led to experimentations with various techniques, from graph-cut energy minimization to artificial neural networks. At the basis of these techniques is a cost function, which is used to evaluate the likelihood of a particular match between points in each image. While at its core, the cost is based on comparing the image pixel data; there is a general lack of consistency as to what image data representation to use. This paper presents an experimental analysis to compare the effectiveness of more common image data representations. The goal is to determine the effectiveness of these data representations to reduce the cost for the correct correspondence relative to other possible matches.

Keywords: Colour data, local stereo matching, stereo correspondence, disparity map.

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Authors: Nabil M. Abdel-Jabbar, Essam A.H. Al Zubaidy, Mehrab Mehrvar

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Waste lubricating oil re-refining adsorption process by different adsorbent materials was investigated. Adsorbent materials such as oil adsorbent, egg shale powder, date palm kernel powder, and acid activated date palm kernel powder were used. The adsorption process over fixed amount of adsorbent at ambient conditions was investigated. The adsorption/extraction process was able to deposit the asphaltenic and metallic contaminants from the waste oil to lower values. It was found that the date palm kernel powder with contact time of 4 h was able to give the best conditions for treating the waste oil. The recovered solvent could be also reused. It was also found that the activated bentonite gave the best physical properties followed by the date palm kernel powder.

Keywords: activated bentonite, egg shale powder, datepalm kernel powder, used oil treatment, used oilcharacteristics.

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Authors: Nazleeni S. Haron, Mohd K. Zaime , Izzatdin A. Aziz, Mohd H. Hasan

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Text-based game is supposed to be a low resource consumption application that delivers good performances when compared to graphical-intensive type of games. But, nowadays, some of the online text-based games are not offering performances that are acceptable to the users. Therefore, an online text-based game called Star_Quest has been developed in order to analyze its behavior under different performance measurements. Performance metrics such as throughput, scalability, response time and page loading time are captured to yield the performance of the game. The techniques in performing the load testing are also disclosed to exhibit the viability of our work. The comparative assessment between the results obtained and the accepted level of performances are conducted as to determine the performance level of the game. The study reveals that the developed game managed to meet all the performance objectives set forth.

Keywords: Online text-based games, performance evaluation

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Authors: Benjamin Anderson-Sackaney, Amr Abdel-Dayem

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This paper presents a comprehensive survey of recent source camera identification (SCI) systems. Then, the performance of various sensor pattern noise (SPN) estimators was experimentally assessed, under common photo response non-uniformity (PRNU) frameworks. The experiments used 1350 natural and 900 flat-field images, captured by 18 individual cameras. 12 different experiments, grouped into three sets, were conducted. The results were analyzed using the receiver operator characteristic (ROC) curves. The experimental results demonstrated that combining the basic SPN estimator with a wavelet-based filtering scheme provides promising results. However, the phase SPN estimator fits better with both patch-based (BM3D) and anisotropic diffusion (AD) filtering schemes.

Keywords: Sensor pattern noise, source camera identification, photo response non-uniformity, anisotropic diffusion, peak to correlation energy ratio.

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Authors: Amir Shafeeq, Ayyaz Muhammad, Noman Hassan, Rofice Dickson

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Different vegetable oil based biodiesel (FAMES) were prepared by alkaline transesterification using refined oils as well as waste frying oil (WFO). Methanol and sodium hydroxide are used as catalyst under similar reaction conditions. To ensure the quality of biodiesel produced, a series of different ASTM Standard tests were carried out. In this context, various testwere done including viscosity, carbon residue, specific gravity, corrosion test, flash point, cloud point and pour point. Results revealed that characteristics of biodiesel depend on the feedstock and it is far better than petroleum diesel.

Keywords: Biodiesel, Edible oils, Separation.

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Authors: Nurul Liyana Abdul Aziz, Nur Aidya Hanum Aizam

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Course timetabling problems occur every semester in a university which includes the allocation of resources (subjects, lecturers and students) to a number of fixed rooms and timeslots. The assignment is carried out in a way such that there are no conflicts within rooms, students and lecturers, as well as fulfilling a range of constraints. The constraints consist of rules and policies set up by the universities as well as lecturers’ and students’ preferences of courses to be allocated in specific timeslots. This paper specifically focuses on the preferences of the course timetabling problem in one of the public universities in Malaysia. The demands will be considered into our existing mathematical model to make it more generalized and can be used widely. We have distributed questionnaires to a number of lecturers and students of the university to investigate their demands and preferences for their desired course timetable. We classify the preferences thus converting them to construct one mathematical model that can produce such timetable.

Keywords: University course timetabling problem, integer programming, preferences, constraints.

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Authors: Labiba I. Hussein, Maher Z. Elsabee, Eid A. Ismail, Hala F. Naguib, Hilda A. Aziz, Moataz A. Elsawy

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Jojoba oil-wax is extracted from the seeds of the jojoba (Simmondsia chinensis Link Schneider), a perennial shrub that grows in semi desert areas in Egypt and in some parts of the world. The main uses of jojoba oil-wax are in the cosmetics and pharmaceutical industry, but new uses could arise related to the search of new energetic crops. This paper summarizes a process to convert the jojoba oil-wax to biodiesel by transesterification with ethanol and a series of aliphatic alcohols using a more economic and energy saving method in a domestic microwave. The effect of time and power of the microwave on the extent of the transesterification using ethanol and other aliphatic alcohols has been studied. The separation of the alkyl esters from the fatty alcohols rich fraction has been done in a single crystallization step at low temperature (−18°C) from low boiling point petroleum ether. Gas chromatography has been used to follow up the transesterification process. All products have been characterized by spectral analysis.

Keywords: Jojoba oil, transesterification, microwave, gas chromatography jojoba esters, Jojoba alcohol.

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Authors: Iman I. Salama, Samia M. Sami, Somaia I. Salama, Zeinab N. Said, Thanaa M. Rabah, Aida M. Abdel-Mohsin

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This is a national community based project to evaluate effectiveness of HBV vaccination program in prevention of infection. HBV markers were tested in the sera of 3600 vaccinated children. Infected children were followed up for 1 year. Prevalence of HBV infection was 0.39 % (0.28% positive for anti-HBc, 0.03% positive for HBsAg and 0.08% positive for both). One year later, 50% of positive anti-HBc children turned negative with sustained positivity for positive HBsAg cases. HBV infection was significantly higher at age above 9 years (0.6%) compared to 0.2% at age 3-9 years and 0% at younger age (P<0.05). Logistic analysis revealed that predictors for HBV infection were history of blood transfusion, regular medical injection, and family history of either HBV infection or drug abuse (adjusted odds ratios 6.2, 5.6, 7.6 & 19.1 respectively). HBV vaccination program produced adequate protection. Adherence to infection control measures and safe blood transfusion are recommended.

Keywords: Children, Egypt, HBV Infection, HBV Vaccine.

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Authors: Z.F. Fadzil, H.S. Hashim, A.I. Che-Ani, S. Aziz

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Campus sustainability is the goal of a university striving for sustainable development. This study found that of 17 popular approaches, two comprehensive campus sustainability assessment frameworks were developed in the context of Sustainability in Higher Education (SHE), and used by many university campuses around the world. Sustainability Tracking Assessment and Rating Systems (STARS) and the Campus Sustainability Assessment Framework (CSAF) approaches are more comprehensive than others. Therefore, the researchers examined aspects and elements used by CSAF and STARS in the approach to develop a campus sustainability assessment framework for Universiti Kebangsaan Malaysia (UKM). Documents analysis found that CSAF and STARS do not focus on physical development, especially the construction industry, as key elements of campus sustainability assessment. This finding is in accordance with the Sustainable UKM Programme which consists of three main components of sustainable community, ecosystem and physical development.

Keywords: Campus sustainability, campus sustainability assessment, sustainability assessment framework, sustainable campus

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Authors: Hassan Haghighi, Seyedeh Zahra Hosseini, Seyedeh Elahe Jalambadani

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ERP systems are often supposed to be implemented and deployed in multi-national companies. On the other hand, an ERP developer may plan to market and sale its product in various countries. Therefore, an EPR system should have the ability to communicate with its users, who usually have different languages and cultures, in a suitable way. EPR support of Multilanguage capability is a solution to achieve this objective. In this paper, an agent oriented architecture including several independent but cooperative agents has been suggested that helps to implement Multilanguage EPR systems.

Keywords: enterprise resource planning, Multilanguage, software architecture, agent oriented architecture, intelligence, learning, translation.

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Authors: M.Y. Pua, M.C. Tan, L.W. Tan, N. Ab.Aziz, F.S. Taip

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The most common type of controller being used in the industry is PI(D) controller which has been used since 1945 and is still being widely used due to its efficiency and simplicity. In most cases, the PI(D) controller was tuned without taking into consideration of the effect of actuator saturation. In real processes, the most common actuator which is valve will act as constraint and restrict the controller output. Since the controller is not designed to encounter saturation, the process may windup and consequently resulted in large oscillation or may become unstable. Usually, an antiwindup compensator is added to the feedback control loop to reduce the deterioration effect of integral windup. This research aims to specifically control processes with constraints. The proposed method was applied to two different types of food processes, which are blending and spray drying. Simulations were done using MATLAB and the performances of the proposed method were compared with other conventional methods. The proposed technique was able to control the processes and avoid saturation such that no anti windup compensator is needed.

Keywords: constraints, food process control, first order plusdead time process, PI

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Authors: Ahmed Abou Elfarag, A. Baith M., Hassan H. Alkhishali

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With the turn of this century, many researchers started showing interest in Embedded Firewall (EF) implementations. These are not the usual firewalls that are used as checkpoints at network gateways. They are, rather, applied near those hosts that need protection. Hence by using them, individual or grouped network components can be protected from the inside as well as from external attacks. This paper presents a study of EF-s, looking at their architecture and problems. A comparative study assesses how practical each kind is. It particularly focuses on the architecture, weak points, and portability of each kind. A look at their use by different categories of users is also presented.

Keywords: Embedded Firewall (EF), Network Interface Card (NIC), Virtual Machine Software (VMware), Virtual Firewall (VF).

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Authors: A. K. Abdel-Fattah, A. B. El-Tawil, N. A. Harraz

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This paper focuses on the operational and strategic planning decisions related to the quayside of container terminals. We introduce an integrated operational research (OR) and system dynamics (SD) approach to solve the Berth Allocation Problem (BAP) and the Quay Crane Assignment Problem (QCAP). A BAP-QCAP optimization modeling approach which considers practical aspects not studied before in the integration of BAP and QCAP is discussed. A conceptual SD model is developed to determine the long-term effect of optimization on the system behavior factors like resource utilization, attractiveness to port, number of incoming vessels to port and port profits. The framework can be used for improving the operational efficiency of container terminals and providing a strategic view after applying optimization.

Keywords: Operational research, system dynamics, container terminal, quayside operational problems, strategic planning decisions.

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Authors: Mutabar Shah, Muhammad Hassan Sayyad, Khasan S. Karimov

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Thin films of Nickel phthalocynine (NiPc) of different thicknesses (100, 150 and 200 nm) were deposited by thermal evaporator on glass substrates with preliminary deposited aluminum electrodes to form Al/NiPc/Al surface-type capacitive humidity sensors. The capacitance-humidity relationships of the sensors were investigated at humidity levels from 35 to 90% RH. It was observed that the capacitance value increases nonlinearly with increasing humidity level. All measurements were taken at room temperature.

Keywords: Capacitive sensor, Humidity, Nickel phthalocyanine, Organic semiconductor.

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Authors: Omer K. Jasim, Safia Abbas, El-Sayed M. El-Horbaty, Abdel-Badeeh M. Salem

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Cloud computing technology is very useful in present day to day life, it uses the internet and the central remote servers to provide and maintain data as well as applications. Such applications in turn can be used by the end users via the cloud communications without any installation. Moreover, the end users’ data files can be accessed and manipulated from any other computer using the internet services. Despite the flexibility of data and application accessing and usage that cloud computing environments provide, there are many questions still coming up on how to gain a trusted environment that protect data and applications in clouds from hackers and intruders. This paper surveys the “keys generation and management” mechanism and encryption/decryption algorithms used in cloud computing environments, we proposed new security architecture for cloud computing environment that considers the various security gaps as much as possible. A new cryptographic environment that implements quantum mechanics in order to gain more trusted with less computation cloud communications is given.

Keywords: Cloud Computing, Cloud Encryption Model, Quantum Key Distribution.

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Authors: Pradip Peter Dey, Bhaskar Raj Sinha, Mohammad Amin, Hassan Badkoobehi

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Mathematical, graphical and intuitive models are often constructed in the development process of computational systems. The Unified Modeling Language (UML) is one of the most popular modeling languages used by practicing software engineers. This paper critically examines UML models and suggests an augmented use case view with the addition of new constructs for modeling software. It also shows how a use case diagram can be enhanced. The improved modeling constructs are presented with examples for clarifying important design and implementation issues.

Keywords: Software architecture, software design, Unified Modeling Language (UML), user interface.

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Authors: Aziz Sezgin

Abstract:

We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: Backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems.

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