Search results for: Mahmoud A. M. Abou Donia

Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

Abstract:

The present work illustrates a parametric study for the effect of stiffeners on the performance of slender built up steel I-columns. To achieve the desired analysis, finite element technique is used to develop nonlinear three-dimensional models representing the investigated columns. The finite element program (ANSYS 13.0) is used as a calculation tool for the necessary nonlinear analysis. A validation of the obtained numerical results is achieved. The considered parameters in the study are the column slenderness ratio and the horizontal stiffener's dimensions as well as the number of stiffeners. The dimensions of the stiffeners considered in the analysis are the stiffener width and the stiffener thickness. Numerical results signify a considerable effect of stiffeners on the performance and failure load of slender built up steel I-columns.

Keywords: Steel I-columns, local buckling, slender, stiffener, thin walled section.

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Authors: I. Goual, M. S. Goual, M. K. Gueddouda, Taïbi Saïd, Abou-Bekr Nabil, A. Ferhat

Abstract:

The aim of the paper is to study the hydro-mechanical behavior of a tuff and calcareous sand mixture. A first experimental phase was carried out in order to find the optimal mixture. This showed that the material composed of 80% tuff and 20% calcareous sand provides the maximum mechanical strength. The second experimental phase concerns the study of the drying-wetting behavior of the optimal mixture was carried out on slurry samples and compacted samples at the MPO. Experimental results let to deduce the parameters necessary for the prediction of the hydro-mechanical behavior of pavement formulated from tuff and calcareous sand mixtures, related to moisture. This optimal mixture satisfies the regulation rules and hence constitutes a good local eco-material, abundantly available, for the conception of pavements.

Keywords: Tuff, sandy calcareous, road engineering, hydro mechanical behaviour, suction.

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Authors: Elnasharty M. A., Abou-Ghanema I. I., Sayed-Ahmed A., A. Abo Elnour

Abstract:

The sequential morphologic changes of rabbit duodenal mucosa-submucosa were studied from primodial stage to birth in 15 fetuses and during the early days of life in 21 rabbit newborns till maturity using light, scanning and transmission electron microscopy. Fetal rabbit duodenum develops from a simple tube of stratified epithelium to a tube containing villus and intervillus regions of simple columnar epithelium. By day 21 of gestation, the first rudimentary villi were appeared and by day 24 the first true villi were appeared. The Crypts of Lieberkuhn did not appear until birth. By the first day of postnatal life the duodenal glands appeared. The histological maturity of the rabbit small intestine occurred one month after birth. In conclusion, at all stages, the sequential morphologic changes of the rabbit small intestine developed to meet the structural and physiological demands during the fetal stage to be prepared to extra uterine life.

Keywords: Duodenum, mucosa, submucosa, morphogenesis, rabbit.

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Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah

Abstract:

Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.

Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.

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Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

Abstract:

This paper presents the effect of stiffeners on the behavior of slender steel I-beams. Nonlinear three dimensional finite element models are developed to represent the stiffened steel I-beams. The well established finite element (ANSYS 13.0) program is used to simulate the geometric and material nonlinear nature of the problem. Verification is achieved by comparing the obtained numerical results with the results of previous published experimental work. The parameters considered in the analysis are the horizontal stiffener's position and the horizontal stiffener's dimensions as well as the number of vertical stiffeners. The studied dimensions of the horizontal stiffeners include the stiffener width, the stiffener thickness and the stiffener length. The results of the achieved numerical parametric study for slender steel I-beams show the significant effect of stiffeners on the beam behavior and its failure load.

Keywords: Steel I-beams, local buckling, slender, stiffener, thin walled section.

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Authors: A. Abou El-Azm Aly, A. Chong, F. Nicolleau, S. Beck

Abstract:

The fractal-shaped orifices are assumed to have a significant effect on the pressure drop downstream pipe flow due to their edge self-similarity shape which enhances the mixing properties. Here, we investigate the pressure drop after these fractals using a digital micro-manometer at different stations downstream a turbulent flow pipe then a direct comparison has been made with the pressure drop measured from regular orifices with the same flow area. Our results showed that the fractal-shaped orifices have a significant effect on the pressure drop downstream the flow. Also the pressure drop measured across the fractal-shaped orifices is noticed to be lower that that from ordinary orifices of the same flow areas. This result could be important in designing piping systems from point of view of losses consideration with the same flow control area. This is promising to use the fractal-shaped orifices as flowmeters as they can sense the pressure drop across them accurately with minimum losses than the regular ones.

Keywords: Fractal-shaped orifice, pressure drop, turbulent flow.

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Authors: Rania A. Abul Seoud, Nahed H. Solouma, Abou-Baker M. Youssef, Yasser M. Kadah

Abstract:

Due to the ever growing amount of publications about protein-protein interactions, information extraction from text is increasingly recognized as one of crucial technologies in bioinformatics. This paper presents a Protein Interaction Extraction System using a Link Grammar Parser from biomedical abstracts (PIELG). PIELG uses linkage given by the Link Grammar Parser to start a case based analysis of contents of various syntactic roles as well as their linguistically significant and meaningful combinations. The system uses phrasal-prepositional verbs patterns to overcome preposition combinations problems. The recall and precision are 74.4% and 62.65%, respectively. Experimental evaluations with two other state-of-the-art extraction systems indicate that PIELG system achieves better performance. For further evaluation, the system is augmented with a graphical package (Cytoscape) for extracting protein interaction information from sequence databases. The result shows that the performance is remarkably promising.

Keywords: Link Grammar Parser, Interaction extraction, protein-protein interaction, Natural language processing.

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Authors: Nour Charara, Iman Jarkass, Maria Sokhn, Elena Mugellini, Omar Abou Khaled

Abstract:

Intelligent Video-Surveillance (IVS) systems are being more and more popular in security applications. The analysis and recognition of abnormal behaviours in a video sequence has gradually drawn the attention in the field of IVS, since it allows filtering out a large number of useless information, which guarantees the high efficiency in the security protection, and save a lot of human and material resources. We present in this paper ADABeV, an intelligent video-surveillance framework for event recognition in crowded scene to detect the abnormal human behaviour. This framework is attended to be able to achieve real-time alarming, reducing the lags in traditional monitoring systems. This architecture proposal addresses four main challenges: behaviour understanding in crowded scenes, hard lighting conditions, multiple input kinds of sensors and contextual-based adaptability to recognize the active context of the scene.

Keywords: Behavior recognition, Crowded scene, Data fusion, Pattern recognition, Video-surveillance

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Authors: Nour Aljafari, Mariam, S. Maani, Serter Atabay, Tarig Ali, Said Daker, Lara Daher, Hamad Bukhammas, Mohammed Abou Shakra

Abstract:

This paper aims at determining the soil characteristics that influence the irrigation process of green landscapes and deciding on the optimum amount of water needed for irrigation. The laboratory experiments were conducted using the constant head methodology to determine the soil infiltration rates. The steady state infiltration rate was reached after 10 minutes of infiltration at a rate of 200 mm/hr. The effects of different water heads on infiltration rates were also investigated, and the head of 11 cm was found to be the optimum head for the test. The experimental results showed consistent infiltration results for the range between 11 cm and 15 cm. The study also involved finding the initial moisture content, which ranged between 5% and 25%, and finding the organic content, which occupied 1% to 2% of the soil. These results will be later utilized, using the water balance approach, to estimate the optimum amount of water needed for irrigation for changing weather conditions.

Keywords: Infiltration rate, moisture content, grass type, organic content.

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Authors: A. Abou El-Azm Aly, F. Nicolleau, T. M. Michelitsch, A. F. Nowakowski

Abstract:

In this study, the dispersion of heavy particles line in an isotropic and incompressible three-dimensional turbulent flow has been studied using the Kinematic Simulation techniques to find out the evolution of the line fractal dimension. The fractal dimension of the line is found in the case of different particle gravity (in practice, different values of particle drift velocity) in the presence of small particle inertia with a comparison with that obtained in the diffusion case of material line at the same Reynolds number. It can be concluded for the dispersion of heavy particles line in turbulent flow that the particle gravity affect the fractal dimension of the line for different particle gravity velocities in the range 0.2 < W < 2. With the increase of the particle drift velocity, the fractal dimension of the line decreases which may be explained as the particles pass many scales in their journey in the direction of the gravity and the particles trajectories do not affect by these scales at high particle drift velocities.

Keywords: Heavy particles, two-phase flow, Kinematic Simulation, Fractal dimension.

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Authors: Nariman O. Kandil, Ehab K. Abou-Elkheir, Amr M. Kotb

Abstract:

Effective IT governance guarantees the strategic alignment of IT and business goals, risk mitigation control, and better IT and business performance. This study seeks to examine empirically the extent of IT governance implementation within the firms listed on the Egyptian Stock Exchange (EGX30) and its determinants. Accordingly, 18 semi-structured interviews, face to face, phone, and video-conferencing, using various tools (e.g., WebEx, Zoom, and Microsoft Teams) were undertaken at the interviewees’ offices in Egypt between the end of November 2019 and the end of August 2020. Results suggest that there are variances in the extent of IT Governance (ITG) implementation within the firms listed on the EGX30, mainly caused by the industry type and internal and external triggers. The results also suggest that the organization size, the type of auditor, the criticality of the industry, the effective processes & key performance indicators (KPIs), and the information intensity expertise of the chief information officers (CIOs) have a significant impact on ITG implementation within the firms.

Keywords: Effective IT governance, Egyptian Market, information security, risk controls.

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Authors: M. A. Elghorab, A. Abou El-Azm Aly, A. S. Elwetedy, M. A. Kotb

Abstract:

Later marine propeller is the main component of ship propulsion system. For a non-series propeller, it is difficult to indicate the open water marine propeller performance without an experimental study to measure the marine propeller parameters. In the present study, the open water performance of a non-series marine propeller has been carried out experimentally. The geometrical aspects of a commercial non-series marine propeller have been measured for a propeller blade area ratio of 0.3985. The measured propeller performance parameters were the thrust and torque coefficients for different propeller rotational speed and different water channel flow velocity, then the open water performance for the propeller has been plotted. In addition, a direct comparison between the obtained experimental results and a theoretical study of a B-series marine propeller of the same blade area ratio has been carried out. A correction factor has been introduced to apply the operating conditions of the experimental results to that of the theoretical study for the studied marine propeller.

Keywords: Advance speed, marine propeller, open water performance, thrust coefficient, torque coefficient.

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Authors: Adnan Al-Smadi, Mahmoud Smadi

Abstract:

This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.

Keywords: Cepstrum, bicepstrum, third order statistics

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Authors: A. Abou El-Azm Aly, F. Nicolleau, T. M. Michelitsch, A. F. Nowakowski

Abstract:

The dispersion of heavy particles line in an isotropic and incompressible three-dimensional turbulent flow has been studied using the Kinematic Simulation techniques to find out the evolution of the line fractal dimension. In this study, the fractal dimension of the line is found for different cases of heavy particles inertia (different Stokes numbers) in the absence of the particle gravity with a comparison with the fractal dimension obtained in the diffusion case of material line at the same Reynolds number. It can be concluded for the dispersion of heavy particles line in turbulent flow that the particle inertia affect the fractal dimension of a line released in a turbulent flow for Stokes numbers 0.02 < St < 2. At the beginning for small times, most of the different cases are not affected by the inertia until a certain time, the particle response time τa, with larger time as the particles inertia increases, the fractal dimension of the line increases owing to the particles becoming more sensitive to the small scales which cause the change in the line shape during its journey.

Keywords: Heavy particles, two-phase flow, Kinematic Simulation, Fractal dimension.

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Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

Avalanche velocity (from start to track zone) has been estimated in the present model for an avalanche which is triggered artificially by an explosive devise. The initial development of the model has been from the concept of micro-continuum theories [1], underwater explosions [2] and from fracture mechanics [3] with appropriate changes to the present model. The model has been computed for different slab depth R, slope angle θ, snow density ¤ü, viscosity μ, eddy viscosity η*and couple stress parameter η. The applicability of the present model in the avalanche forecasting has been highlighted.

Keywords: Snow avalanche velocity, avalanche zones, shockwave, couple stress fluids.

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Authors: Thanaa Abdel Moghny, Mohamed Keshawy, Mahmoud Fathy, Abdul-Raheim M. Abdul-Raheim, Khalid I. Kabel, Ahmed F. El-Kafrawy, Mahmoud Ahmed Mousa, Ahmed E. Awadallah

Abstract:

Ecological pollution is of great concern for human health and the environment. Numerous organic and inorganic pollutants usually discharged into the water caused carcinogenic or toxic effect for human and different life form. In this respect, this work aims to treat water contaminated by organic and inorganic waste using sorbent based on polystyrene. Therefore, two different series of adsorbent material were prepared; the first one included the preparation of polymeric sorbent from the reaction of styrene acrylate ester and alkyl acrylate. The second series involved syntheses of composite ion exchange resins of waste polystyrene and   amorphous carbon thin film (WPS/ACTF) by solvent evaporation using micro emulsion polymerization. The produced ACTF/WPS nanocomposite was sulfonated to produce cation exchange resins ACTF/WPSS nanocomposite. The sorbents of the first series were characterized using FTIR, ¹H NMR, and gel permeation chromatography. The thermal properties of the cross-linked sorbents were investigated using thermogravimetric analysis, and the morphology was characterized by scanning electron microscope (SEM). The removal of organic pollutant was determined through absorption tests in a various organic solvent. The chemical and crystalline structure of nanocomposite of second series has been proven by studies of FTIR spectrum, X-rays, thermal analysis, SEM and TEM analysis to study morphology of resins and ACTF that assembled with polystyrene chain. It is found that the composite resins ACTF/WPSS are thermally stable and show higher chemical stability than ion exchange WPSS resins. The composite resin was evaluated for calcium hardness removal. The result is evident that the ACTF/WPSS composite has more prominent inorganic pollutant removal than WPSS resin. So, we recommend the using of nanocomposite resin as new potential applications for water treatment process.

Keywords: Nanocomposite, sorbent materials, waste water, waste polystyrene.

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Authors: Mahmoud E. Mohamed, Ahmed F. Shalash, Hanan A. Kamal

Abstract:

In communication systems, frequency jump is a serious problem caused by the oscillators used. Kalman filters are used to detect that jump, despite the tradeoff between the noise level and the speed of the detection. In this paper, an improvement is introduced in the Kalman filter, through a nonlinear change in the bandwidth of the filter. Simulation results show a considerable improvement in the filter speed with a very low noise level. Additionally, the effect on the response to false alarms is also presented and false alarm rate show improvement.

Keywords: Kalman Filter, Innovation, False Detection.

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Authors: Mahmoud A. Hassan, Mohammed A. Khalili

Abstract:

We are proposing a simple watermarking method based on visual cryptography. The method is based on selection of specific pixels from the original image instead of random selection of pixels as per Hwang [1] paper. Verification information is generated which will be used to verify the ownership of the image without the need to embed the watermark pattern into the original digital data. Experimental results show the proposed method can recover the watermark pattern from the marked data even if some changes are made to the original digital data.

Keywords: Watermarking, visual cryptography, visualthreshold.

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Authors: Mahmoud Zarrini, Sanaz Torkaman

Abstract:

In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

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Authors: Ahmed M. Elhabashy, A. Baes Mohamed, Abou El Nasr Mohamad

Abstract:

Distributed Computing Systems are usually considered the most suitable model for practical solutions of many parallel algorithms. In this paper an enhanced distributed system is presented to improve the time complexity of Binary Indexed Trees (BIT). The proposed system uses multi-uniform processors with identical architectures and a specially designed distributed memory system. The analysis of this system has shown that it has reduced the time complexity of the read query to O(Log(Log(N))), and the update query to constant complexity, while the naive solution has a time complexity of O(Log(N)) for both queries. The system was implemented and simulated using VHDL and Verilog Hardware Description Languages, with xilinx ISE 10.1, as the development environment and ModelSim 6.1c, similarly as the simulation tool. The simulation has shown that the overhead resulting by the wiring and communication between the system fragments could be fairly neglected, which makes it applicable to practically reach the maximum speed up offered by the proposed model.

Keywords: Binary Index Tree (BIT), Least Significant Bit (LSB), Parallel Adder (PA), Very High Speed Integrated Circuits HardwareDescription Language (VHDL), Distributed Parallel Computing System(DPCS).

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Authors: Mahmoud Beshr, Ivan Andonovic, Moustafa H. Aly

Abstract:

Visible Light Communication (VLC) offers advantages of low energy consumption, licence free and RF interference free operation. One application area for VLC is in the provision of health centred services circumventing issues of interference with any biomedical device within the environment. VLC performamce is affected by natural light restricting systems avilability and relibility. The paper presents an analysis of the performance of VLC systems under different meteorological conditions. The evaluation considered the impact of natural light as a function of different reflection surfaces in different room sizes.

Keywords: Visible light communication, impulse reponse , performance analysis , natural light.

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Authors: Abdallah S. Abdallah, A. Lynn Abbott, Mohamad Abou El-Nasr

Abstract:

This paper presents a new technique for detection of human faces within color images. The approach relies on image segmentation based on skin color, features extracted from the two-dimensional discrete cosine transform (DCT), and self-organizing maps (SOM). After candidate skin regions are extracted, feature vectors are constructed using DCT coefficients computed from those regions. A supervised SOM training session is used to cluster feature vectors into groups, and to assign “face" or “non-face" labels to those clusters. Evaluation was performed using a new image database of 286 images, containing 1027 faces. After training, our detection technique achieved a detection rate of 77.94% during subsequent tests, with a false positive rate of 5.14%. To our knowledge, the proposed technique is the first to combine DCT-based feature extraction with a SOM for detecting human faces within color images. It is also one of a few attempts to combine a feature-invariant approach, such as color-based skin segmentation, together with appearance-based face detection. The main advantage of the new technique is its low computational requirements, in terms of both processing speed and memory utilization.

Keywords: Face detection, skin color segmentation, self-organizingmap.

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Authors: Khalid Al-Tahat, Khaled Zuhair Mahmoud, Ahmad Al-Mughrabi

Abstract:

This paper proposes a novel methodology for enabling debugging and tracing of production web applications without affecting its normal flow and functionality. This method of debugging enables developers and maintenance engineers to replace a set of existing resources such as images, server side scripts, cascading style sheets with another set of resources per web session. The new resources will only be active in the debug session and other sessions will not be affected. This methodology will help developers in tracing defects, especially those that appear only in production environments and in exploring the behaviour of the system. A realization of the proposed methodology has been implemented in Java.

Keywords: Live debugging, web application, web resources, inconsistent bugs, tracing.

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Authors: Younies Mahmoud, Mai Mabrouk, Elsayed Sallam

Abstract:

Analyzing DNA microarray data sets is a great challenge, which faces the bioinformaticians due to the complication of using statistical and machine learning techniques. The challenge will be doubled if the microarray data sets contain missing data, which happens regularly because these techniques cannot deal with missing data. One of the most important data analysis process on the microarray data set is feature selection. This process finds the most important genes that affect certain disease. In this paper, we introduce a technique for imputing the missing data in microarray data sets while performing feature selection.

Keywords: DNA microarray, feature selection, missing data, bioinformatics.

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Authors: Amer Al Mahmoud Alsheikh, Jan Žídek, František Krčma

Abstract:

Using ab initio theoretical calculations, we present analysis of fragmentation process. The analysis is performed in two steps. The first step is calculation of fragmentation energies by ab initio calculations. The second step is application of the energies to kinetic description of process. The energies of fragments are presented in this paper. The kinetics of fragmentation process can be described by numerical models. The method for kinetic analysis is described in this paper. The result - composition of fragmentation products - will be calculated in future. The results from model can be compared to the concentrations of fragments from mass spectrum.

Keywords: Ab initio, Density functional theory, Fragmentation energy, Geometry optimization.

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Authors: Mohammad Soliman, Mohamed A. Abou-Shouk

Abstract:

Knowledge management focuses on the development, storage, retrieval, and dissemination of information and expertise. It has become an important tool to improve performance in tourism enterprises. This includes improving decision-making, developing customer services, and increasing sales and profits. Knowledge management adoption depends on human, organizational and technological factors. This study aims to explore the concept of knowledge management in travel agents in Egypt. It explores the requirements of adoption and its impact on performance in these agencies. The study targets Category A travel agents in Egypt. The population of the study encompasses Category A travel agents having online presence. An online questionnaire is used to collect data from managers of travel agents. This study is useful for travel agents who are in urgent need to restructure their intermediary role and support their survival in the global travel market. The study sheds light on the requirements of adoption and the expected impact on performance. This could help travel agents identify their situation and the determine the extent to which they are ready to adopt knowledge management. This study is contributing to knowledge by providing insights from the tourism sector in a developing country where the concept of knowledge management is still in its infancy stages.

Keywords: Benefits, determinants, Egypt, knowledge management, travel agents.

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Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

In this paper, mathematical modeling of detonation in the ground is studied. Estimation of flow parameters such as velocity, maximum velocity, acceleration, maximum acceleration, shock pressure as a result of an explosion in the ground have been computed in an appropriate dynamic model approach. The variation of these parameters with the diameter of detonation place (L), density of earth or stone (¤ü), time decay of detonation (T), peak pressure (Pm), and time (t) have been analyzed. The model has been developed from the concept of underwater explosions [Refs. [1]-[3]] with appropriate changes to the present model requirements.

Keywords: Shock velocity, detonation, shock acceleration, shock pressure.

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Authors: Mahmoud Zarrini, R.N. Pralhad

Abstract:

In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.

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Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

Abstract:

Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: Double extreme ranked set sampling, Extreme ranked set sampling, Ranked set sampling, Stratified double extreme ranked set sampling.

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Authors: Bassem Roushdy, Nahed Sobhy, Abdelrhim Abdelhamid, Ahmed Mahmoud

Abstract:

Most papers model Joint Replenishment Problem (JRP) as a (kT,S) where kT is a multiple value for a common review period T,and S is a predefined order up to level. In general the (T,S) policy is characterized by a long out of control period which requires a large amount of safety stock compared to the (R,Q) policy. In this paper a probabilistic model is built where an item, call it item(i), with the shortest order time between interval (T)is modeled under (R,Q) policy and its inventory is continuously reviewed, while the rest of items (j) are periodically reviewed at a definite time corresponding to item

Keywords: Inventory management, Joint replenishment, policy evaluation, stochastic process

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