Search results for: Y. Khalid

Authors: Khalid Salhi, El Miloud Jaara, Mohammed Talibi Alaoui

Abstract:

In this paper, we present a neural approach for unsupervised natural color-texture image segmentation, which is based on both Kohonen maps and mathematical morphology, using a combination of the texture and the image color information of the image, namely, the fractal features based on fractal dimension are selected to present the information texture, and the color features presented in RGB color space. These features are then used to train the network Kohonen, which will be represented by the underlying probability density function, the segmentation of this map is made by morphological watershed transformation. The performance of our color-texture segmentation approach is compared first, to color-based methods or texture-based methods only, and then to k-means method.

Keywords: Segmentation, color-texture, neural networks, fractal, watershed.

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Authors: Kalsom Abd Wahab, Khalid Hassan Abdesamed

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The purpose of this paper is to examine the financing practices of SMEs in Libya in two different phases of business life cycle: start-up and matured stages. Moreover, SMEs- accessing bank loan issues is also identified. The study was conducted by taking into account the aspect of demand. The findings are based on a sample of 76 SMEs in Libya through the adoption of questionnaires. The results have pinpointed several things- evidently, SMEs use informal financing sources which prefer personal savings; SME owners are willing to apply for bank loan, that the most pressing problem has been identified, not to apply bank loan is loan with interest (religion factor).

Keywords: SMEs, Formal Finance (loan from bank), Informal Finance, Loan with interest (religion factor), Libya.

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Authors: Aleem Khalid Alvi, M. Yousuf Bin Azhar, Mehmood Usman, Suleman Mumtaz, Sameer Rafiq, RaziUr Rehman, Israr Ahmed

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Sign language recognition has been a topic of research since the first data glove was developed. Many researchers have attempted to recognize sign language through various techniques. However none of them have ventured into the area of Pakistan Sign Language (PSL). The Boltay Haath project aims at recognizing PSL gestures using Statistical Template Matching. The primary input device is the DataGlove5 developed by 5DT. Alternative approaches use camera-based recognition which, being sensitive to environmental changes are not always a good choice.This paper explains the use of Statistical Template Matching for gesture recognition in Boltay Haath. The system recognizes one handed alphabet signs from PSL.

Keywords: Gesture Recognition, Pakistan Sign Language, DataGlove, Human Computer Interaction, Template Matching, BoltayHaath

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Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

Periodicities in the environmetric time series can be idyllically assessed by utilizing periodic models. In this communication fugitive emission of gases from open sewer channel Lyari which follows periodic behaviour are approximated by employing periodic autoregressive model of order p. The orders of periodic model for each season are selected through the examination of periodic partial autocorrelation or information criteria. The parameters for the selected order of season are estimated individually for each emitted air toxin. Subsequently, adequacies of fitted models are established by examining the properties of the residual for each season. These models are beneficial for schemer and administrative bodies for the improvement of implemented policies to surmount future environmental problems.

Keywords: Exchange of Gases, Goodness of Fit, Open Sewer Channel, PAR(p) Models, Periodicities, Season Wise Models.

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Authors: M. Khalid Imran, Syed Masood, Milan Brandt, Sudip Bhattacharya, Jyotirmoy Mazumder

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In the present investigation, H13 tool steel has been deposited on copper alloy substrate using both CO2 and diode laser. A detailed parametric analysis has been carried out in order to find out optimum processing zone for coating defect free H13 tool steel on copper alloy substrate. Followed by parametric optimization, the microstructure and microhardness of the deposited clads have been evaluated. SEM micrographs revealed dendritic microstructure in both clads. However, the microhardness of CO2 laser deposited clad was much higher compared to diode laser deposited clad.

Keywords: CO2 laser, Diode laser, Direct Metal Deposition, Microstructure, Microhardness, Porosity.

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Authors: Marzuki Khalid, RubiyahYusof, AnisSalwaMohdKhairuddin

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An automated wood recognition system is designed to classify tropical wood species.The wood features are extracted based on two feature extractors: Basic Grey Level Aura Matrix (BGLAM) technique and statistical properties of pores distribution (SPPD) technique. Due to the nonlinearity of the tropical wood species separation boundaries, a pre classification stage is proposed which consists ofKmeans clusteringand kernel discriminant analysis (KDA). Finally, Linear Discriminant Analysis (LDA) classifier and KNearest Neighbour (KNN) are implemented for comparison purposes. The study involves comparison of the system with and without pre classification using KNN classifier and LDA classifier.The results show that the inclusion of the pre classification stage has improved the accuracy of both the LDA and KNN classifiers by more than 12%.

Keywords: Tropical wood species, nonlinear data, featureextractors, classification

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Authors: Khalid Khan, Atique Ahmad Zafar, Mohammed A. Alnuem, Hashim Khan

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Global Software Development (GSD) projects are passing through different boundaries of a company, country and even in other continents where time zone differs between both sites. Beside many benefits of such development, research declared plenty of negative impacts on these GSD projects. It is important to understand problems which may lie during the execution of GSD project with different time zones. This research project discussed and provided different issues related to time delays in GSD projects. In this paper, authors investigated some of the time delay factors which usually lie in GSD projects with different time zones. This investigation is done through systematic review of literature. Furthermore, the practices to overcome these delay factors which have already been reported in literature and GSD organizations are also explored through literature survey and case studies.

Keywords: Case Studies, Global Software Development, Global Software Engineering, Temporal Difference, Time Delay

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

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The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: Khalid A. Kaabneh

Abstract:

This paper introduces and studies new indexing techniques for content-based queries in images databases. Indexing is the key to providing sophisticated, accurate and fast searches for queries in image data. This research describes a new indexing approach, which depends on linear modeling of signals, using bases for modeling. A basis is a set of chosen images, and modeling an image is a least-squares approximation of the image as a linear combination of the basis images. The coefficients of the basis images are taken together to serve as index for that image. The paper describes the implementation of the indexing scheme, and presents the findings of our extensive evaluation that was conducted to optimize (1) the choice of the basis matrix (B), and (2) the size of the index A (N). Furthermore, we compare the performance of our indexing scheme with other schemes. Our results show that our scheme has significantly higher performance.

Keywords: Axial Projection, images, indexing, multimedia database, searching.

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Authors: Khalid M. Aamir, Mohammad A. Maud

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Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.

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Authors: Hamad K. Al-Khalid, Ayman M. Alaskari, Samy E. Oraby

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Hardness of the widely used structural steel is of vital importance since it may help in the determination of many mechanical properties of a material under loading situations. In order to obtain reliable information for design, properties homogeneity should be validated. In the current study the hardness variation over the different diameters of the same AISI 4140 bar is investigated. Measurements were taken on the two faces of the stock at equally spaced eight sectors and fifteen layers. Statistical and graphical analysis are performed to asses the distribution of hardness measurements over the specified area. Hardness measurements showed some degree of dispersion with about ± 10% of its nominal value provided by manufacturer. Hardness value is found to have a slight decrease trend as the diameter is reduced. However, an opposite behavior is noticed regarding the sequence of the sector indicating a nonuniform distribution over the same area either on the same face or considering the corresponding sector on the other face (cross section) of the same material bar.

Keywords: Hardness; Hardness variation; AISI 4140 steel; Bardiameter; Statistical Analysis.

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Authors: Khoshnaw Khalid Hama Saleh, Ergun Ercelebi

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Increasingly complex modern power systems require stability, especially for transient and small disturbances. Transient stability plays a major role in stability during fault and large disturbance. This paper compares a power system stabilizer (PSS) and static Var compensator (SVC) to improve damping oscillation and enhance transient stability. The effectiveness of a PSS connected to the exciter and/or governor in damping electromechanical oscillations of isolated synchronous generator was tested. The SVC device is a member of the shunt FACTS (flexible alternating current transmission system) family, utilized in power transmission systems. The designed model was tested with a multi-machine system consisting of four machines six bus, using MATLAB/SIMULINK software. The results obtained indicate that SVC solutions are better than PSS.

Keywords: FACTS, MATLAB/SIMULINK, multi-machine system, PSS, SVC, transient stability.

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Authors: Zahra Khalid, Gul Muhammad Khan, Arbab Masood Ahmad

Abstract:

Cartesian Genetic Programming (CGP) is explored to design an optimal circuit capable of early stage breast cancer detection. CGP is used to evolve simple multiplexer circuits for detection of malignancy in the Fine Needle Aspiration (FNA) samples of breast. The data set used is extracted from Wisconsins Breast Cancer Database (WBCD). A range of experiments were performed, each with different set of network parameters. The best evolved network detected malignancy with an accuracy of 99.14%, which is higher than that produced with most of the contemporary non-linear techniques that are computational expensive than the proposed system. The evolved network comprises of simple multiplexers and can be implemented easily in hardware without any further complications or inaccuracy, being the digital circuit.

Keywords: Breast cancer detection, cartesian genetic programming, evolvable hardware, fine needle aspiration (FNA).

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Authors: Rachid Ed-Dali, Khalid Elasri

Abstract:

Mass media seem to provide a rich content for language acquisition. Exposure to television, the Internet, the mobile phone and other technological gadgets and devices helps enrich the student’s lexicon positively as well as negatively. The difficulties encountered by students while learning and acquiring second languages in addition to their eagerness to comprehend the content of a particular program prompt them to diversify their methods so as to achieve their targets. The present study highlights the significance of certain media channels and their involvement in language acquisition with the employment of the Natural Approach to further grasp whether students, especially secondary and high school students, learn and acquire errors through watching subtitled television programs. The chief objective is investigating the deductive and inductive relevance of certain programs beside the involvement of peripheral learning while acquiring mistakes.

Keywords: Errors, mistakes, natural Approach, peripheral learning, solecism.

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Authors: Khalid Alnafjan, Tazar Hussain, Hanif Ullah, Zia ul haq Paracha

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Software and applications are subjected to serious and damaging security threats, these threats are increasing as a result of increased number of potential vulnerabilities. Security testing is an indispensable process to validate software security requirements and to identify security related vulnerabilities. In this paper we analyze and compare different available vulnerabilities testing techniques based on a pre defined criteria using analytical hierarchy process (AHP). We have selected five testing techniques which includes Source code analysis, Fault code injection, Robustness, Stress and Penetration testing techniques. These testing techniques have been evaluated against five criteria which include cost, thoroughness, Ease of use, effectiveness and efficiency. The outcome of the study is helpful for researchers, testers and developers to understand effectiveness of each technique in its respective domain. Also the study helps to compare the inner working of testing techniques against a selected criterion to achieve optimum testing results.

Keywords: Software Security, Security Testing, Testing techniques, vulnerability, AHP.

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Authors: Ishrar Tabassum, Jay Andrew Saptok, Khalid Raihan Kabir, Elmee Tabassum

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The purpose of this study is to bring light to the current state of the working environments in the corporate environment and other such institutions with a particular focus on the Bangladesh National Building Code (BNBC) and its guidelines for accommodating the physically disabled. Data were collected via semi-formal interviews, site visits and focus groups conducted using a preset questionnaire as the guidelines. After conducting surveys at corporate offices of 20 organizations from major commercial sectors in Dhaka city, the auditing showed many inadequacies, as aside from the larger corporate offices, the offices have little to no accessibility for the physically disabled. This study hopes to shed light on the fact that the existing BNBCs lack of emphasis on ensuring the accessibility of the handicapped in corporate buildings in the hope that, in the future, the physically disabled will have greater opportunities at being productive members of the workforce.

Keywords: Person with disability, PWD, corporate buildings, Dhaka City.

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Authors: Khalid Ghoulam, Belaid Bouikhalene, Zakaria Harmouch, Hicham Mouncif

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One of the essential topics in the information systems is the registration management. The objective of this project is to create a web portal designed to help new students on the first access to the Sultan Moulay Slimane University SMSU (Practical Information, Pre-Registration, Placement Test, Terms of use ... etc.) while creating a secure space protecting both data from the institutions of the University and student information. This portal is accessible from any computer connected to the Internet inside and outside the campus. In this work, we present a platform on the first access to the SMSU which is essential for authentication in the digital work space of the university. This platform allows university to make better decisions for students clustering, to avoid traditional manual method, and to reduce the cost in human and material resources.

Keywords: Registration, SMSU, Security, FAUSMS, digital work space, Placement test.

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Authors: Zuwairie Ibrahim, Yusei Tsuboi, Osamu Ono, Marzuki Khalid

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Deoxyribonucleic Acid or DNA computing has emerged as an interdisciplinary field that draws together chemistry, molecular biology, computer science and mathematics. Thus, in this paper, the possibility of DNA-based computing to solve an absolute 1-center problem by molecular manipulations is presented. This is truly the first attempt to solve such a problem by DNA-based computing approach. Since, part of the procedures involve with shortest path computation, research works on DNA computing for shortest path Traveling Salesman Problem, in short, TSP are reviewed. These approaches are studied and only the appropriate one is adapted in designing the computation procedures. This DNA-based computation is designed in such a way that every path is encoded by oligonucleotides and the path-s length is directly proportional to the length of oligonucleotides. Using these properties, gel electrophoresis is performed in order to separate the respective DNA molecules according to their length. One expectation arise from this paper is that it is possible to verify the instance absolute 1-center problem using DNA computing by laboratory experiments.

Keywords: DNA computing, operation research, 1-center problem.

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Authors: Khalid Abd, Kazem Abhary, Romeo Marian

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Multiple criteria decision making (MCDM) is an approach to ranking the solutions and finding the best one when two or more solutions are provided. In this study, MCDM approach is proposed to select the most suitable scheduling rule of robotic flexible assembly cells (RFACs). Two MCDM approaches, Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are proposed for solving the scheduling rule selection problem. The AHP method is employed to determine the weights of the evaluation criteria, while the TOPSIS method is employed to obtain final ranking order of scheduling rules. Four criteria are used to evaluate the scheduling rules. Also, four scheduling policies of RFAC are examined to choose the most appropriate one for this purpose. A numerical example illustrates applications of the suggested methodology. The results show that the methodology is practical and works in RFAC settings.

Keywords: AHP, TOPSIS, Scheduling rules selection

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Authors: Sheikh Muhammad Azam, Masood-ur-Rehman, Adnan Khalid Bhatti, Nadeem Daudpota

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Very Large and/or computationally complex optimization problems sometimes require parallel or highperformance computing for achieving a reasonable time for computation. One of the most popular and most complicate problems of this family is “Traveling Salesman Problem". In this paper we have introduced a Branch & Bound based algorithm for the solution of such complicated problems. The main focus of the algorithm is to solve the “symmetric traveling salesman problem". We reviewed some of already available algorithms and felt that there is need of new algorithm which should give optimal solution or near to the optimal solution. On the basis of the use of logarithmic sampling, it was found that the proposed algorithm produced a relatively optimal solution for the problem and results excellent performance as compared with the traditional algorithms of this series.

Keywords: Parallel execution, symmetric traveling salesman problem, branch and bound algorithm, logarithmic sampling.

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Authors: Khalid Ghoulam, Belaid Bouikhalene, Zakaria Harmouch, Hicham Mouncif

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The goal of engineering education is to prepare students to cope with problems of real devices and systems. Usually there are not enough devices or time for conducting experiments in a real lab. Other factors that prevent the use of lab devices directly by students are inaccessible or dangerous phenomena, or polluting chemical reactions. The technology brings additional strategies of learning and teaching, there are two types of online labs, virtual and remote labs RL. We present an example of a successful development and deployment of a remote lab in the field of engineering education, integrated in the Moodle platform, using very low-coast, high documented devices and free software. The remote lab is user friendly for both teachers and students. Our web 2.0 based user interface would attract and motivate students, as well as solving the problem of larger classes and expensive lab devices.

Keywords: Remote lab, online learning, Moodle, Arduino, SMSU, lab experimentation, engineering education, online engineering education.

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Authors: Muhammad Haroon Siddiqui, Muhammad Rehan Khalid

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This paper evaluates the performance of a novel algorithm for tracking of a mobile node, interms of execution time and root mean square error (RMSE). Particle Filter algorithm is used to track the mobile node, however a new technique in particle filter algorithm is also proposed to reduce the execution time. The stationary points were calculated through trilateration and finally by averaging the number of points collected for a specific time, whereas tracking is done through trilateration as well as particle filter algorithm. Wi-Fi signal is used to get initial guess of the position of mobile node in x-y coordinates system. Commercially available software “Wireless Mon" was used to read the WiFi signal strength from the WiFi card. Visual Cµ version 6 was used to interact with this software to read only the required data from the log-file generated by “Wireless Mon" software. Results are evaluated through mathematical modeling and MATLAB simulation.

Keywords: Particle Filter, Tracking, Wireless Local Area Network, WiFi, Trilateration

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Authors: Mohammed Benbrahim, Adil Daoudi, Khalid Benjelloun, Aomar Ibenbrahim

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The automatic discrimination of seismic signals is an important practical goal for earth-science observatories due to the large amount of information that they receive continuously. An essential discrimination task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, two classes of seismic signals recorded routinely in geophysical laboratory of the National Center for Scientific and Technical Research in Morocco are considered. They correspond to signals associated to local earthquakes and chemical explosions. The approach adopted for the development of an automatic discrimination system is a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "modified Mexican hat wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis.

Keywords: Seismic signals, Wavelets, Dimensionality reduction, Artificial neural networks, Classification.

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Authors: Yousry El-Gamal, Khalid El-Gazzar, Magdy Saeb

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The development of distributed systems has been affected by the need to accommodate an increasing degree of flexibility, adaptability, and autonomy. The Mobile Agent technology is emerging as an alternative to build a smart generation of highly distributed systems. In this work, we investigate the performance aspect of agent-based technologies for information retrieval. We present a comparative performance evaluation model of Mobile Agents versus Remote Method Invocation by means of an analytical approach. We demonstrate the effectiveness of mobile agents for dynamic code deployment and remote data processing by reducing total latency and at the same time producing minimum network traffic. We argue that exploiting agent-based technologies significantly enhances the performance of distributed systems in the domain of information retrieval.

Keywords: Mobile Agent, performance evaluation, RMI, information retrieval, distributed systems, database.

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Authors: Sadaf Khalid, Jahanzaib Sarwar, Rabia Tauseef

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No matter how much perfect we become in our practical skills regarding the implementation of learned ideas, the need of technical writing capability cannot be neglected being a professional. Technical writing is a way of communicating the ideas in written which otherwise need to be presented orally. Technical writing skills have always been the need of the time, as they are required for internal as well as external official communication in both formal and informal manner. Moreover, they are the best way to capture the attention of your customers by presenting information in effective manner. This paper aims to analyze the importance of technical writing skills in professional industries of Pakistan by conducting a survey. Survey results presented in this paper clearly depicts the importance of formal and informal written communication media used in different professional industries in Pakistan. Analysis and discussion of the extent to which the alternative ways of communication besides technical writing have got importance in Pakistan is also an important aspect of this survey.

Keywords: Technical writing, Survey, Oral communication, Globalization, Communication trends, Formal Communication Media, Informal Communication, Audience

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Authors: Siti Juryiah Mohd Khalid, Norazlina Dol

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Academic libraries in Malaysia are still not prepared for disaster even though several occasions have been reported. The study sets out to assess the current status of preparedness in disaster management among Malaysian academic libraries in the State of Selangor and the Federal Territory of Kuala Lumpur. To obtain a base level of knowledge on disaster preparedness of current practices, a questionnaire was distributed to chief librarians or their assignees in charge of disaster or emergency preparedness at 40 academic libraries and 34 responses were received. The study revolved around the current status of preparedness, on various issues including existence of disaster preparedness plan among academic libraries in Malaysia, disaster experiences by the academic libraries, funding, risk assessment activities and involvement of library staff in disaster management. Frequency and percentage tables were used in the analysis of the data collected. Some of the academic libraries under study have experienced one form of disaster or the other. Most of the academic libraries do not have a written disaster preparedness plan. The risk assessments and staff involvement in disaster preparedness by these libraries were generally adequate.

Keywords: Academic libraries, disaster preparedness plan, disaster management, emergency plan.

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Authors: Mohamed M. Saleh, Khalid S. Al-Hagla

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By taking advantage of computer-s processing power, an unlimited number of variations and parameters in both spatial and environmental can be provided while following the same set of rules and constraints. This paper focuses on using the tools of parametric urbanism towards a more responsive environmental and sustainable urban morphology. It presents an understanding to Parametric Urban Comfort Envelope (PUCE) as an interactive computational assessment urban model. In addition, it investigates the applicability potentials of this model to generate an optimized urban form to Borg El Arab city (a new Egyptian Community) concerning the human comfort values specially wind and solar envelopes. Finally, this paper utilizes its application outcomes -both visual and numerical- to extend the designer-s limitations by decrease the concern of controlling and manipulation of geometry, and increase the designer-s awareness about the various potentials of using the parametric tools to create relationships that generate multiple geometric alternatives.

Keywords: Assessment model, human comfort, parametric urbanism, sustainable urban morphology.

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Authors: B. Manshoor, M. Jaat, Amir Khalid

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Circle grid space filling plate is a flow conditioner with a fractal pattern and used to eliminate turbulence originating from pipe fittings in experimental fluid flow applications. In this paper, steady state, incompressible, swirling turbulent flow through circle grid space filling plate has been studied. The solution and the analysis were carried out using finite volume CFD solver FLUENT 6.2. Three turbulence models were used in the numerical investigation and their results were compared with the pressure drop correlation of BS EN ISO 5167-2:2003. The turbulence models investigated here are the standard k-ε, realizable k-ε, and the Reynolds Stress Model (RSM). The results showed that the RSM model gave the best agreement with the ISO pressure drop correlation. The effects of circle grids space filling plate thickness and Reynolds number on the flow characteristics have been investigated as well.

Keywords: Flow conditioning, turbulent flow, turbulent modeling, CFD.

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Authors: El Kaak, Rachid, El Bikri, Khalid, Benamar, Rhali

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This paper describes a study of geometrically nonlinear free vibration of thin circular functionally graded (CFGP) plates resting on Winkler elastic foundations. The material properties of the functionally graded composites examined here are assumed to be graded smoothly and continuously through the direction of the plate thickness according to a power law and are estimated using the rule of mixture. The theoretical model is based on the classical Plate theory and the Von-Kármán geometrical nonlinearity assumptions. An homogenization procedure (HP) is developed to reduce the problem considered here to that of isotropic homogeneous circular plates resting on Winkler foundation. Hamilton-s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear fundamental frequency has also been analysed.

Keywords: Functionally graded materials, nonlinear vibrations, Winkler foundation.

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