Search results for: file format.

Authors: M. Padmavathi, R. M. Suresh

Abstract:

Every machine plays roles of client and server simultaneously in a peer-to-peer (P2P) network. Though a P2P network has many advantages over traditional client-server models regarding efficiency and fault-tolerance, it also faces additional security threats. Users/IT administrators should be aware of risks from malicious code propagation, downloaded content legality, and P2P software’s vulnerabilities. Security and preventative measures are a must to protect networks from potential sensitive information leakage and security breaches. Bit Torrent is a popular and scalable P2P file distribution mechanism which successfully distributes large files quickly and efficiently without problems for origin server. Bit Torrent achieved excellent upload utilization according to measurement studies, but it also raised many questions as regards utilization in settings, than those measuring, fairness, and Bit Torrent’s mechanisms choice. This work proposed a block selection technique using Fuzzy ACO with optimal rules selected using ACO.

Keywords: Ant Colony Optimization (ACO), Bit Torrent, Download time, Peer-to-Peer (P2P) network, Performance.

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Authors: Faraji Sepideh

Abstract:

Nowadays, purchase rate of the smart device is increasing and user authentication is one of the important issues in information security. Alphanumeric strong passwords are difficult to memorize and also owners write them down on papers or save them in a computer file. In addition, text password has its own flaws and is vulnerable to attacks. Graphical password can be used as an alternative to alphanumeric password that users choose images as a password. This type of password is easier to use and memorize and also more secure from pervious password types. In this paper we have designed a more secure graphical password system to prevent shoulder surfing, smudge and brute force attack. This scheme is a combination of two types of graphical passwords recognition based and Cued recall based. Evaluation the usability and security of our proposed scheme have been explained in conclusion part.

Keywords: Brute force attack, graphical password, shoulder surfing attack, smudge attack.

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Authors: Jinghua Zhang, Charles B. Owen, Jinsheng Xu

Abstract:

A new hybrid coding method for compressing animated polygonal meshes is presented. This paper assumes the simplistic representation of the geometric data: a temporal sequence of polygonal meshes for each discrete frame of the animated sequence. The method utilizes a delta coding and an octree-based method. In this hybrid method, both the octree approach and the delta coding approach are applied to each single frame in the animation sequence in parallel. The approach that generates the smaller encoded file size is chosen to encode the current frame. Given the same quality requirement, the hybrid coding method can achieve much higher compression ratio than the octree-only method or the delta-only method. The hybrid approach can represent 3D animated sequences with higher compression factors while maintaining reasonable quality. It is easy to implement and have a low cost encoding process and a fast decoding process, which make it a better choice for real time application.

Keywords: animated polygonal meshes, compression, deltacoding, octree.

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Authors: Jasraj Meena, Malay Kumar, Manu Vardhan

Abstract:

Cloud computing is a new technology in industry and academia. The technology has grown and matured in last half decade and proven their significant role in changing environment of IT infrastructure where cloud services and resources are offered over the network. Cloud technology enables users to use services and resources without being concerned about the technical implications of technology. There are substantial research work has been performed for the usage of cloud computing in educational institutes and majority of them provides cloud services over high-end blade servers or other high-end CPUs. However, this paper proposes a new stack called “CiCKAStack” which provide cloud services over unutilized computing resources, named as commodity computers. “CiCKAStack” provides IaaS and PaaS using underlying commodity computers. This will not only increasing the utilization of existing computing resources but also provide organize file system, on demand computing resource and design and development environment.

Keywords: Commodity Computers, Cloud Computing, KVM, Cloudstack, Appscale.

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Authors: Li Li, Li-Ru Xia, He-Ye Wang, Xiao-Dong Bi

Abstract:

In this paper, we presented a highly sensitive immune-affinity monolithic array for detection of α-fetoprotein (AFP) and carcinoembryonic antigen (CEA). Firstly, the epoxy functionalized monolith arrays were fabricated using UV initiated copolymerization method. Scanning electron microscopy (SEM) image showed that the poly(BABEA-co-GMA) monolith exhibited a well-controlled skeletal and well-distributed porous structure. Then, AFP and CEA immune-affinity monolithic arrays were prepared by immobilization of AFP and CEA antibodies on epoxy functionalized monolith arrays. With a non-competitive immune response format, the presented AFP and CEA immune-affinity arrays were demonstrated as an inexpensive, flexible, homogeneous and stable array for detection of AFP and CEA.

Keywords: Chemiluminescent detection, immune-affinity, monolithic copolymer array, UV-initiated copolymerization.

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Authors: Tawiwat V., Phermsak S., Noppasit C.

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This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

Keywords: Under actuator, Dynamic optimal control, Minimumjerk, Minimum energy.

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Authors: A. Goel, S.C. Gupta, S.K.Wasan

Abstract:

Testable software has two inherent properties – observability and controllability. Observability facilitates observation of internal behavior of software to required degree of detail. Controllability allows creation of difficult-to-achieve states prior to execution of various tests. In this paper, we describe COTT, a Controllability and Observability Testing Tool, to create testable object-oriented software. COTT provides a framework that helps the user to instrument object-oriented software to build the required controllability and observability. During testing, the tool facilitates creation of difficult-to-achieve states required for testing of difficultto- test conditions and observation of internal details of execution at unit, integration and system levels. The execution observations are logged in a test log file, which are used for post analysis and to generate test coverage reports.

Keywords: Controllability, Observability, Test Coverage and Testing Tool.

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Authors: K. Daud, A. F. Abidin, N. Hamzah, H. S. Nagindar Singh

Abstract:

This paper produces a new approach for power quality analysis using a windowing technique based on Continuous S-transform (CST). This half-cycle window technique approach can detect almost correctly for initial detection of disturbances i.e. voltage sags, swells, and transients. Samples in half cycle window has been analyzed based continuous S-transform for entire disturbance waveform. The modified parameter has been produced by MATLAB programming m-file based on continuous s-transform. CST has better time frequency and localization property than traditional and also has ability to detect the disturbance under noisy condition correctly. The excellent time-frequency resolution characteristic of the CST makes it the most an attractive candidate for analysis of power system disturbances signals.

Keywords: Power quality disturbances, initial detection, half cycle windowing, continuous S-transform.

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Authors: Yuan L. Lai, Jian H. Chen, Jui P. Hung

Abstract:

Owning to the high-speed feed rate and ultra spindle speed have been used in modern machine tools, the tool-path generation plays a key role in the successful application of a High-Speed Machining (HSM) system. Because of its importance in both high-speed machining and tool-path generation, approximating a contour by NURBS format is a potential function in CAD/CAM/CNC systems. It is much more convenient to represent an ellipse by parametric form than to connect points laboriously determined in a CNC system. A new approximating method based on optimum processes and NURBS curves of any degree to the ellipses is presented in this study. Such operations can be the foundation of tool-radius compensation interpolator of NURBS curves in CNC system. All operating processes for a CAD tool is presented and demonstrated by practical models.

Keywords: Ellipse, Approximation, NURBS, Optimum.

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Authors: T. Kumaresan, S. Sanjushree, C. Palanisamy

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Image spam is a kind of email spam where the spam text is embedded with an image. It is a new spamming technique being used by spammers to send their messages to bulk of internet users. Spam email has become a big problem in the lives of internet users, causing time consumption and economic losses. The main objective of this paper is to detect the image spam by using histogram properties of an image. Though there are many techniques to automatically detect and avoid this problem, spammers employing new tricks to bypass those techniques, as a result those techniques are inefficient to detect the spam mails. In this paper we have proposed a new method to detect the image spam. Here the image features are extracted by using RGB histogram, HSV histogram and combination of both RGB and HSV histogram. Based on the optimized image feature set classification is done by using k- Nearest Neighbor(k-NN) algorithm. Experimental result shows that our method has achieved better accuracy. From the result it is known that combination of RGB and HSV histogram with k-NN algorithm gives the best accuracy in spam detection.

Keywords: File Type, HSV Histogram, k-NN, RGB Histogram, Spam Detection.

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Authors: N. Zhang, J. S. Kuang, S. Mogili

Abstract:

To investigate seismic performance of beam-column knee joints, four full-scale reinforced concrete beam-column knee joints, which were fabricated to simulate those in as-built RC frame buildings designed to ACI 318-14 and ACI-ASCE 352R-02, were tested under reversed cyclic loading. In the experimental programme, particular emphasis was given to the effect of horizontal reinforcement (in format of inverted U-shape bars) on the shear strength and ductility capacity of knee joints. Test results are compared with those predicted by four seismic design codes, including ACI 318-14, EC8, NZS3101 and GB50010. It is seen that the current design codes of practice cannot accurately predict the shear strength of seismically designed knee joints.

Keywords: Large-scale tests, RC beam-column knee joints, seismic performance, shear strength.

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Authors: Aref Ghafouri, Mohammad Javad Mollakazemi, Farhad Asadi

Abstract:

In this paper, model order reduction method is used for approximation in linear and nonlinearity aspects in some experimental data. This method can be used for obtaining offline reduced model for approximation of experimental data and can produce and follow the data and order of system and also it can match to experimental data in some frequency ratios. In this study, the method is compared in different experimental data and influence of choosing of order of the model reduction for obtaining the best and sufficient matching condition for following the data is investigated in format of imaginary and reality part of the frequency response curve and finally the effect and important parameter of number of order reduction in nonlinear experimental data is explained further.

Keywords: Frequency response, Order of model reduction, frequency matching condition.

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Authors: Federica Fornaciari

Abstract:

The current study begins with an awareness that today-s media environment is characterized by technological development and a new way of reading caused by the introduction of the Internet. The researcher conducted a meta analysis framed within Technological Determinism to investigate the process of hypertext reading, its differences from linear reading and the effects such differences can have on people-s ways of mentally structuring their world. The relationship between literacy and the comprehension achieved by reading hypertexts is also investigated. The results show hypertexts are not always user friendly. People experience hyperlinks as interruptions that distract their attention generating comprehension and disorientation. On one hand hypertextual jumping reading generates interruptions that finally make people lose their concentration. On the other hand hypertexts fascinate people who would rather read a document in such a format even though the outcome is often frustrating and affects their ability to elaborate and retain information.

Keywords: Hypertext reading, Internet, non-linearity.

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Authors: Weifeng Pan

Abstract:

The stability of a software system is one of the most important quality attributes affecting the maintenance effort. Many techniques have been proposed to support the analysis of software stability at the architecture, file, and class level of software systems, but little effort has been made for that at the feature (i.e., method and attribute) level. And the assumptions the existing techniques based on always do not meet the practice to a certain degree. Considering that, in this paper, we present a novel metric, Stability of Software (SoS), to measure the stability of object-oriented software systems by software change propagation analysis using a simulation way in software dependency networks at feature level. The approach is evaluated by case studies on eight open source Java programs using different software structures (one employs design patterns versus one does not) for the same object-oriented program. The results of the case studies validate the effectiveness of the proposed metric. The approach has been fully automated by a tool written in Java.

Keywords: Software stability, change propagation, design pattern, software maintenance, object-oriented (OO) software.

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Authors: Noppakit Nawalikit, Pattarasinee Bhattarakosol

Abstract:

Since Software testing becomes an important part of Software development in order to improve the quality of software, many automation tools are created to help testing functionality of software. There are a few issues about usability of these tools, one is that the result log which is generated from tools contains useless information that the tester cannot use result log to communicate efficiently, or the result log needs to use a specific application to open. This paper introduces a new method, SBTAR that improves usability of automated test tools in a part of a result log. The practice will use the capability of tools named as IBM Rational Robot to create a customized function, the function would generate new format of a result log which contains useful information faster and easier to understand than using the original result log which was generated from the tools. This result log also increases flexibility by Microsoft Word or WordPad to make them readable.

Keywords: Software Automation Testing, Automated test tool, IBM Rational Robot.

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Authors: S. Mohamed Rabeek, Mi Kyoung Park, M. Annamalai Arasu

Abstract:

This paper presents a design of a wireless read out system for tracking the frequency shift of the polymer coated piezoelectric micro electromechanical resonator due to gas absorption. The measure of this frequency shift indicates the percentage of a particular gas the sensor is exposed to. It is measured using an oscillator and an FPGA based frequency counter by employing the resonator as a frequency determining element in the oscillator. This system consists of a Gas Sensing Wireless Readout (GSWR) and an USB Wireless Transceiver (UWT). GSWR consists of an oscillator based on a trans-impedance sustaining amplifier, an FPGA based frequency readout, a sub 1GHz wireless transceiver and a micro controller. UWT can be plugged into the computer via USB port and function as a wireless module to transfer gas sensor data from GSWR to the computer through its USB port. GUI program running on the computer periodically polls for sensor data through UWT - GSWR wireless link, the response from GSWR is logged in a file for post processing as well as displayed on screen.

Keywords: Gas sensor, GSWR, micro-mechanical system, UWT, volatile emissions.

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Authors: F. Raja, M. Rahgozar, F. Oroumchian

Abstract:

XML is a markup language which is becoming the standard format for information representation and data exchange. A major purpose of XML is the explicit representation of the logical structure of a document. Much research has been performed to exploit logical structure of documents in information retrieval in order to precisely extract user information need from large collections of XML documents. In this paper, we describe an XML information retrieval weighting scheme that tries to find the most relevant elements in XML documents in response to a user query. We present this weighting model for information retrieval systems that utilize plausible inferences to infer the relevance of elements in XML documents. We also add to this model the Dempster-Shafer theory of evidence to express the uncertainty in plausible inferences and Dempster-Shafer rule of combination to combine evidences derived from different inferences.

Keywords: Dempster-Shafer theory, plausible inferences, XMLinformation retrieval.

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Authors: Shaila Rana, Wasim Alhamdani

Abstract:

Effective cybersecurity learning relies on an engaging, interactive, and entertaining activity that fosters positive learning outcomes. VR cybersecurity training may provide a training format that is engaging, interactive, and entertaining. A methodological approach and framework are needed to allow trainers and educators to employ VR cybersecurity training methods to promote positive learning outcomes. Thus, this paper aims to create an approach that cybersecurity trainers can follow to create a VR cybersecurity training module. This methodology utilizes concepts from other cybersecurity training frameworks, such as NICE and CyTrONE. Other cybersecurity training frameworks do not incorporate the use of VR. VR training proposes unique challenges that cannot be addressed in current cybersecurity training frameworks. Subsequently, this ontology utilizes concepts to develop VR training to create a relevant methodology for creating VR cybersecurity training modules.

Keywords: Virtual reality cybersecurity training, VR cybersecurity training, traditional cybersecurity training, ontology.

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Authors: Pek Chuen-Khee, Jamal Othman

Abstract:

This paper estimates the economic values of household preference for enhanced solid waste disposal services in Malaysia. The contingent valuation (CV) method estimates an average additional monthly willingness-to-pay (WTP) in solid waste management charges of Ôé¼0.77 to 0.80 for improved waste disposal services quality. The finding of a slightly higher WTP from the generic CV question than that of label-specific, further reveals a higher WTP for sanitary landfill, at Ôé¼0.90, than incineration, at Ôé¼0.63. This suggests that sanitary landfill is a more preferred alternative. The logistic regression estimation procedure reveals that household-s concern of where their rubbish is disposed, age, ownership of house, household income and format of CV question are significant factors in influencing WTP.

Keywords: contingent valuation, logistic regression, solid waste disposal, willingness-to-pay.

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Authors: Hassan Ezzaidi, Jean Rouat

Abstract:

Recently many research has been conducted to retrieve pertinent parameters and adequate models for automatic music genre classification. In this paper, two measures based upon information theory concepts are investigated for mapping the features space to decision space. A Gaussian Mixture Model (GMM) is used as a baseline and reference system. Various strategies are proposed for training and testing sessions with matched or mismatched conditions, long training and long testing, long training and short testing. For all experiments, the file sections used for testing are never been used during training. With matched conditions all examined measures yield the best and similar scores (almost 100%). With mismatched conditions, the proposed measures yield better scores than the GMM baseline system, especially for the short testing case. It is also observed that the average discrimination information measure is most appropriate for music category classifications and on the other hand the divergence measure is more suitable for music subcategory classifications.

Keywords: Audio feature, information measures, music genre.

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Authors: Harkishen Singh, Gavin Mangeni

Abstract:

This project aims at building an efficient and automatic power monitoring SCADA system, which is capable of monitoring the electrical parameters of high voltage powered devices in real time for example RMS voltage and current, frequency, energy consumed, power factor etc. The system uses RS-485 serial communication interface to transfer data over longer distances. Embedded C programming is the platform used to develop two hardware modules namely: RTU and Master Station modules, which both use the CC2540 BLE 4.0 microcontroller configured in slave / master mode. The Si8900 galvanic ally isolated microchip is used to perform ADC externally. The hardware communicates via UART port and sends data to the user PC using the USB port. Labview software is used to design a user interface to display current state of the power loads being monitored as well as logs data to excel spreadsheet file. An understanding of the Si8900’s auto baud rate process is key to successful implementation of this project.

Keywords: SCADA, RS485, CC2540, Labview, Si8900.

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Authors: C. Ardil

Abstract:

This paper presents the open science philosophy and paradigm of scientific research on how to transform classical research and innovation approaches. Open science is the practice of providing free and unrestricted online access to the products of scholarly research. Open science advocates for the immediate and unrestricted online access to published, peer-reviewed research in digital format. Open science research is made available for free in perpetuity and includes guidelines and/or licenses that communicate how researchers and readers can share and re-use the digital content. The emergence of open science has changed the scholarly research and publishing landscape, making research more broadly accessible to academic and non-academic audiences alike. Consequently, open science philosophy and its practice are discussed to cover all aspects of cyberscience in the context of research and innovation excellence for the benefit of global society.

Keywords: Open science, open data, open access, cyberscience , cybertechnology.

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Authors: Nermine Ahmed Hendy, Hania Farag

Abstract:

Emotion recognition is an important research field that finds lots of applications nowadays. This work emphasizes on recognizing different emotions from speech signal. The extracted features are related to statistics of pitch, formants, and energy contours, as well as spectral, perceptual and temporal features, jitter, and shimmer. The Artificial Neural Networks (ANN) was chosen as the classifier. Working on finding a robust and fast ANN classifier suitable for different real life application is our concern. Several experiments were carried out on different ANN to investigate the different factors that impact the classification success rate. Using a database containing 7 different emotions, it will be shown that with a proper and careful adjustment of features format, training data sorting, number of features selected and even the ANN type and architecture used, a success rate of 85% or even more can be achieved without increasing the system complicity and the computation time

Keywords: Classification, emotion recognition, features extraction, feature selection, neural network

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Authors: R. Lokeshkumar, P. Sengottuvelan

Abstract:

Web mining is to discover and extract useful Information. Different users may have different search goals when they search by giving queries and submitting it to a search engine. The inference and analysis of user search goals can be very useful for providing an experience result for a user search query. In this project, we propose a novel approach to infer user search goals by analyzing search web logs. First, we propose a novel approach to infer user search goals by analyzing search engine query logs, the feedback sessions are constructed from user click-through logs and it efficiently reflect the information needed for users. Second we propose a preprocessing technique to clean the unnecessary data’s from web log file (feedback session). Third we propose a technique to generate pseudo-documents to representation of feedback sessions for clustering. Finally we implement k-medoids clustering algorithm to discover different user search goals and to provide a more optimal result for a search query based on feedback sessions for the user.

Keywords: Data Preprocessing, Session Identification, Web log mining, Web Personalization.

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Authors: Ajay Joshi, Surya Ismail

Abstract:

This paper will present the initial findings of a research into distributed computer rendering. The goal of the research is to create a distributed computer system capable of rendering a 3D model into an MPEG-4 stream. This paper outlines the initial design, software architecture and hardware setup for the system. Distributed computing means designing and implementing programs that run on two or more interconnected computing systems. Distributed computing is often used to speed up the rendering of graphical imaging. Distributed computing systems are used to generate images for movies, games and simulations. A topic of interest is the application of distributed computing to the MPEG-4 standard. During the course of the research, a distributed system will be created that can render a 3D model into an MPEG-4 stream. It is expected that applying distributed computing principals will speed up rendering, thus improving the usefulness and efficiency of the MPEG-4 standard

Keywords: Cluster, parallel architecture, rendering, MPEG-4.

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Authors: Ashutosh Kumar Singh, Ravi Kumar P

Abstract:

This paper gives an introduction to Web mining, then describes Web Structure mining in detail, and explores the data structure used by the Web. This paper also explores different Page Rank algorithms and compare those algorithms used for Information Retrieval. In Web Mining, the basics of Web mining and the Web mining categories are explained. Different Page Rank based algorithms like PageRank (PR), WPR (Weighted PageRank), HITS (Hyperlink-Induced Topic Search), DistanceRank and DirichletRank algorithms are discussed and compared. PageRanks are calculated for PageRank and Weighted PageRank algorithms for a given hyperlink structure. Simulation Program is developed for PageRank algorithm because PageRank is the only ranking algorithm implemented in the search engine (Google). The outputs are shown in a table and chart format.

Keywords: Web Mining, Web Structure, Web Graph, LinkAnalysis, PageRank, Weighted PageRank, HITS, DistanceRank, DirichletRank,

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Authors: A. Mavrikos, N. Petsas, E. Kaltsi, D. Kaliampakos

Abstract:

The lignite-fired power plants in the Western Macedonia Lignite Center produce more than 810⁶ t of fly ash per year. Approximately 90% of this quantity is used for restoration-reclamation of exhausted open-cast lignite mines and slope stabilization of the overburden. The purpose of this work is to evaluate the environmental behavior of the mixture of waste rock and fly ash that is being used in the external deposition site of the South Field lignite mine. For this reason, a borehole was made within the site and 86 samples were taken and subjected to chemical analyses and leaching tests. The results showed very limited leaching of trace elements and heavy metals from this mixture. Moreover, when compared to the limit values set for waste acceptable in inert waste landfills, only few excesses were observed, indicating only minor risk for groundwater pollution. However, due to the complexity of both the leaching process and the contaminant pathway, more boreholes and analyses should be made in nearby locations and a systematic groundwater monitoring program should be implemented both downstream and within the external deposition site.

Keywords: Co-deposition, fly ash, leaching tests, lignite, waste rock.

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Authors: Ali Awde, Yacine Bellik, Chakib Tadj

Abstract:

Our adaptive multimodal system aims at correctly presenting a mathematical expression to visually impaired users. Given an interaction context (i.e. combination of user, environment and system resources) as well as the complexity of the expression itself and the user-s preferences, the suitability scores of different presentation format are calculated. Unlike the current state-of-the art solutions, our approach takes into account the user-s situation and not imposes a solution that is not suitable to his context and capacity. In this wok, we present our methodology for calculating the mathematical expression complexity and the results of our experiment. Finally, this paper discusses the concepts and principles applied on our system as well as their validation through cases studies. This work is our original contribution to an ongoing research to make informatics more accessible to handicapped users.

Keywords: Adaptive system, intelligent multi-agent system, mathematics for visually-impaired users.

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Authors: Sa’ed Abed, Mohammad H. Al Shayeji, Ovais Ahmed, Sahel Alouneh

Abstract:

Session Initiation Protocol (SIP) is a signaling layer protocol for building, adjusting and ending sessions among participants including Internet conferences, telephone calls and multimedia distribution. SIP facilitates user movement by proxying and forwarding requests to the present location of the user. In this paper, we provide a formal Specification and Description Language (SDL) and Message Sequence Chart (MSC) to model and define the Internet Engineering Task Force (IETF) SIP protocol and its sample services resulted from informal SIP specification. We create an “Abstract User Interface” using case analysis so that can be applied to identify SIP services more explicitly. The issued sample SIP features are then used as case scenarios; they are revised in MSCs format and validated to their corresponding SDL models.

Keywords: Modeling, MSC, SDL, SIP, validating.

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Authors: Manduth Ramchander

Abstract:

Evaluating expressions involving multiplication and division can give rise to the fallacy that brackets can be arbitrarily inserted into expressions involving multiplication and division. The aim of this article was to draw upon mathematical theory to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division and in particular in expressions where division precedes multiplication. In doing so, it demonstrates that the notion that two different answers are possible, when evaluating expressions involving multiplication and division, is indeed a false one. Searches conducted in a number of scholarly databases unearthed the rules to be applied when removing brackets from expressions, which revealed that consideration needs to be given to sign changes when brackets are removed. The rule pertaining to expressions involving multiplication and division was then extended upon, in its reverse format, to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division. The application of the rule demonstrates that an expression involving multiplication and division can have only one correct answer. It is recommended that both the rule and its reverse be included in the curriculum, preferably at the juncture when manipulation with brackets is introduced.

Keywords: Brackets, multiplication, division, operations, order.

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