Search results for: mathematical data analysis.

Authors: S. Habte, K. Ouazzane, P. Patel, S. Patel

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The dynamic and highly competitive nature of the consumer electronics retail industry means that businesses in this industry are experiencing different decision making challenges in relation to pricing, inventory control, consumer satisfaction and product offerings. To overcome the challenges facing retailers and create opportunities, we propose a generic data warehousing solution which can be applied to a wide range of consumer electronics retailers with a minimum configuration. The solution includes a dimensional data model, a template SQL script, a high level architectural descriptions, ETL tool developed using C#, a set of APIs, and data access tools. It has been successfully applied by ASK Outlets Ltd UK resulting in improved productivity and enhanced sales growth.

Keywords: Consumer electronics retail, dimensional data model, data analysis, generic data warehousing, reporting.

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Authors: SangWon Han, MuWook Pyeon, Sujung Moon, DaeKyo Seo

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Recently, technologies based on three-dimensional (3D) space information are being developed and quality of life is improving as a result. Research on real-time digital map (RDM) is being conducted now to provide 3D space information. RDM is a service that creates and supplies 3D space information in real time based on location/shape detection. Research subjects on RDM include the construction of 3D space information with matching image data, complementing the weaknesses of image acquisition using multi-source data, and data collection methods using big data. Using RDM will be effective for space analysis using 3D space information in a U-City and for other space information utilization technologies.

Keywords: RDM, multi-source data, big data, U-City.

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Authors: Shyh-Ming Chern

Abstract:

Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and reasonable accuracy, are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, they often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance at and above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: Equation of state, EoS, supercritical water, SCW.

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Authors: Sunita Verma , Divya Tiwari, Ajay Verma

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Water samples were collected from river Pandu at six stations where human and animal activities were high. Composite samples were analyzed for dissolved oxygen (DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD) , pH values during dry and wet seasons as well as the harmattan period. The total data points were used to establish relationships between the parameters and data were also subjected to statistical analysis and expressed as mean ± standard error of mean (SEM) at a level of significance of p<0.05. Regression analysis was carried out to establish relationships if any between studied parameters and relationships in form of scatter plots were obtained between DO/BOD, COD/DO, BOD/COD, COD/pH, BOD/pH and DO/pH. The high to moderate correlation coefficient observed, R2 ranged from 0.68 to 0.15 between these parameters.

Keywords: BOD, DO, COD, pH, Regression analysis.

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of rootmean- squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous - time.

Keywords: Mathematical expectation, filtration, anomalous noise, memory.

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Authors: Laor Boongasame, Veera Boonjing, Ho-fung Leung

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Buyer coalition with a combination of items is a group of buyers joining together to purchase a combination of items with a larger discount. The primary aim of existing buyer coalition with a combination of items research is to generate a large total discount. However, the aim is hard to achieve because this research is based on the assumption that each buyer completely knows other buyers- information or at least one buyer knows other buyers- information in a coalition by exchange of information. These assumption contrast with the real world environment where buyers join a coalition with incomplete information, i.e., they concerned only with their expected discounts. Therefore, this paper proposes a new buyer community coalition formation with a combination of items scheme, called the Community Compromised Combinatorial Coalition scheme, under such an environment of incomplete information. In order to generate a larger total discount, after buyers who want to join a coalition propose their minimum required saving, a coalition structure that gives a maximum total retail prices is formed. Then, the total discount division of the coalition is divided among buyers in the coalition depending on their minimum required saving and is a Pareto optimal. In mathematical analysis, we compare concepts of this scheme with concepts of the existing buyer coalition scheme. Our mathematical analysis results show that the total discount of the coalition in this scheme is larger than that in the existing buyer coalition scheme.

Keywords: group decision and negotiations, group buying, gametheory, combinatorial coalition formation, Pareto optimality

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Authors: Amir Farkhonde

Abstract:

The major objective of this study was to devise a method for solving mathematical problems. Three concepts including faculty of understanding, faculty of guess, and free mind or beginner's mind provided the foundation for this method. An explanatory approach along with a hermeneutic process was taken in this study to support the assumption that mathematical knowledge is constantly developing and it seems essential for students to solve math problems on their own using their faculty of understanding (interpretive dialogue) and faculty of guess. For doing so, a kind of movement from the mathematical problem to mathematical knowledge should be adopted for teaching students a new math topic. The research method of this paper is review, descriptive and conception development. This paper first reviews the research findings on the NRICH’S project (NRICH is part of the family of activities in the Millennium Mathematics Project) with the aim that these findings form the theoretical basis of the problem-solving method. Then, the curriculum, the conceptual structure of the new method, how to design the problem and an example of it are discussed. In this way, students are immersed in the story of discovering and understanding the problem formula, and interpretive dialogue with the text continues by following the questions posed by the problem and constantly reconstructing the answer to find a formula or solution to solve the problem.

Keywords: Interpretive dialogue, NRICH, inventing, a method of problem solving.

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Authors: A. M. Fahim, G. Saake, A. M. Salem, F. A. Torkey, M. A. Ramadan

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Data clustering is an important data exploration technique with many applications in data mining. The k-means algorithm is well known for its efficiency in clustering large data sets. However, this algorithm is suitable for spherical shaped clusters of similar sizes and densities. The quality of the resulting clusters decreases when the data set contains spherical shaped with large variance in sizes. In this paper, we introduce a competent procedure to overcome this problem. The proposed method is based on shifting the center of the large cluster toward the small cluster, and recomputing the membership of small cluster points, the experimental results reveal that the proposed algorithm produces satisfactory results.

Keywords: K-Means, Data Clustering, Cluster Analysis.

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Authors: Bhed Bahadur Bista, Danda B. Rawat

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In this paper, we investigate multihop polling and data gathering schemes in layered sensor networks in order to extend the life time of the networks. A network consists of three layers. The lowest layer contains sensors. The middle layer contains so called super nodes with higher computational power, energy supply and longer transmission range than sensor nodes. The top layer contains a sink node. A node in each layer controls a number of nodes in lower layer by polling mechanism to gather data. We will present four types of data gathering schemes: intermediate nodes do not queue data packet, queue single packet, queue multiple packets and aggregate data, to see which data gathering scheme is more energy efficient for multihop polling in layered sensor networks.

Keywords: layered sensor network, polling, data gatheringschemes.

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Authors: Arpan Dwivedi, Yogesh Pahariya

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In this paper, optimal design of hybrid standalone power supply system (SAPS) is done for off grid applications in remote areas where transmission of power is difficult. The hybrid SAPS system uses two primary energy sources, wind and solar, and in addition to these diesel generator is also connected to meet the load demand in case of failure of wind and solar system. This paper presents mathematical modeling of 1.4 MW hybrid SAPS system for rural electrification. This paper firstly focuses on mathematical modeling of PV module connected in a string, secondly focuses on modeling of permanent magnet wind turbine generator (PMWTG). The hybrid controller is also designed for selection of power from the source available as per the load demand. The power output of hybrid SAPS system is analyzed for meeting load demands at urban as well as for rural areas.

Keywords: SAPS, DG, PMWTG, rural area, off grid, PV module.

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Authors: Yeliz Ekinci, Raife Merve Ön

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Nowadays, technological progress is one of the most important components of economic growth and the efficiency of R&D activities is particularly essential for countries. This study is an attempt to analyze the R&D efficiencies of EU countries. The indicators related to R&D efficiencies should be determined in advance in order to use DEA. For this reason a list of input and output indicators are derived from the literature review. Considering the data availability, a final list is given for the numerical analysis for future research.

Keywords: Data envelopment analysis, economic growth, EU Countries, R&D efficiency.

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Authors: Radek Malinský, Ivan Jelínek

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This article deals with the popularity of candidates for the president of the United States of America. The popularity is assessed according to public comments on the Web 2.0. Social networking, blogging and online forums (collectively Web 2.0) are for common Internet users the easiest way to share their personal opinions, thoughts, and ideas with the entire world. However, the web content diversity, variety of technologies and website structure differences, all of these make the Web 2.0 a network of heterogeneous data, where things are difficult to find for common users. The introductory part of the article describes methodology for gathering and processing data from Web 2.0. The next part of the article is focused on the evaluation and content analysis of obtained information, which write about presidential candidates.

Keywords: Sentiment Analysis, Web 2.0, Webometrics.

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Authors: Mikel Niño, Roberto V. Zicari, Todor Ivanov, Kim Hee, Naveed Mushtaq, Marten Rosselli, Concha Sánchez-Ocaña, Karsten Tolle, José Miguel Blanco, Arantza Illarramendi, Jörg Besier, Harry Underwood

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One of the application fields for data analysis techniques and technologies gaining momentum is the area of social good or “common good”, covering cases related to humanitarian crises, global health care, or ecology and environmental issues, among others. The promotion of data-driven projects in this field aims at increasing the efficacy and efficiency of social initiatives, improving the way these actions help humanity in general and people in need in particular. This application field, however, poses its own barriers and challenges when developing data-driven projects, lagging behind in comparison with other scenarios. These challenges derive from aspects such as the scope and scale of the social issue to solve, cultural and political barriers, the skills of main stakeholders and the technological resources available, the motivation to be engaged in such projects, or the ethical and legal issues related to sensitive data. This paper analyzes the application of data projects in the field of social good, reviewing its current state and noteworthy initiatives, and presenting a framework covering the key aspects to analyze in such projects. The goal is to provide guidelines to understand the main challenges and opportunities for this type of data project, as well as identifying the main differential issues compared to “classical” data projects in general. A case study is presented on the initial steps and stakeholder analysis of a data project for the inclusion of refugees in the city of Frankfurt, Germany, in order to empirically confront the framework with a real example.

Keywords: Data-Driven projects, humanitarian operations, personal and sensitive data, social good, stakeholders analysis.

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Authors: J. R. Wang, Y. Chiang, W. S. Hsu, H. C. Chen, S. H. Chen, J. H. Yang, S. W. Chen, C. Shih

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In this study, the RASCAL and ALOHA codes are used to establish an analysis methodology for hydrogen fluoride (HF) evaluation. There are three main steps in this study. First, the UF₆ data were collected. Second, one postulated case was analyzed by using the RASCAL and UF₆ data. This postulated case assumes that fire occurring and UF₆ is releasing from a building. Third, the results of RASCAL for HF mass were as the input data of ALOHA. Two postulated cases of HF were analyzed by using ALOHA code and the results of RASCAL. These postulated cases assume fire occurring and HF is releasing with no raining (Case 1) or raining (Case 2) condition. According to the analysis results of ALOHA, the HF concentration of Case 2 is smaller than Case 1. The results can be a reference for the preparing of emergency plans for the release of HF.

Keywords: RASCAL, ALOHA, UF6, hydrogen fluoride.

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Authors: Easa Ali Abbasi, Akbar Allahverdizadeh, Reza Jahangiri, Behnam Dadashzadeh

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Electrical current measurement is a suitable method for the performance determination of electrical devices. There are two contact and noncontact methods in this measuring process. Contact method has some disadvantages like having direct connection with wire which may endamage the system. Thus, in this paper, a bimorph piezoelectric cantilever beam which has a permanent magnet on its free end is used to measure electrical current in a noncontact way. In mathematical modeling, based on Galerkin method, the governing equation of the cantilever beam is solved, and the equation presenting the relation between applied force and beam’s output voltage is presented. Magnetic force resulting from current carrying wire is considered as the external excitation force of the system. The results are compared with other references in order to demonstrate the accuracy of the mathematical model. Finally, the effects of geometric parameters on the output voltage and natural frequency are presented.

Keywords: Cantilever beam, electrical current measurement, forced excitation, piezoelectric.

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Authors: Campisi Domenico, Costa Roberta

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Intellectual capital measurement is a central aspect of knowledge management. The measurement and the evaluation of intangible assets play a key role in allowing an effective management of these assets as sources of competitiveness. For these reasons, managers and practitioners need conceptual and analytical tools taking into account the unique characteristics and economic significance of Intellectual Capital. Following this lead, we propose an efficiency and productivity analysis of Intellectual Capital, as a determinant factor of the company competitive advantage. The analysis is carried out by means of Data Envelopment Analysis (DEA) and Malmquist Productivity Index (MPI). These techniques identify Bests Practice companies that have accomplished competitive advantage implementing successful strategies of Intellectual Capital management, and offer to inefficient companies development paths by means of benchmarking. The proposed methodology is employed on the Biotechnology industry in the period 2007-2010.

Keywords: Data Envelopment Analysis, Innovation, Intangible assets, Intellectual Capital, Malmquist Productivity Index.

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Authors: Abdellghani Bellaachia, Edward Jimenez

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Music Information Retrieval (MIR) and modern data mining techniques are applied to identify style markers in midi music for stylometric analysis and author attribution. Over 100 attributes are extracted from a library of 2830 songs then mined using supervised learning data mining techniques. Two attributes are identified that provide high informational gain. These attributes are then used as style markers to predict authorship. Using these style markers the authors are able to correctly distinguish songs written by the Beatles from those that were not with a precision and accuracy of over 98 per cent. The identification of these style markers as well as the architecture for this research provides a foundation for future research in musical stylometry.

Keywords: Music Information Retrieval, Music Data Mining, Stylometry.

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Authors: D. S. C. Soares, D. G. Costa, J. T. S., A. K. S. Abud, T. P. Nunes, A. M. Oliveira Júnior

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Mathematical models of drying are used for the purpose of understanding the drying process in order to determine important parameters for design and operation of the dryer. The jackfruit is a fruit with high consumption in the Northeast and perishability. It is necessary to apply techniques to improve their conservation for longer in order to diffuse it by regions with low consumption. This study aimed to analyze several mathematical models (Page, Lewis, and Midilli) to indicate one that best fits the conditions of convective drying process using performance indicators associated with each model: accuracy (Af) and noise factors (Bf), mean square error (RMSE) and standard error of prediction (% SEP). Jackfruit drying was carried out in convective type tray dryer at a temperature of 50°C for 9 hours. It is observed that the model Midili was more accurate with Af: 1.39, Bf: 1.33, RMSE: 0.01%, and SEP: 5.34. However, the use of the Model Midilli is not appropriate for purposes of control process due to need four tuning parameters. With the performance indicators used in this paper, the Page model showed similar results with only two parameters. It is concluded that the best correlation between the experimental and estimated data is given by the Page’s model.

Keywords: Drying, models, jackfruit.

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Authors: J. R. Wang, Y. Chiang, W. Y. Li, H. T. Lin, H. C. Chen, C. Shih, S. W. Chen

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The dry-storage systems of nuclear power plants (NPPs) in Taiwan have become one of the major safety concerns. There are two steps considered in this study. The first step is the verification of the TRACE by using VSC-17 experimental data. The results of TRACE were similar to the VSC-17 data. It indicates that TRACE has the respectable accuracy in the simulation and analysis of the dry-storage systems. The next step is the application of TRACE in the dry-storage system of Kuosheng NPP (BWR/6). Kuosheng NPP is the second BWR NPP of Taiwan Power Company. In order to solve the storage of the spent fuels, Taiwan Power Company developed the new dry-storage system for Kuosheng NPP. In this step, the dry-storage system model of Kuosheng NPP was established by TRACE. Then, the steady state simulation of this model was performed and the results of TRACE were compared with the Kuosheng NPP data. Finally, this model was used to perform the safety analysis of Kuosheng NPP dry-storage system. Besides, FRAPTRAN was used tocalculate the transient performance of fuel rods.

Keywords: BWR, TRACE, FRAPTRAN, Dry-Storage.

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Authors: Xu Du, Aparna S. Varde

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In this research, we propose to conduct diagnostic and predictive analysis about the key factors and consequences of urban population relocation. To achieve this goal, urban simulation models extract the urban development trends as land use change patterns from a variety of data sources. The results are treated as part of urban big data with other information such as population change and economic conditions. Multiple data mining methods are deployed on this data to analyze nonlinear relationships between parameters. The result determines the driving force of population relocation with respect to urban sprawl and urban sustainability and their related parameters. This work sets the stage for developing a comprehensive urban simulation model for catering to specific questions by targeted users. It contributes towards achieving sustainability as a whole.

Keywords: Data Mining, Environmental Modeling, Sustainability, Urban Planning.

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Authors: Andreas Theissler, Ian Dear

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In the automotive industry test drives are being conducted during the development of new vehicle models or as a part of quality assurance of series-production vehicles. The communication on the in-vehicle network, data from external sensors, or internal data from the electronic control units is recorded by automotive data loggers during the test drives. The recordings are used for fault analysis. Since the resulting data volume is tremendous, manually analysing each recording in great detail is not feasible. This paper proposes to use machine learning to support domainexperts by preventing them from contemplating irrelevant data and rather pointing them to the relevant parts in the recordings. The underlying idea is to learn the normal behaviour from available recordings, i.e. a training set, and then to autonomously detect unexpected deviations and report them as anomalies. The one-class support vector machine “support vector data description” is utilised to calculate distances of feature vectors. SVDDSUBSEQ is proposed as a novel approach, allowing to classify subsequences in multivariate time series data. The approach allows to detect unexpected faults without modelling effort as is shown with experimental results on recordings from test drives.

Keywords: Anomaly detection, fault detection, test drive analysis, machine learning.

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Authors: R.M.Rani

Abstract:

Chess is one of the indoor games, which improves the level of human confidence, concentration, planning skills and knowledge. The main objective of this paper is to help the chess players to improve their chess openings using data mining techniques. Budding Chess Players usually do practices by analyzing various existing openings. When they analyze and correlate thousands of openings it becomes tedious and complex for them. The work done in this paper is to analyze the best lines of Blackmar- Diemer Gambit(BDG) which opens with White D4... using data mining analysis. It is carried out on the collection of winning games by applying association rules. The first step of this analysis is assigning variables to each different sequence moves. In the second step, the sequence association rules were generated to calculate support and confidence factor which help us to find the best subsequence chess moves that may lead to winning position.

Keywords: Blackmar-Diemer Gambit(BDG), Confidence, sequence Association Rules, Support.

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Authors: J. R. Wang, H. T. Lin, H. C. Chang, W. K. Lin, W. Y. Li, C. Shih

Abstract:

This analysis of Kuosheng nuclear power plant (NPP) was performed mainly by TRACE, assisted with FRAPTRAN and FRAPCON. SNAP v2.2.1 and TRACE v5.0p3 are used to develop the Kuosheng NPP SPU TRACE model which can simulate the turbine trip without bypass transient. From the analysis of TRACE, the important parameters such as dome pressure, coolant temperature and pressure can be determined. Through these parameters, comparing with the criteria which were formulated by United States Nuclear Regulatory Commission (U.S. NRC), we can determine whether the Kuoshengnuclear power plant failed or not in the accident analysis. However, from the data of TRACE, the fuel rods status cannot be determined. With the information from TRACE and burn-up analysis obtained from FRAPCON, FRAPTRAN analyzes more details about the fuel rods in this transient. Besides, through the SNAP interface, the data results can be presented as an animation. From the animation, the TRACE and FRAPTRAN data can be merged together that may be realized by the readers more easily. In this research, TRACE showed that the maximum dome pressure of the reactor reaches to 8.32 MPa, which is lower than the acceptance limit 9.58 MPa. Furthermore, FRAPTRAN revels that the maximum strain is about 0.00165, which is below the criteria 0.01. In addition, cladding enthalpy is 52.44 cal/g which is lower than 170 cal/g specified by the USNRC NUREG-0800 Standard Review Plan.

Keywords: Turbine trip without bypass, Kuosheng NPP, TRACE, FRAPTRAN, SNAP animation.

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Authors: Shaival H. Nagarsheth, Utpal Pandya, Hemant J. Nagarsheth

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Cross flow water tube heat exchanger can be designed and made operational using methods of model building and simulation of the system. This paper projects the design and development of a model of cross flow water tube heat-exchanger system, simulation and validation of control analysis of different tuning methods. Feedback and override control system is developed using inputs acquired with the help of sensory system. A mathematical model is formulated for analysis of system behaviour. The temperature is regulated at the desired set point automatically.

Keywords: Heat Exchanger, Feedback, Override, Temperature, PID.

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Authors: Zhila Safari, Ali Ashrafizadeh, Najaf Hedayat

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Thermodynamics characterization Sesame oil extraction by Acetone, Hexane and Benzene has been evaluated. The 120 hours experimental Data were described by a simple mathematical model. According to the simulation results and the essential criteria, Acetone is superior to other solvents but under certain conditions where oil extraction takes place Hexane is superior catalyst.

Keywords: Liquid-solid extraction, seed oil, ThermodynamicStudy.

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Authors: S. Liangwongsan, A. Oonsivilai

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Nowadays, hard disk is one of the most popular storage components. In hard disk industry, the hard disk drive must pass various complex processes and tested systems. In each step, there are some failures. To reduce waste from these failures, we must find the root cause of those failures. Conventionall data analysis method is not effective enough to analyze the large capacity of data. In this paper, we proposed the Hough method for straight line detection that helps to detect straight line defect patterns that occurs in hard disk drive. The proposed method will help to increase more speed and accuracy in failure analysis.

Keywords: Hough Transform, Failure Analysis, Media, Hard Disk Drive

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Authors: B. S. Jatau, Nandom Abu

Abstract:

Structural interpretation of aeromagnetic data and Landsat imagery over the Middle Benue Trough was carried out to determine the depth to basement, delineate the basement morphology and relief, and the structural features within the basin. The aeromagnetic and Landsat data were subjected to various image and data enhancement and transformation routines. Results of the study revealed lineaments with trend directions in the N-S, NE-SW, NWSE and E-W directions, with the NE-SW trends been dominant. The depths to basement within the trough were established to be at 1.8, 0.3 and 0.8km, as shown from the spectral analysis plot. The Source Parameter Imaging (SPI) plot generated showed the centralsouth/ eastern portion of the study area as being deeper in contrast to the western-south-west portion. The basement morphology of the trough was interpreted as having parallel sets of micro-basins which could be considered as grabens and horsts in agreement with the general features interpreted by early workers.

Keywords: Morphology, Middle Benue Trough, Spectral Analysis, Source Parameter Imaging.

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Authors: Cheng-Hong Yang, Tsung-Mu Shih, Li-Yeh Chuang

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Serial Analysis of Gene Expression is a powerful quantification technique for generating cell or tissue gene expression data. The profile of the gene expression of cell or tissue in several different states is difficult for biologists to analyze because of the large number of genes typically involved. However, feature selection in machine learning can successfully reduce this problem. The method allows reducing the features (genes) in specific SAGE data, and determines only relevant genes. In this study, we used a genetic algorithm to implement feature selection, and evaluate the classification accuracy of the selected features with the K-nearest neighbor method. In order to validate the proposed method, we used two SAGE data sets for testing. The results of this study conclusively prove that the number of features of the original SAGE data set can be significantly reduced and higher classification accuracy can be achieved.

Keywords: Serial Analysis of Gene Expression, Feature selection, Genetic Algorithm, K-nearest neighbor method.

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Authors: A. El-Domiaty, H. M. Abd El-Hafez, M. A. Shaker

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Drilling of glass sheets with different thicknesses have been carried out by Abrasive Jet Machining process (AJM) in order to determine its machinability under different controlling parameters of the AJM process. The present study has been introduced a mathematical model and the obtained results have been compared with that obtained from other models published earlier [1-6]. The experimental results of the present work are used to discuss the validity of the proposed model as well as the other models.

Keywords: Abrasive Jet Machining, Erosion rate, Glass, Mathematical model.

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Authors: Mubina Nazmeen, Iram Rubab

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Formal Specification languages are being widely used for system specification and testing. Highly critical systems such as real time systems, avionics, and medical systems are represented using Formal specification languages. Formal specifications based testing is mostly performed using black box testing approaches thus testing only the set of inputs and outputs of the system. The formal specification language such as VDMµ can be used for white box testing as they provide enough constructs as any other high level programming language. In this work, we perform data and control flow analysis of VDMµ class specifications. The proposed work is discussed with an example of SavingAccount.

Keywords: VDM-SL, VDMµ, data flow graph, control flowgraph, testing, formal specification.

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