Search results for: copy number variation

Authors: A. Ghafouri, A. Falavand Jozaei, M. Salari

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In this paper, effects of using Alumina-water nanofluid on the rate of heat transfer have been investigated numerically. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the Richardson number 0.1 to 10 and the solid volume fraction 0 to 0.04. Results are presented by isotherms lines, average Nusselt number and normalized Nusselt number in different range of φ and Ri for forced, combined and natural convection dominated regime. It is found that higher heat transfer rate is predicted when the effects of nanoparticle is taken into account.

Keywords: Nanofluid, Heat Transfer Enhancement, Square Enclosure, Nusselt number.

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Authors: S. Damodaran, T. V. S.Sekhar

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The motion of a sphere moving along the axis of a rotating viscous fluid is studied at high Reynolds numbers and moderate values of Taylor number. The Higher Order Compact Scheme is used to solve the governing Navier-Stokes equations. The equations are written in the form of Stream function, Vorticity function and angular velocity which are highly non-linear, coupled and elliptic partial differential equations. The flow is governed by two parameters Reynolds number (Re) and Taylor number (T). For very low values of Re and T, the results agree with the available experimental and theoretical results in the literature. The results are obtained at higher values of Re and moderate values of T and compared with the experimental results. The results are fourth order accurate.

Keywords: Navier_Stokes equations, Taylor number, Reynolds number, Higher order compact scheme, Rotating Fluid.

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Authors: Viriyavudh Sim, Woo Young Jung

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Performance of Basalt Fiber Reinforced Polymer (BFRP) sandwich infill panel system under diagonal compression was studied by means of numerical analysis. Furthermore, the variation of temperature was considered to affect the mechanical properties of BFRP, since their composition was based on polymeric material. Moreover, commercial finite element analysis platform ABAQUS was used to model and analyze this infill panel system. Consequently, results of the analyses show that the overall performance of BFRP panel had a 15% increase compared to that of GFRP infill panel system. However, the variation of buckling load in terms of temperature for the BFRP system showed a more sensitive nature compared to those of GFRP system.

Keywords: Basalt Fiber Reinforced Polymer, Buckling performance, numerical simulation, temperature dependent materials.

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Authors: Keonwoo Kim, Dowon Hong, Kyoil Chung, Jae-Cheol Ryou

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Cell phone forensics to acquire and analyze data in the cellular phone is nowadays being used in a national investigation organization and a private company. In order to collect cellular phone flash memory data, we have two methods. Firstly, it is a logical method which acquires files and directories from the file system of the cell phone flash memory. Secondly, we can get all data from bit-by-bit copy of entire physical memory using a low level access method. In this paper, we describe a forensic tool to acquire cell phone flash memory data using a logical level approach. By our tool, we can get EFS file system and peek memory data with an arbitrary region from Korea CDMA cell phone.

Keywords: Forensics, logical method, acquisition, cell phone, flash memory.

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Authors: Novi Khila Firani, Elisa Nesdyaningtyas

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Kwashiorkor is one of nutritional problem in Indonesia, which lead to decrease immune system. This condition causes susceptibility to infectious disease, especially tuberculosis. Development of new tuberculosis vaccine will be an important strategy to eliminate tuberculosis in kwashiorkor. Previous research showed that 38-kDa Mycobacterium tuberculosis protein is one of the potent immunogen. However, the role of oral immunization with 38- kDa Mycobacterium tuberculosis protein to the number of lymphocytes in the rat model of kwashiorkor is still unknown. We used kwashiorkor rat model groups with 4% and 2% low protein diet. Oral immunization with 38-kDa Mycobacterium tuberculosis protein given with 2 booster every week. The lymphocytes number were measured by flowcytometry. There was no significant difference between the number of lymphocytes in the normal rat group and the kwashiorkor rat groups. It may reveal the role of 38-kDa Mycobacterium tuberculosis protein as a potent immunogen that can increase the lymphocytes number from kwashiorkor rat model same as normal rat.

Keywords: kwashiorkor rat, lymphocytes, 38-kDa Mycobacterium tuberculosis protein

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Authors: T. V. S. Sekhar, B. Hema Sundar Raju

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Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.

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Authors: Seyedehzahra Mirrahimi, Nik Lukman Nik Ibrahim, M. Surat

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This paper investigated the impact of ceiling height and window head heights variation on daylighting inside architectural teaching studio with a full width window. In architectural education, using the studio is more than normal classroom in most credit hours. Therefore, window position, size and dimension of studio have direct influence on level of daylighting. Daylighting design is a critical factor that improves student learning, concentration and behavior, in addition to these, it also reduces energy consumption. The methodology of analysis involves using Radiance in IES software under overcast and cloudy sky in Malaysia. It has been established that presentation of daylighting of architecture studio can be enhanced by changing the ceiling heights and window level, because, different ceiling heights and window head heights can contribute to different range of daylight levels.

Keywords: Ceiling height, window head height, daylighting, studio architecture, simulation.

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Authors: Naoya Ozaki, Takuya Watanabe, Ryosuke Matsumoto, Noriko Fukasawa

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In the metropolitan areas in Japan, in many stations, shopping areas are set up, and escalators and elevators are installed to make the stations be barrier-free. Further, many areas around the stations are being redeveloped. Railway business operators want to know how much effect these circumstances have on attractiveness of the station or number of passengers using the station. So, we performed a questionnaire survey of the station users in the metropolitan areas for finding factors to affect the attractiveness of stations. Then, based on the analysis of the survey, we developed a method to quantitatively evaluate attractiveness of the stations. We also developed an estimation method for number of passengers based on combination of attractiveness of the station quantitatively evaluated and the residential and labor population around the station. Then, we derived precise linear regression models estimating the attractiveness of the station and number of passengers of the station.

Keywords: Attractiveness of the station, estimation method, number of passengers of the station, redevelopment around the station, renovation of the station.

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Authors: Hyun Bae Jin, Myung Jin Kim, Wui Jun Chung

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The impeller and the casing are the key components of a centrifugal pump. Although there have been many studies on the impeller and the volute casing of centrifugal pump, further study of the volute casing to improve the performance of centrifugal pumps is needed. In this paper, the effect of cross-sectional area on the performance of volute casing was investigated using a commercial CFD code. The performance characteristics, not only at the off-design point but also for a full type model are required these days. So we conducted numerical analysis for all operating points by using complete geometry through transient analysis. Transient analysis on the complete geometry of a real product has the advantage of simulating realistic flow. The results of this study show the variation of a performance curve by modifying the above-mentioned design parameter.

Keywords: Centrifugal Pump, Volute Casing, Cross-Section area, CFD

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Authors: Sanjib Kr Pal, S. Bhattacharyya

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Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.

Keywords: Entropy generation, mixed convection, conjugate heat transfer, numerical, nanofluid, wall waviness.

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Authors: Nien-Zheng Yew, Kung-Ming Tiong, Su-Ting Yong

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Number Link is a Japanese logic puzzle where pairs of same numbers are connected using lines. Number Link can be regarded as a dynamic multiple travelers, multiple entries and exits maze, where the walls and passages are dynamically changing as the travelers move. In this paper, we apply the Tremaux’s algorithm to solve Number Link puzzles of size 8x8, 10x10 and 15x20. The algorithm works well and produces a solution for puzzles of size 8x8 and 10x10. However, solving a puzzle of size 15x20 requires high computer processing power and is time consuming.

Keywords: Number Link, maze, puzzle, Tremaux’s algorithm

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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: Wei-Lun Hsu, Mon-Jyh Lin, Jyh-Ping Hsu

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The dissolution of spherical particles in liquids is analyzed dynamically. Here, we consider the case the dissolution of solute yields a solute-free solid phase in the outer portion of a particle. As dissolution proceeds, the interface between the undissolved solid phase and the solute-free solid phase moves towards the center of the particle. We assume that there exist two resistances for the diffusion of solute molecules: the resistance due to the solute-free portion of the particle and that due to a surface layer near solid-liquid interface. In general, the equation governing the dynamic behavior of dissolution needs to be solved numerically. However, analytical expressions for the temporal variation of the size of the undissoved portion of a particle and the variation of dissolution time can be obtained in some special cases. The present analysis takes the effect of variable bulk solute concentration on dissolution into account.

Keywords: dissolution of particles, surface layer, shrinking core model, dissolution time.

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Authors: A. Ameur, B. Mokhtari, N. Essounbouli, L. Mokrani

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This paper presents a speed sensorless direct torque control scheme using space vector modulation (DTC-SVM) for permanent magnet synchronous motor (PMSM) drive based a Model Reference Adaptive System (MRAS) algorithm and stator resistance estimator. The MRAS is utilized to estimate speed and stator resistance and compensate the effects of parameter variation on stator resistance, which makes flux and torque estimation more accurate and insensitive to parameter variation. In other hand the use of SVM method reduces the torque ripple while achieving a good dynamic response. Simulation results are presented and show the effectiveness of the proposed method.

Keywords: MRAS, PMSM, SVM, DTC, Speed and Resistance estimation, Sensorless drive

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Authors: J.Morris, D.Allinson, J.Harrison, K.J. Lomas

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The UK Government has emphasized the role of Local Authorities as a key player in its flagship residential energy efficiency strategies, by identifying and targeting areas for energy efficiency improvements. Residential energy consumption in England is characterized by significant geographical variation in energy demand, which makes centralized targeting of areas for energy efficiency intervention difficult. This paper draws on research which aims to understand how demographic, social, economic, urban form and climatic factors influence the geographical variations in English residential gas consumption. The paper reports the findings of a multiple regression model that shows how 64% of the geographical variation in residential gas consumption is accounted for by variations in these factors. Results from this study, after further refinement and validation, can be used by Local Authorities to identify areas within their boundaries that have higher than expected gas consumption, these may be prime targets for energy efficiency initiatives.

Keywords: UK Housing, Heating Energy, Socio-Economics, Statistical Modelling

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Authors: M. R. Naghavi, S. Rashidi Monfared, A. H. Ahkami, M. A. Ombidbakhsh

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Knowledge of patterns of genetic diversity enhances the efficiency of germplasm conservation and improvement. In this study 96 Iranian landraces of Triticum turgidum originating from different geographical areas of Iran, along with 18 durum cultivars from ten countries were evaluated for variation in morphological and high molecular weight glutenin subunit (HMW-GS) composition. The first two principal components clearly separated the Iranian landraces from cultivars. Three alleles were present at the Glu-A1 locus and 11 alleles at Glu-B1. In both cultivars and landraces of durum wheat, the null allele (Glu-A1c) was observed more frequently than the Glu-A1a and Glu-A1b alleles. Two alleles, namely Glu-B1a (subunit 7) and Glu-B1e (subunit 20) represented the more frequent alleles at Glu-B1 locus. The results showed that the evaluated Iranian landraces formed an interesting source of favourable glutenin subunits that might be very desirable in breeding activities for improving pasta-making quality.

Keywords: Triticum turgidum var. durum, glutenin subunits, morphological characters.

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Authors: Liu Shu, Dong Shangjia

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Our goal is to effectively increase the number of boats in the river during a six month period. The main factors of determining the number of boats are duration and “select the priority trip". In the microcosmic simulation model, the best result is 4 to 24 nights with DSCF, and the number of boats is 812 with an increasing ratio of 9.0% related to the second best result. However, the number of boats is related to 31.6% less than the best one in 6 to 18 nights with FCFS. In the discrete duration model, we get from 6 to 18 nights, the numbers of boats have increased to 848 with an increase ratio of 29.7% than the best result in model I for the same time range. Moreover, from 4 to 24 nights, the numbers of boats have increase to 1194 with an increase ratio of 47.0% than the best result in model I for the same time range.

Keywords: Discrete duration model, “select the priority trip”, microcosmic simulation model.

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Authors: Sukhbaatar Dorj, Erdenebaatar Altangerel

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As alternative to existing e-government measuring models, here proposed a new customer centric, service oriented, simple approach for measuring countries e-Governments. If successfully implemented, built infrastructure will provide a single egovernment index number for countries. Main schema is as follows. Country CIO or equal position government official, at the beginning of each year will provide to United Nations dedicated web site 4 numbers on behalf of own country: 1) Ratio of available online public services, to total number of public services, 2) Ratio of interagency inter ministry online public services to total number of available online public services, 3) Ratio of total number of citizen and business entities served online annually to total number of citizen and business entities served annually online and physically on those services, 4) Simple index for geographical spread of online served citizen and business entities. 4 numbers then combined into one index number by mathematical Average function. In addition to 4 numbers 5th number can be introduced as service quality indicator of online public services. If in ordering of countries index number is equal, 5th criteria will be used. Notice: This approach is for country’s current e-government achievement assessment, not for e-government readiness assessment.

Keywords: Countries e-government index, e-government, infrastructure for measuring e-government, measuring e-government.

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Authors: John M. Ikome, Martha E. Ikome, Therese Van Wyk

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Productivity optimization of a company can significantly increase the company’s output and productivity which can be in the form of corrective actions of ineffective activities, process simplification, and reduction of variations, responsiveness, and reduction of set-up-time which are all under the classification of waste within the manufacturing environment. Deriving a means to eliminate a number of these issues has a key importance for manufacturing organization. This paper focused on a number of industrial engineering techniques which include a cause and effect diagram, to identify and optimize the method or systems being used. Based on our results, it shows that there are a number of variations within the production processes that can significantly disrupt the expected output.

Keywords: Optimization, fishbone diagram, productivity.

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Authors: Ghaleb Y. Abbasi, Sufyan Al-Mrayat

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This study examined the contribution of 36 factors to building construction project’s cost overrun in Jordan. A questionnaire was distributed to a random sample of 350 stakeholders comprised of owners, consultants, and contractors, of which 285 responded. SPSS analysis was conducted to identify the top five causes of cost overrun, which were a large number of variation orders, inadequate quantities provided in the contract, misunderstanding of the project plan, incomplete bid documents, and choosing the lowest price in the contract bidding. There was an agreement among the study participants in ranking the factors contributing to cost overrun, which indicated that these factors were very commonly encountered in most construction projects in Jordan. Thus, it is crucial to enhance the collaboration among the different project stakeholders to understand the project’s objectives and set a realistic plan that takes into consideration all the factors that might influence the project cost, which might eventually prevent cost overrun.

Keywords: Cost, overrun, building construction projects, Jordan.

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Authors: Hassan Faraji Baghtash

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In this paper, a low voltage high performance current mirror is presented. Its most important specifications, which are improved in this work, are analyzed and formulated proving that it has such outstanding merits as: Very low input resistance of 26mΩ, very wide current dynamic range of 8 decades from 10pA to 1mA (160dB) together with an extremely low current copy error of less than 0.6ppm, and very low input and output voltages. Furthermore, the proposed current mirror bandwidth is 944MHz utilizing very low power consumption (267μW) and transistors count. HSPICE simulation results are performed using TSMC 0.18μm CMOS technology utilizing 1.8V single power supply, confirming the theoretically proved outstanding performance of the proposed current mirror. Monte Carlo simulation of its most important parameter is also examined showing its sufficiently resistance against technology process variations.

Keywords: Current mirror/source, high accuracy, low voltage, wide dynamic range.

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Authors: Sadi Vural, Hiromi Tomii, Hironori Yamauchi

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As the development of digital technology is increasing, Digital cinema is getting more spread. However, content copy and attack against the digital cinema becomes a serious problem. To solve the above security problem, we propose “Additional Watermarking" for digital cinema delivery system. With this proposed “Additional watermarking" method, we protect content copyrights at encoder and user side information at decoder. It realizes the traceability of the watermark embedded at encoder. The watermark is embedded into the random-selected frames using Hash function. Using it, the embedding position is distributed by Hash Function so that third parties do not break off the watermarking algorithm. Finally, our experimental results show that proposed method is much better than the convenient watermarking techniques in terms of robustness, image quality and its simple but unbreakable algorithm.

Keywords: Decoder, Digital content, JPEG2000 Frame, System-On-Chip and additional watermark.

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Authors: Oznur Korukcu, Kamile Kukulu, Mehmet Z. Firat

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The propose of this study is to investigate the factor structures of the W-DEQ, originally developed on UK and Swedish women, were confirmed in Turkish samples, and to obtain a new modified factor structure appropriate to Turkish culture. Statistical analyses of the data obtained were performed using SPSS© for Windows version 13.0 and the SAS statistical software Version 9.1. Both confirmatory and exploratory factor analysis of W-DEQ were performed in the study. Factor analysis yielded four factors related to hope, fear, lack of positive anticipation and riskiness. The alpha estimates of the total W-DEQ score were somewhat higher, being 0.92 for the parous and 0.90 for the nulliparous sample. These are well above the accepted limit of 0.70 and indicate excellent levels of internal reliability, thus showing that the questions were appropriate to the Turkish culture and useful scale for the evaluation of fear of childbirth in Turkish pregnants.

Keywords: Confirmatory factor analysis, cross-cultural research, exploratory factor analysis, fear of childbirth.

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Authors: Laura Gjyli, Pirro Prifti, Lindita Mukli, Silvana Gjyli, Irida Ikonomi, Jerina Kolitari

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Microbial air contamination of the outdoor air in Marine Durres-s Harbour (Durres, Albania) was estimated by sedimentation technique in August-October 2008. The sampling areas were: Ferry Terminal (FT), Fishery Harbor (FH), East Zone (EZ), Fuel Quay (FQ) and Apollonian Beach (AB). The aim of this study was to measure the number of aerobic plate count (mesophilic aerobic bacteria) and fungi (yeasts and molds) in the outdoor air in these areas. The number of colonies that were formed determines the number of cells at the moment in the outdoor air; respectively the number of mesophilic aerobic bacteria and yeasts and molds. The measure of bacteria and fungi used is CFU (Colony Forming Units) per Petri dish. It is said that marine harbours are very polluted areas. The aim of study was the definition of mesophilic aerobic bacteria and yeasts and molds number, and the comparison of microorganisms number in air sampling areas.

Keywords: Air microbiology, colony forming units, Marine Durres's Harbour, mesophilic aerobic bacteria, outdoor air, yeasts and molds.

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Authors: Sadi Vural, Hiromi Tomii, Hironori Yamauchi

Abstract:

As far as the latest technological improvements are concerned, digital systems more become popular than the past. Despite this growing demand to the digital systems, content copy and attack against the digital cinema contents becomes a serious problem. To solve the above security problem, we propose “traceable watermarking using Hash functions for digital cinema system. Digital Cinema is a great application for traceable watermarking since it uses watermarking technology during content play as well as content transmission. The watermark is embedded into the randomly selected movie frames using CRC-32 techniques. CRC-32 is a Hash function. Using it, the embedding position is distributed by Hash Function so that any party cannot break off the watermarking or will not be able to change. Finally, our experimental results show that proposed DWT watermarking method using CRC-32 is much better than the convenient watermarking techniques in terms of robustness, image quality and its simple but unbreakable algorithm.

Keywords: Decoder, Digital content, JPEG2000 Frame, System-On-Chip, traceable watermark, Hash Function, CRC-32.

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Authors: A. Szabó Nagy, J. Szabó, Zs. Csanádi, J. Erdős

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The main objective of this study was to assess the seasonal variation of atmospheric polycyclic aromatic hydrocarbon (PAH) concentrations associated with PM10 in an urban site of Győr, Hungary. A total of 112 PM10 aerosol samples were collected in the years of 2012 and 2013 and analyzed for PAHs by gas chromatography method. The total PAH concentrations (sum of the concentrations of 19 individual PAH compounds) ranged from 0.19 to 70.16 ng/m3 with the mean value of 12.29 ng/m3. Higher concentrations of both total PAHs and benzo[a]pyrene (BaP) were detected in samples collected in the heating seasons. Using BaPequivalent potency index on the carcinogenic PAH concentration data, the local population appears to be exposed to significantly higher cancer risk in the heating seasons. However, the comparison of the BaP and total PAH concentrations observed for Győr with other cities it was found that the PAH levels in Győr generally corresponded to the EU average.

Keywords: Air quality, benzo[a]pyrene, PAHs, polycyclic aromatic hydrocarbons.

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Authors: Chen Chou, Feng-Tyan Lin

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Big Data has been attracted a lot of attentions in many fields for analyzing research issues based on a large number of maternal data. Electronic Toll Collection (ETC) is one of Intelligent Transportation System (ITS) applications in Taiwan, used to record starting point, end point, distance and travel time of vehicle on the national freeway. This study, taking advantage of ETC big data, combined with urban planning theory, attempts to explore various phenomena of inter-city transportation activities. ETC, one of government's open data, is numerous, complete and quick-update. One may recall that living area has been delimited with location, population, area and subjective consciousness. However, these factors cannot appropriately reflect what people’s movement path is in daily life. In this study, the concept of "Living Area" is replaced by "Influence Range" to show dynamic and variation with time and purposes of activities. This study uses data mining with Python and Excel, and visualizes the number of trips with GIS to explore influence range of Tainan city and the purpose of trips, and discuss living area delimited in current. It dialogues between the concepts of "Central Place Theory" and "Living Area", presents the new point of view, integrates the application of big data, urban planning and transportation. The finding will be valuable for resource allocation and land apportionment of spatial planning.

Keywords: Big Data, ITS, influence range, living area, central place theory, visualization.

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Authors: Kazuyoshi Mori

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In this paper, we consider the parametrization of the discrete-time systems without the unit-delay element within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters. We consider single-input single-output systems in this paper. By the investigation, we find, on the discrete-time systems without the unit-delay element, three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: Linear systems, parametrization, Coprime Factorization, number of parameters.

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Authors: R. M. Kashim

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The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: Conceptual knowledge, primary school teachers, procedural knowledge, rational numbers.

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Authors: Wongsakorn Charoenpanitseri

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The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: Total colorings, the total chromatic number, 3-degenerated.

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