Search results for: line sleeve

Authors: Sanjeev Kumar Appicharla

Abstract:

This paper presents the results of the modelling and analysis of the European Railway Traffic Management (ERTMS) safety critical incident to raise awareness of biases in systems engineering process on the Cambrian Railway in the UK using the RAIB 17/2019 as a primary input. The RAIB, the UK independent accident investigator, published the Report- RAIB 17/2019 giving the details of their investigation of the focal event in the form of immediate cause, causal factors and underlying factors and recommendations to prevent a repeat of the safety-critical incident on the Cambrian Line. The Systems for Investigation of Railway Interfaces (SIRI) is the Methodology used to model and analyse the safety-critical incident. The SIRI Methodology uses the Swiss Cheese Model to model the incident and identify latent failure conditions (potentially less than adequate conditions) by means of the Management Oversight and Risk Tree technique. The benefits of the SIRI Methodology are threefold: first is that it incorporates “Heuristics and Biases” approach, in the Management Oversight and Risk Tree technique to identify systematic errors. Civil engineering and programme management railway professionals are aware of role “optimism bias” plays in programme cost overruns and are aware of bow tie (fault and event tree) model-based safety risk modelling technique. However, the role of systematic errors due to “Heuristics and Biases” is not appreciated as yet. This overcomes the problems of omission of human and organisational factors from accident analysis. Second, the scope of the investigation includes all levels of the socio-technical system, including government, regulatory, railway safety bodies, duty holders, signalling firms and transport planners, and front-line staff such that lessons learned at the decision making and implementation level as well. Third, the author’s past accident case studies are supplemented with research pieces of evidence drawn from the practitioner’s and academic researchers’ publications as well. This is to discuss the role of system thinking to improve the decision making and risk management processes and practices in the IEC 15288 Systems Engineering standard, and in the industrial context such as the GB railways and Artificial Intelligence (AI) contexts as well.

Keywords: Accident analysis, AI algorithm internal audit, bounded rationality, Byzantine failures, heuristics and biases approach.

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Authors: L. Novakova-Marcincinova, J. Novak-Marcincin, M. Janak

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The computer aided for design, analysis, control, visualization and simulation of robotized workcells is very interesting in this time. Computer Aided Robot Control (CARC) is a subsystem of the system CIM including the computer aided systems of all activities connected with visualization and working of robotized workcells. There are three basic ideas: current CAD/CAM/CAE systems for design and 3D visualization, special PC based control and simulation systems and Augmented Reality Aided Manufacturing (ARAM) systems. This paper describes example of Open Source software application that can to be utilized at planning of the robotized workcells, visualization and off-line programming the automated processes realized by authors.

Keywords: Intelligent control, augmented reality, robot.

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Authors: Norma Rodrigues Gomes

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This paper presents initiatives of Knowledge Management (KM) applied to Forensic Sciences field, especially developed at the Forensic Science Institute of the Brazilian Federal Police. Successful projects, related to knowledge sharing, drugs analysis and environmental crimes, are reported in the KM perspective. The described results are related to: a) the importance of having an information repository, like a digital library, in such a multidisciplinary organization; b) the fight against drug dealing and environmental crimes, enabling the possibility to map the evolution of crimes, drug trafficking flows, and the advance of deforestation in Amazon rain forest. Perspectives of new KM projects under development and studies are also presented, tracing an evolution line of the KM view at the Forensic Science Institute.

Keywords: Business Intelligence, Digital Library, Forensic Science, Knowledge Management

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Authors: Azah Kamilah Muda, Siti Mariyam Shamsuddin, Maslina Darus

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Writer identification is one of the areas in pattern recognition that attract many researchers to work in, particularly in forensic and biometric application, where the writing style can be used as biometric features for authenticating an identity. The challenging task in writer identification is the extraction of unique features, in which the individualistic of such handwriting styles can be adopted into bio-inspired generalized global shape for writer identification. In this paper, the feasibility of generalized global shape concept of complimentary binding in Artificial Immune System (AIS) for writer identification is explored. An experiment based on the proposed framework has been conducted to proof the validity and feasibility of the proposed approach for off-line writer identification.

Keywords: Writer identification, generalized global shape, individualistic, pattern recognition.

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Authors: Alexandra Gheorghiu, Marie-Line Félonneau

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Speeding represents one of the main concerns for road safety and it still is a subject for research. The need to address this problem and to understand why drivers over speed increases especially in Romania, where in 2011, speed was the main cause of car accidents. This article addresses this problem by using the theory of planned behaviour. A questionnaire was administered to a sample of young Romanian drivers (18 to 25 years) and several path analyses were made in order to verify if the model proposed by the theory of planned behaviour fits the data. One interesting result is that perceived behavioural control does not predict the intention to speed or self-reported driving speed, but subjective norms do. This implies that peers and social environment have a greater impact on young Romanian drivers than we thought.

Keywords: Speed, traffic safety, theory of planned behaviour, young drivers.

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Authors: Tlotlollo Sidwell Hlalele, Shengzhi Du

Abstract:

High-voltage power transmission lines are the back bone of electrical power utilities. The stability and continuous monitoring of this critical infrastructure is pivotal. Nine-Sigma representing Eskom Holding SOC limited, South Africa has a major problem on proactive detection of fallen power lines and real time sagging measurement together with slipping of such conductors. The main objective of this research is to innovate RFID technology to solve this challenge. Various options and technologies such as GPS, PLC, image processing, MR sensors and etc., have been reviewed and draw backs were made. The potential of RFID to give precision measurement will be observed and presented. The future research will look at magnetic and electrical interference as well as corona effect on the technology.

Keywords: Precision Measurement, RFID and Sag.

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Authors: A. Zanj, F. He

Abstract:

In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: Multi-physical domain, conduction model, port-based modeling, dynamic interaction, physical modeling.

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Authors: Mohd Azman Abdul Latif, Erwan Basiron

Abstract:

A flaw or drift from expected operational performance in one component (NAND, PMIC, controller, DRAM, etc.) may affect the reliability of the entire Solid State Drive (SSD) system. Therefore, it is important to ensure the required quality of each individual component through qualification testing specified using standards or user requirements. Qualification testing is time-consuming and comes at a substantial cost for product manufacturers. A highly technical team, from all the eminent stakeholders is embarking on reliability prediction from beginning of new product development, identify critical to reliability parameters, perform full-blown characterization to embed margin into product reliability and establish control to ensure the product reliability is sustainable in the mass production. The paper will discuss a comprehensive development framework, comprehending SSD end to end from design to assembly, in-line inspection, in-line testing and will be able to predict and to validate the product reliability at the early stage of new product development. During the design stage, the SSD will go through intense reliability margin investigation with focus on assembly process attributes, process equipment control, in-process metrology and also comprehending forward looking product roadmap. Once these pillars are completed, the next step is to perform process characterization and build up reliability prediction modeling. Next, for the design validation process, the reliability prediction specifically solder joint simulator will be established. The SSD will be stratified into Non-Operating and Operating tests with focus on solder joint reliability and connectivity/component latent failures by prevention through design intervention and containment through Temperature Cycle Test (TCT). Some of the SSDs will be subjected to the physical solder joint analysis called Dye and Pry (DP) and Cross Section analysis. The result will be feedbacked to the simulation team for any corrective actions required to further improve the design. Once the SSD is validated and is proven working, it will be subjected to implementation of the monitor phase whereby Design for Assembly (DFA) rules will be updated. At this stage, the design change, process and equipment parameters are in control. Predictable product reliability at early product development will enable on-time sample qualification delivery to customer and will optimize product development validation, effective development resource and will avoid forced late investment to bandage the end-of-life product failures. Understanding the critical to reliability parameters earlier will allow focus on increasing the product margin that will increase customer confidence to product reliability.

Keywords: e2e reliability prediction, SSD, TCT, Solder Joint Reliability, NUDD, connectivity issues, qualifications, characterization and control.

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Authors: José L. Jiménez

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The use of technology in the classroom is an issue that is constantly evolving. Digital age students learn differently than their teachers did, so now the teacher should be constantly evolving their methods and teaching techniques to be more in touch with the student. In this paper a case study presents how were used some of these technologies by accompanying a classroom course, this in order to provide students with a different and innovative experience as their teacher usually presented the activities to develop. As students worked in the various activities, they increased their digital skills by employing unknown tools that helped them in their professional training. The twenty-first century teacher should consider the use of Information and Communication Technologies in the classroom thinking in skills that students of the digital age should possess. It also takes a brief look at the history of distance education and it is also highlighted the importance of integrating technology as part of the student's training.

Keywords: Digital tools, on-line learning, social networks, technology.

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Authors: R. Nandikeswari, M. Sambasivam, V. Anandan

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In the present study fecundity of Terapon jarbua was estimated for 41 matured females from the Bay of Bengal, Pondicherry. The fecundity (F) was found to range from 13,475 to 115,920 in fishes between 173-278mm Total length (TL) and 65- 298 gm weight respectively. The co-efficient of correlation for F/TL (log F = - 4.821 + 4.146 log TL), F/SL (log F = -3.936 + 3.867 log SL), F/WF (log F = 1.229 + 0.730 log TW) and F/GW (log F = 0.724 + 1.113 log GW) were obtained as 0.474, 0.537, 0.641 and 0.908 respectively. The regression line for the TL, SL, WF and GW of the fishes were found to be linear when they were plotted against their fecundity on logarithmic scales. Highly significant (P<0.01) relationship was obtained for all the variables. Hence Total Length, Standard Length, Weight of Fish and Gonad Weight were found to be the best indicators of the fecundity of Terapon jarbua. Gonadosomatic indices of Terapon jarbua showed that the spawning took place in February to July. The overall sex ratio of male to female is 1.28:1 with chi-square value 5.719, significant at 5% level.

Keywords: Fecundity, Gonadosomatic index, Reproductive biology, spawning, Terapon jarbua.

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Authors: Zhang Yu, Ding Yi

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The discussion about elements of cultural heritage and their relevance among the ancient villages is comparably insufficient. The protection work is strongly influenced by touristic development and cultural gimmick, resulting in low protection efficiency and many omissions. Historical villages as the cultural settlement patterns bear a large number of heritage relics. They were regionally scattered with a clear characteristic of gathering. First of all, this study proposes the association and similarities of the forming mechanism between four historic cultural villages in Mian Mountain. Secondly, the study reveals that these villages own the strategic pass, underground passage, and the mountain barrier. Thirdly, based on the differentiated characteristics of villages’ space, the study discusses about the integrated conservation from three levels: the regional heritage conservation, the cultural line shaping, and the featured brand building.

Keywords: Mian Mountain, fortress, historical villages, conservation.

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Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

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This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Ruchika, Munish Vashisht, S. Qamar

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Detection of small ship is crucial task in many automatic surveillance systems which are employed for security of maritime boundaries of a country. To address this problem, image de-noising is technique to identify the target ship in between many other ships in the sea. Image de-noising technique needs to extract the ship’s image from sea background for the analysis as the ship’s image may submerge in the background and flooding waves. In this paper, a noise filter is presented that is based on fuzzy linguistic ‘most’ quantifier. Ordered weighted averaging (OWA) function is used to remove salt-pepper noise of ship’s image. Results obtained are in line with the results available by other well-known median filters and OWA based approach shows better performance.

Keywords: Linguistic quantifier, impulse noise, OWA filter, median filter.

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Authors: Jong-Ian Tsai, Chi-Chuan Chen, Tung-Sheng Zhan, Rong-Ching Wu

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Single-pole switching scheme is widely used in the Extra High Voltage system. However, the substantial negativesequence current injected to the turbine-generators imposes the electromagnetic (E/M) torque of double system- frequency components during the dead time (between single-pole clearing and line reclosing). This would induce supersynchronous resonance (SPSR) torque amplifications on low pressure turbine generator blades and even lead to fatigue damage. This paper proposes the design of a mechanical filter (MF) with natural frequency close to double-system frequency. From the simulation results, it is found that such a filter not only successfully damps the resonant effect, but also has the characteristics of feasibility and compact.

Keywords: Single-pole, Supersynchronous, Blade, Unbalance, filter

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Authors: Hongjun Liu, Cunxiao Gao, Jintao Tao, Wei Zhao, Yishan Wang

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A compact tunable 10 W picosecond source based on Yb-doped fiber amplification of gain switch laser diode has been demonstrated. A gain switch semiconductor laser diode was used as the seed source, and a multi-stage single mode Yb-doped fiber preamplifier was combined with two large mode area double-clad Yb-doped fiber main amplifiers to construct the amplification system. The tunable pulses with high stability and excellent beam quality (M2<1.2) of 10 W average power 150 ps pulse duration at 1 MHz repetition rate were obtained. The central wavelength with the line width of 2.5-3 nm was tunable from 1053 nm to 1073 nm.

Keywords: Fiber laser, fiber amplifier, picosecond laser, highpower laser

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Authors: Raquel P. F. Guiné, Daniela V. T. A. Costa, Paula M. R. Correia, Moisés Castro, Luis T. Guerra, Cristina A. Costa

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The aim of this work was to characterize a potential target group of people interested in participating into a training program in organic farming in the context of mobile-learning. The information sought addressed in particular, but not exclusively, possible contents, formats and forms of evaluation that will contribute to define the course objectives and curriculum, as well as to ensure that the course meets the needs of the learners and their preferences. The sample was selected among different European countries. The questionnaires were delivered electronically for answering on-line and in the end 135 consented valid questionnaires were obtained. The results allowed characterizing the target group and identifying their training needs and preferences towards m-learning formats, giving valuable tools to design the training offer.

Keywords: Mobile-learning, organic farming, rural development, survey.

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Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: Shiva Abdoli, Daniel T. Semere

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Several researches have been conducted to study consumption of energy in cutting process. Most of these researches are focusing to measure the consumption and propose consumption reduction methods. In this work, the relation between the cutting parameters and the consumption is investigated in order to establish a generalized energy consumption model that can be used for process and production planning in real production lines. Using the generalized model, the process planning will be carried out by taking into account the energy as a function of the selected process parameters. Similarly, the generalized model can be used in production planning to select the right operational parameters like batch sizes, routing, buffer size, etc. in a production line. The description and derivation of the model as well as a case study are given in this paper to illustrate the applicability and validity of the model.

Keywords: Process parameters, cutting process, energy efficiency, Material Removal Rate (MRR).

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Authors: Faten A. Khorshid

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Breast cancer is the most common malignancy in the world among women. Many therapies have been designed to treat this disease. Mamectomy, chemotherapy and radiotherapy are still the main therapies of breast cancer. However, the results were unsatisfactory and still far from the ideal treatment. PM 701is a natural product, has anticancer activity. The bioactive fraction PMF and subfraction PMFK had been isolated from PM701. PM 701 and its fractions were proved to have a cytotoxic properties against different cancer cell lines. This article is directed for the further examination of lyophilized PM701 and its active fractions on the growth of breast cancer cells (MCF-7). PM 701, PMF or PMFK were adding to the cultural medium, where MCF-7 is incubated. PM 701, PMF or PMFK were able to inhibit significantly the proliferation of MCF-7 cells, Moreover these new agents were proved to induce apoptosis of the breast cancer cells; through its direct effect on the nuclei.

Keywords: Anticancer agent, breast carcinoma, MCF-7 cell line, PM 701

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Authors: Sezen Yildirim, Tahir Çetin Akinci, Serhat Seker, Nazmi Ekren

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Ferroresonance is an electrical phenomenon in nonlinear character, which frequently occurs in power system due to transmission line faults and single or more-phase switching on the lines as well as usage of the saturable transformers. In this study, the ferroresonance phenomena are investigated under the modeling of the West Anatolian Electric Power Network of 380 kV in Turkey. The ferroresonance event is observed as a result of removing the loads at the end of the lines. In this sense, two different cases are considered. At first, the switching is applied at 2nd second and the ferroresonance affects are observed between 2nd and 4th seconds in the voltage variations of the phase-R. Hence the ferroresonance and nonferroresonance parts of the overall data are compared with each others using the Fourier transform techniques to show the ferroresonance affects.

Keywords: Ferroresonance, West Anatolian Electric Power System, Power System Modeling, Switching, Spectral Analysis.

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Authors: Hadi Adibi-Asl, Alireza Doosthosseini, Amir Taghavipour

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This paper studies the design of an adaptive control strategy to tune an active steering system for better drivability and maneuverability. In the first step, adaptive control strategy is applied to estimate the uncertain parameters on-line (e.g. cornering stiffness), then the estimated parameters are fed into the pole placement controller to generate corrective feedback gain to improve the steering system dynamic’s characteristics. The simulations are evaluated for three types of road conditions (dry, wet, and icy), and the performance of the adaptive pole placement control (APPC) are compared with pole placement control (PPC) and a passive system. The results show that the APPC strategy significantly improves the yaw rate and side slip angle of a bicycle plant model.

Keywords: Adaptive control, active steering, pole placement, vehicle dynamics.

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Authors: Komlan Sedzro

Abstract:

We apply the non-parametric, unconditional, hyperbolic order-α quantile estimator to appraise the relative efficiency of Microfinance Institutions in Africa in terms of outreach. Our purpose is to verify if these institutions, which must constantly try to strike a compromise between their social role and financial sustainability are operationally efficient. Using data on African MFIs extracted from the Microfinance Information eXchange (MIX) database and covering the 2004 to 2006 periods, we find that more efficient MFIs are also the most profitable. This result is in line with the view that social performance is not in contradiction with the pursuit of excellent financial performance. Our results also show that large MFIs in terms of asset and those charging the highest fees are not necessarily the most efficient.

Keywords: Data envelopment analysis, microfinance institutions, quantile estimation of efficiency, social and financial performance.

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Authors: Manoj Kumar Dutta

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Wavelength Division Multiplexing (WDM) technology is the most promising technology for the proper utilization of huge raw bandwidth provided by an optical fiber. One of the key problems in implementing the all-optical WDM network is the packet contention. This problem can be solved by several different techniques. In time domain approach the packet contention can be reduced by incorporating Fiber Delay Lines (FDLs) as optical buffer in the switch architecture. Different types of buffering architectures are reported in literatures. In the present paper a comparative performance analysis of three most popular FDL architectures are presented in order to obtain the best contention resolution performance. The analysis is further extended to consider the effect of different fiber non-linearities on the network performance.

Keywords: WDM network, contention resolution, optical buffering, non-linearity, throughput.

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Authors: Jasmin Velagic, Nedim Osmic, Bakir Lacevic

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In this paper the neural network-based controller is designed for motion control of a mobile robot. This paper treats the problems of trajectory following and posture stabilization of the mobile robot with nonholonomic constraints. For this purpose the recurrent neural network with one hidden layer is used. It learns relationship between linear velocities and error positions of the mobile robot. This neural network is trained on-line using the backpropagation optimization algorithm with an adaptive learning rate. The optimization algorithm is performed at each sample time to compute the optimal control inputs. The performance of the proposed system is investigated using a kinematic model of the mobile robot.

Keywords: Mobile robot, kinematic model, neural network, motion control, adaptive learning rate.

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Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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Authors: Noor Sulastry Yurni Ahmad , Ki-Soo Eun

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The 2008 Candlelight Protests of Korea was very significant to portray the political environment among the South Korean youth. Many challenges and new advanced technologies have driven the youth community to be engaged in the political arena that has shifted them from traditional Korean youth to a very greater community. Due to historical perspective with the people of North Korea, the young generation has embraced different view of ethnic nationalism. This study examines the youth involvement in politics in line with their level of acceptance the practice of democracy. The increase usage of new media has shown great results in the survey results whereby the youth used as a platform to gain political information and brought higher degree of their sociopolitical interests among them. Furthermore, the rise of nationalism and patriotism will be discussed in this paper to the dynamism of the political approaches used by the Korea government

Keywords: Nationalism, new media, political participation, youth

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Authors: H. Gholami, M. Jalali Azizpour

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Stress Corrosion Crack (SCC) in pipeline is a type of environmentally assisted cracking (EAC), since its discovery in 1965 as a possible cause of failure in pipeline, SCC has caused, on average, one of two failures per year in the U.S, According to the NACE SCC DA a pipe line segment is considered susceptible to SCC if all of the following factors are met: The operating stress exceeds 60% of specified minimum yield strength (SMYS), the operating temperature exceeds 38°C, the segment is less than 32 km downstream from a compressor station, the age of the pipeline is greater than 10 years and the coating type is other than Fusion Bonded Epoxy(FBE). In this paper as a practical experience in NISOC, Direct Assessment (DA) Method is used for identification SCC defect in unpiggable pipeline located downstream of compressor station.

Keywords: Stress Corrosion Crack, Direct Assessment, Disbondment, Transgranular SCC, Compressor Station.

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Authors: Cem Karacal, Sohyung Cho, William Yu

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In metal cutting industries, mathematical/statistical models are typically used to predict tool replacement time. These off-line methods usually result in less than optimum replacement time thereby either wasting resources or causing quality problems. The few online real-time methods proposed use indirect measurement techniques and are prone to similar errors. Our idea is based on identifying the optimal replacement time using an electronic nose to detect the airborne compounds released when the tool wear reaches to a chemical substrate doped into tool material during the fabrication. The study investigates the feasibility of the idea, possible doping materials and methods along with data stream mining techniques for detection and monitoring different phases of tool wear.

Keywords: Tool condition monitoring, cutting tool replacement, data stream mining, e-Nose.

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Authors: Youssef Chahir, Messaoud Mostefai, Salah Khodja

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This paper presents the development of a 2D visual marker, derived from a recent patented work in the field of numbering systems. The proposed fiducial uses a group of projective invariant straight-line patterns, easily detectable and remotely recognizable. Based on an efficient data coding scheme, the developed marker enables producing a large panel of unique real time identifiers with highly distinguishable patterns. The proposed marker Incorporates simultaneously decimal and binary information, making it readable by both humans and machines. This important feature opens up new opportunities for the development of efficient visual human-machine communication and monitoring protocols. Extensive experiment tests validate the robustness of the marker against acquisition and geometric distortions.

Keywords: visual marker, projective invariants, distance map, level set

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Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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