Search results for: parts
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 796

Search results for: parts

586 Identifying and Prioritizing Goals of Joint Venture between Manufacturing Cooperative Firms, using TOPSIS

Authors: H. Zare Amadabadi, S. Soltani Gerdefaramarzi

Abstract:

In recent years, strategic alliances have taken increasing importance as a means to control competitive forces and to enter into new markets. Joint ventures are one of the most frequently used contractual forms in strategic alliances. There are various motivations for cooperation between two or more firms e.g., accessing to technical know-how, accessing to financial resources and managing risks. The firms must know about these motivations to encourage for establishing joint venture. So, it is important for managers to understand about these motives. On the other hand, the cooperation section is one of the most effective parts in each country. In this way, our study identifies goals of joint venture between cooperative manufacturing firms, and prioritizes those using TOPSIS1. The results show that the most important of joint venture goals are: accessing to managerial know-how, sharing total capital investment.

Keywords: Cooperative, Joint Venture, TOPSIS

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585 Introducing Fast Robot Roller Hemming Process in Automotive Industry

Authors: Babak Saboori, Behzad Saboori, Johan S. Carlson, Rikard Söderberg

Abstract:

As product life cycle becomes less and less every day, having flexible manufacturing processes for any companies seems more demanding. In the assembling of closures, i.e. opening parts in car body, hemming process is the one which needs more attention. This paper focused on the robot roller hemming process and how to reduce its cycle time by introducing a fast roller hemming process. A robot roller hemming process of a tailgate of Saab 93 SportCombi model is investigated as a case study in this paper. By applying task separation, robot coordination, and robot cell configuration principles in the roller hemming process, three alternatives are proposed, developed, and remarkable reduction in cycle times achieved [1].

Keywords: Cell configuration, cycle time, robot coordination, roller hemming.

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584 The Investigation of Crack's Parameters on the V-Notch using Photoelasticity Method

Authors: M. Saravani, M. Azizi,

Abstract:

The V-notches are most possible case for initiation of cracks in parts. The specifications of cracks on the tip of the notch will be influenced via opening angle, tip radius and depth of V-notch. In this study, the effects of V-notch-s opening angle on stress intensity factor and T-stress of crack on the notch has been investigated. The experiment has been done in different opening angles and various crack length in mode (I) loading using Photoelasticity method. The results illustrate that while angle increases in constant crack-s length, SIF and T-stress will decrease. Beside, the effect of V-notch angle in short crack is more than long crack. These V-notch affects are negligible by increasing the length of crack, and the crack-s behavior can be considered as a single-edge crack specimen. Finally, the results have been evaluated with numerical finite element analysis and good agreement was obvious.

Keywords: Photoelasticity, Stress intensity factor, T-stress, V-notch.

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583 Information System for Data Selection and New Information Acquisition for Reconfigurable Multifunctional Machine Tools

Authors: Sasho Guergov

Abstract:

The purpose of the paper is to develop an informationcontrol environment for overall management and self-reconfiguration of the reconfigurable multifunctional machine tool for machining both rotation and prismatic parts and high concentration of different technological operations - turning, milling, drilling, grinding, etc. For the realization of this purpose on the basis of defined sub-processes for the implementation of the technological process, architecture of the information-search system for machine control is suggested. By using the object-oriented method, a structure and organization of the search system based on agents and manager with central control are developed. Thus conditions for identification of available information in DBs, self-reconfiguration of technological system and entire control of the reconfigurable multifunctional machine tool are created.

Keywords: Information system, multifunctional machine tool, reconfigurable machine tool, search system.

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582 Thermodynamic Analysis of an Ejector-Absorption Refrigeration Cycle with Using NH3-H2O

Authors: Samad Jafarmadar, Amin Habibzadeh, Mohammad Mehdi Rashidi, Sayed Sina Rezaei, Abbas Aghagoli

Abstract:

In this paper, the ejector-absorption refrigeration cycle is presented. This article deals with the thermodynamic simulation and the first and second law analysis of an ammonia-water. The effects of parameters such as condenser, absorber, generator, and evaporator temperatures have been investigated. The influence of the various operating parameters on the performance coefficient and exergy efficiency of this cycle has been studied. The results show that when the temperature of different parts increases, the performance coefficient and the exergy efficiency of the cycle decrease, except for evaporator and generator, that causes an increase in coefficient of performance (COP). According to the results, absorber and ejector have the highest exergy losses in the studied conditions.

Keywords: Absorption refrigeration, COP, ejector, exergy efficiency.

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581 A Low Cost Knowledge Base System Framework for Design of Deep Drawing Die

Authors: Vishal Naranje, S. Kumar

Abstract:

In this paper a low cost knowledge base system (KBS) framework is proposed for design of deep drawing die and procedure for developing system modules. The task of building the system is structured into different modules for major activities of design of deep drawing die. A manufacturability assessment module of the proposed framework is developed to check the manufacturability of deep drawn parts. The technological knowledge is represented by using IF- THEN rules and it is coded in AutoLISP language. The module is designed to be loaded into the prompt area of AutoCAD. The cost of implementation of proposed system makes it affordable for small and medium scale sheet metal industries.

Keywords: Knowledge base system, Deep drawing die, Manufacturability, Sheet metal.

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580 Antibacterial Activity of the Chennopodium album Leaves and Flowers Extract

Authors: Leila Amjad, Zohreh Alizad

Abstract:

Recent years have instance that there is a invigoration of interest in drug discovery from medicinal plants for the support of health in all parts of the world . This study was designed to examine the in vitro antimicrobial activities of the flowers and leaves methanolic and ethanolic extracts of Chenopodium album L. Chenopodium album Linn. flowers and leaves were collected from East Esfahan, Iran. The effects of methanolic and ethanolic extracts were tested against 4 bacterial strains by using disc,well-diffusion method. Results showed that flowers and leaves methanolic and ethanolic extracts of C.album don-t have any activity against the selected bacterial strains. Our study has indicated that ,there are effective different factors on antimicrobial properties of plant extracts

Keywords: Chennopodium album, antibacterial activity, extract

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579 Development of User Interface for Multiple Devices Connecting Path Planning System for Bus Network

Authors: Takahiro Takayama, Takao Kawamura, Toshihiko Sasama, Kazunori Sugahara

Abstract:

Recently, web services to access from many type devices are often used. We have developed the shortest path planning system called "Bus-Net" in Tottori prefecture as a web application to sustain the public transport. And it used the same user interface for both devices. To support both devices, the interface cannot use JavaScript and so on. Thus, we developed the method that use individual user interface for each device type to improve its convenience. To be concrete, we defined formats of condition input to the path planning system and result output from it and separate the system into the request processing part and user interface parts that depend on device types. By this method, we have also developed special device for Bus-Net named "Intelligent-Bus-Stop".

Keywords: Bus, Path planning, Public transport, User interface

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578 Hydrological Method to Evaluate Environmental Flow (Case Study: Gharasou River, Ardabil)

Authors: Mehdi Fuladipanah, Mehdi Jorabloo

Abstract:

Water flow management is one of the most important parts of river engineering. Non-uniformity distribution of rainfall and various flow demand with unreasonable flow management will be caused destroyed of river ecosystem. Then, it is very serious to determine ecosystem flow requirement. In this paper, Flow duration curve indices method which has hydrological based was used to evaluate environmental flow in Gharasou River, Ardabil, Iran. Using flow duration curve, Q90 and Q95 for different return periods were calculated. Their magnitude were determined as 1-day, 3-day, 7-day and 30 day. According the second method, hydraulic alteration indices often had low and medium range. In order to maintain river at an acceptable ecological condition, minimum daily discharge of index Q95 is 0.7 m3.s-1.

Keywords: Ardabil, Environmental flow, Flow Duration Curve, Gharasou River.

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577 A Practical Method for Load Balancing in the LV Distribution Networks Case Study: Tabriz Electrical Network

Authors: A. Raminfard, S. M. Shahrtash

Abstract:

In this paper, a new efficient method for load balancing in low voltage distribution systems is presented. The proposed method introduces an improved Leap-frog method for optimization. The proposed objective function includes the difference between three phase currents, as well as two other terms to provide the integer property of the variables; where the latter are the status of the connection of loads to different phases. Afterwards, a new algorithm is supplemented to undertake the integer values for the load connection status. Finally, the method is applied to different parts of Tabriz low voltage network, where the results have shown the good performance of the proposed method.

Keywords: Load balancing, improved leap-frog method, optimization algorithm, low voltage distribution systems.

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576 Order Reduction by Least-Squares Methods about General Point ''a''

Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

Abstract:

The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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575 Discrimination in Primary Education in the Slums of Turkey: Problems about Equity of Education

Authors: Erten Gokce

Abstract:

This study was carried out in Ankara, the capital city of Turkey, in order to determine how people living in the slums of Ankara benefit from educational equality. Within the scope of the research, interviews were made with 64 families whose children have been getting education from the primary schools of these parts and the data of the study was collected by the researcher. The results of the research demonstrate that the children getting education in the slums of Ankara can not experience educational equality and justice. The results of this study show that the opportunities of the schools in the slums of Ankara are very limited, so the individuals in these districts can not equally benefit from the education. The families are aware of the problem they are faced with. KeywordsDiscrimination, inequality, primary education, slums of Turkey.

Keywords: Discrimination, inequality, primary education, slums of Turkey.

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574 Extraction and Analysis of Hypericum perforatum L. from Turkey

Authors: E. Moroydor Derun, Z. Eslek, S. Piskin

Abstract:

Hypericum perforatum L. is a member of the Hypericaceae (Guttiferae) family and commonly known as St. John’s wort. There is a growing interest in this medicinal plant because of the constituents of this genus. A number of species have been shown to possess various biological activities such as antiviral, wound healing, analgesic, hepatoprotective, antimicrobial and antioxidant activities and also have therapeutic effects on burns, bruises, swelling, anxiety and mild to moderate depression. In this study, the aerial parts of Hypericum perforatum L. are extracted and the main and effective constituents are determined. The analysis of the extracts was performed by GC-MS and LC-MS. As a next step, it is aimed to investigate the usage of the main constituents of the medicinal plant.

Keywords: Hypericaceae, Hypericum perforatum L., GC-MS, Guttiferae, LC-MS, Medicinal plant, St. John’s wort.

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573 On Dialogue Systems Based on Deep Learning

Authors: Yifan Fan, Xudong Luo, Pingping Lin

Abstract:

Nowadays, dialogue systems increasingly become the way for humans to access many computer systems. So, humans can interact with computers in natural language. A dialogue system consists of three parts: understanding what humans say in natural language, managing dialogue, and generating responses in natural language. In this paper, we survey deep learning based methods for dialogue management, response generation and dialogue evaluation. Specifically, these methods are based on neural network, long short-term memory network, deep reinforcement learning, pre-training and generative adversarial network. We compare these methods and point out the further research directions.

Keywords: Dialogue management, response generation, reinforcement learning, deep learning, evaluation.

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572 Seismic Analysis of URM Buildings in S. Africa

Authors: Trevor N. Haas, Thomas van der Kolf

Abstract:

South Africa has some regions which are susceptible to moderate seismic activity. A peak ground acceleration of between 0.1g and 0.15g can be expected in the southern parts of the Western Cape. Unreinforced Masonry (URM) is commonly used as a construction material for 2 to 5 storey buildings in underprivileged areas in and around Cape Town. URM is typically regarded as the material most vulnerable to damage when subjected to earthquake excitation. In this study, a three-storey URM building was analysed by applying seven earthquake time-histories, which can be expected to occur in South Africa using a finite element approach. Experimental data was used to calibrate the in- and out-of-plane stiffness of the URM. The results indicated that tensile cracking of the in-plane piers was the dominant failure mode. It is concluded that URM buildings of this type are at risk of failure especially if sufficient ductility is not provided. The results also showed that connection failure must be investigated further.

Keywords: URM, Seismic Analysis, FEM.

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571 2D Fracture Analysis of the First Compression Piston Ring

Authors: I. Razmi, N. Choupani

Abstract:

The incidence of mechanical fracture of an automobile piston rings prompted development of fracture analysis method on this case. The three rings (two compression rings and one oil ring) were smashed into several parts during the power-test (after manufacturing the engine) causing piston and liner to be damaged. The radial and oblique cracking happened on the failed piston rings. The aim of the fracture mechanics simulations presented in this paper was the calculation of particular effective fracture mechanics parameters, such as J-integrals and stress intensity factors. Crack propagation angles were calculated as well. Two-dimensional fracture analysis of the first compression ring has been developed in this paper using ABAQUS CAE6.5-1 software. Moreover, SEM fractography was developed on fracture surfaces and is discussed in this paper. Results of numerical calculations constitute the basis for further research on real object.

Keywords: Compression piston ring, Crack, Fracture mechanics, SEM fractography.

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570 Integrating Process Planning and Scheduling for Prismatic Parts Regard to Due Date

Authors: M. Haddadzade, M. R. Razfar, M. Farahnakian

Abstract:

Integration of process planning and scheduling functions is necessary to achieve superior overall system performance. This paper proposes a methodology for integration of process planning and scheduling for prismatic component that can be implemented in a company with existing departments. The developed model considers technological constraints whereas available time for machining in shop floor is the limiting factor to produce multiple process plan (MPP). It takes advantage of MPP while guarantied the fulfillment of the due dates via using overtime. This study has been proposed to determinate machining parameters, tools, machine and amount of over time within the minimum cost objective while overtime is considered for this. At last the illustration shows that the system performance is improved by as measured by cost and compatible with due date.

Keywords: Due date, Integration, Multiple process plan, Process planning, Scheduling.

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569 Face Recognition Using Discrete Orthogonal Hahn Moments

Authors: Fatima Akhmedova, Simon Liao

Abstract:

One of the most critical decision points in the design of a face recognition system is the choice of an appropriate face representation. Effective feature descriptors are expected to convey sufficient, invariant and non-redundant facial information. In this work we propose a set of Hahn moments as a new approach for feature description. Hahn moments have been widely used in image analysis due to their invariance, nonredundancy and the ability to extract features either globally and locally. To assess the applicability of Hahn moments to Face Recognition we conduct two experiments on the Olivetti Research Laboratory (ORL) database and University of Notre-Dame (UND) X1 biometric collection. Fusion of the global features along with the features from local facial regions are used as an input for the conventional k-NN classifier. The method reaches an accuracy of 93% of correctly recognized subjects for the ORL database and 94% for the UND database.

Keywords: Face Recognition, Hahn moments, Recognition-by-parts, Time-lapse.

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568 Heavy Metal Contamination of the Landscape at the ─¢ubietová Deposit (Slovakia)

Authors: Peter Andráš, Adam Lichý, Jana Rusková, Lenka Matúšková

Abstract:

The heavy metal contamination of the technogenous sediments and soils at the investigated dump-field show irregular planar distribution. Also the heavy metal content in the surface water, drainage water and in the groundwater was studied both in the dry as well as during the rainy periods. The cementation process causes substitution of iron by copper. Natural installation and development of plant species was observed at the old mine waste dumps, specific to the local chemical conditions such as low content of essential nutrients and high content of heavy metals. The individual parts of the plant tissues (roots, branches/stems, leaves/needles, flowers/ fruits) are contaminated by heavy metals and tissues are damaged differently, respectively.

Keywords: Contamination, dump-field, heavy metals, plants, sediment, water.

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567 Determination of the Characteristics for Ferroresonance Phenomenon in Electric Power Systems

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

Abstract:

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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566 Development of the Measurement Apparatus for the Effective Thermal Conductivity of Core Material

Authors: Jongmin Kim, Tae-Ho Song

Abstract:

A measurement apparatus is designed and fabricated to measure the effective thermal conductivity (keff) of a VIP (vacuum insulation panel) core specimen under various vacuum states and external loads. The apparatus consists of part for measuring keff, and parts for controlling external load and vacuum condition. Uncertainty of the apparatus is validated by measuring the standard reference material and comparing with commercial devices with VIP samples. Assessed uncertainty is maximum 2.5 % in case of the standard reference material, 10 % in case of VIP samples. Using the apparatus, keff of glass paper under various vacuum levels is examined.

Keywords: Effective thermal conductivity, guarded hot plate method, vacuum insulation panel

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565 Design Calculation and Performance Testing of Heating Coil in Induction Surface Hardening Machine

Authors: Soe Sandar Aung, Han Phyo Wai, Nyein Nyein Soe

Abstract:

The induction hardening machines are utilized in the industries which modify machine parts and tools needed to achieve high ware resistance. This paper describes the model of induction heating process design of inverter circuit and the results of induction surface hardening of heating coil. In the design of heating coil, the shape and the turn numbers of the coil are very important design factors because they decide the overall operating performance of induction heater including resonant frequency, Q factor, efficiency and power factor. The performance will be tested by experiments in some cases high frequency induction hardening machine.

Keywords: Induction Heating, Resonant Circuit, InverterCircuit, Coil Design, Induction Hardening Machine.

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564 Curvelet Transform Based Two Class Motor Imagery Classification

Authors: Nebi Gedik

Abstract:

One of the important parts of the brain-computer interface (BCI) studies is the classification of motor imagery (MI) obtained by electroencephalography (EEG). The major goal is to provide non-muscular communication and control via assistive technologies to people with severe motor disorders so that they can communicate with the outside world. In this study, an EEG signal classification approach based on multiscale and multi-resolution transform method is presented. The proposed approach is used to decompose the EEG signal containing motor image information (right- and left-hand movement imagery). The decomposition process is performed using curvelet transform which is a multiscale and multiresolution analysis method, and the transform output was evaluated as feature data. The obtained feature set is subjected to feature selection process to obtain the most effective ones using t-test methods. SVM and k-NN algorithms are assigned for classification.

Keywords: motor imagery, EEG, curvelet transform, SVM, k-NN

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563 Review and Experiments on SDMSCue

Authors: Ashraf Anwar

Abstract:

In this work, I present a review on Sparse Distributed Memory for Small Cues (SDMSCue), a variant of Sparse Distributed Memory (SDM) that is capable of handling small cues. I then conduct and show some cognitive experiments on SDMSCue to test its cognitive soundness compared to SDM. Small cues refer to input cues that are presented to memory for reading associations; but have many missing parts or fields from them. The original SDM failed to handle such a problem. SDMSCue handles and overcomes this pitfall. The main idea in SDMSCue; is the repeated projection of the semantic space on smaller subspaces; that are selected based on the input cue length and pattern. This process allows for Read/Write operations using an input cue that is missing a large portion. SDMSCue is augmented with the use of genetic algorithms for memory allocation and initialization. I claim that SDM functionality is a subset of SDMSCue functionality.

Keywords: Artificial intelligence, recall, recognition, SDM, SDMSCue.

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562 Comanche – A Compiler-Driven I/O Management System

Authors: Wendy Zhang, Ernst L. Leiss, Huilin Ye

Abstract:

Most scientific programs have large input and output data sets that require out-of-core programming or use virtual memory management (VMM). Out-of-core programming is very error-prone and tedious; as a result, it is generally avoided. However, in many instance, VMM is not an effective approach because it often results in substantial performance reduction. In contrast, compiler driven I/O management will allow a program-s data sets to be retrieved in parts, called blocks or tiles. Comanche (COmpiler MANaged caCHE) is a compiler combined with a user level runtime system that can be used to replace standard VMM for out-of-core programs. We describe Comanche and demonstrate on a number of representative problems that it substantially out-performs VMM. Significantly our system does not require any special services from the operating system and does not require modification of the operating system kernel.

Keywords: I/O Management, Out-of-core, Compiler, Tile mapping.

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561 Modelling and Simulation of the Freezing Systems and Heat Pumps Using Unisim® Design

Authors: C. Patrascioiu

Abstract:

The paper describes the modeling and simulation of the heat pumps domain processes. The main objective of the study is the use of the heat pump in propene–propane distillation processes. The modeling and simulation instrument is the Unisim® Design simulator. The paper is structured in three parts: An overview of the compressing gases, the modeling and simulation of the freezing systems, and the modeling and simulation of the heat pumps. For each of these systems, there are presented the Unisim® Design simulation diagrams, the input–output system structure and the numerical results. Future studies will consider modeling and simulation of the propene–propane distillation process with heat pump.

Keywords: Distillation, heat pump, simulation, Unisim Design.

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560 Multi-Font Farsi/Arabic Isolated Character Recognition Using Chain Codes

Authors: H. Izakian, S. A. Monadjemi, B. Tork Ladani, K. Zamanifar

Abstract:

Nowadays, OCR systems have got several applications and are increasingly employed in daily life. Much research has been done regarding the identification of Latin, Japanese, and Chinese characters. However, very little investigation has been performed regarding Farsi/Arabic characters recognition. Probably the reason is difficulty and complexity of those characters identification compared to the others and limitation of IT activities in Farsi and Arabic speaking countries. In this paper, a technique has been employed to identify isolated Farsi/Arabic characters. A chain code based algorithm along with other significant peculiarities such as number and location of dots and auxiliary parts, and the number of holes existing in the isolated character has been used in this study to identify Farsi/Arabic characters. Experimental results show the relatively high accuracy of the method developed when it is tested on several standard Farsi fonts.

Keywords: Farsi characters, OCR, feature extraction, chain code.

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559 CT Reconstruction from a Limited Number of X-Ray Projections

Authors: Tao Quang Bang, Insu Jeon

Abstract:

Most CT reconstruction system x-ray computed tomography (CT) is a well established visualization technique in medicine and nondestructive testing. However, since CT scanning requires sampling of radiographic projections from different viewing angles, common CT systems with mechanically moving parts are too slow for dynamic imaging, for instance of multiphase flows or live animals. A large number of X-ray projections are needed to reconstruct CT images, so the collection and calculation of the projection data consume too much time and harmful for patient. For the purpose of solving the problem, in this study, we proposed a method for tomographic reconstruction of a sample from a limited number of x-ray projections by using linear interpolation method. In simulation, we presented reconstruction from an experimental x-ray CT scan of a Aluminum phantom that follows to two steps: X-ray projections will be interpolated using linear interpolation method and using it for CT reconstruction based upon Ordered Subsets Expectation Maximization (OSEM) method.

Keywords: CT reconstruction, X-ray projections, Interpolation technique, OSEM

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558 Geometrical Structure and Layer Orientation Effects on Strength, Material Consumption and Building Time of FDM Rapid Prototyped Samples

Authors: Ahmed A. D. Sarhan, Chong Feng Duan, Mum Wai Yip, M. Sayuti

Abstract:

Rapid Prototyping (RP) technologies enable physical parts to be produced from various materials without depending on the conventional tooling. Fused Deposition Modeling (FDM) is one of the famous RP processes used at present. Tensile strength and compressive strength resistance will be identified for different sample structures and different layer orientations of ABS rapid prototype solid models. The samples will be fabricated by a FDM rapid prototyping machine in different layer orientations with variations in internal geometrical structure. The 0° orientation where layers were deposited along the length of the samples displayed superior strength and impact resistance over all the other orientations. The anisotropic properties were probably caused by weak interlayer bonding and interlayer porosity.

Keywords: Building orientation, compression strength, rapid prototyping, tensile strength.

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557 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations

Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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