Search results for: Nonlinear system.

Authors: B. Rajkumarsingh, S. Goolaup, A. Galleegadoo

Abstract:

Laboratory classes in Electrical Engineering are often hampered by safety issues, as students have to work on high voltage lines. One solution is to make use of virtual laboratory simulations, to help students understand the concepts taught in their coursework. In this context, we have conceived and implemented virtual lab experiments in connection with the study of earthing arrangements. In this work, software was developed, which aid student in understanding the working of a residual current device (RCD) in a TT earthing system. Various parameters, such as the earthing resistances, leakage currents and harmonics were included for a TT system with RCD connection.

Keywords: TT system, RCD, LabVIEW, Learning aids.

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Authors: Rizauddin Ramli, Jaber Abu Qudeiri, Hidehiko Yamamoto

Abstract:

Nowadays the market for industrial companies is becoming more and more globalized and highly competitive, forcing them to shorten the duration of the manufacturing system development time in order to reduce the time to market. In order to achieve this target, the hierarchical systems used in previous manufacturing systems are not enough because they cannot deal effectively with unexpected situations. To achieve flexibility in manufacturing systems, the concept of an Autonomous Decentralized Flexible Manufacturing System (AD-FMS) is useful. In this paper, we introduce a hypothetical reasoning based algorithm called the Algorithm for Future Anticipative Reasoning (AFAR) which is able to decide on a conceivable next action of an Automated Guided Vehicle (AGV) that works autonomously in the AD-FMS.

Keywords: Flexible Manufacturing System, Automated GuidedVehicle, Hypothetical Reasoning, Autonomous Decentralized.

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Authors: Pan Wang, Yongkun Li

Abstract:

In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result.

Keywords: Periodic solution, predator-prey system, harvesting terms, continuation theorem.

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Authors: Shinji Kajiwara, Tadamasa Fukuoka

Abstract:

The formula project of Kinki University has been involved in the student Formula SAE of Japan (JSAE) since the second year the competition was held. The vehicle developed in the project uses a ZX-6R engine, which has been manufactured by Kawasaki Heavy Industries for the JSAE competition for the eighth time. The limited performance of the concept vehicle was improved through the development of a power train. The supercharger loading, engine dry sump, and engine cooling management of the vehicle were also enhanced. The supercharger loading enabled the vehicle to achieve a maximum output of 59.6 kW (80.6 PS)/9000 rpm and a maximum torque of 70.6 Nm (7.2 kgf m)/8000 rpm. We successfully achieved 90% of the engine’s torque band (4000–10000 rpm) with 50% of the revolutions in regular engine use (2000–12000 rpm). Using a dry sump system, we periodically managed hydraulic pressure during engine operation. A system that controls engine stoppage when hydraulic pressure falls was also constructed. Using the dry sump system at 80 mm reduced the required engine load and the vehicle’s center of gravity. Even when engine motion was suspended by the electromotive force exerted by the water pump, the circulation of cooling water was still possible. These findings enabled us to create a cooling system in accordance with the requirements of the competition.

Keywords: Engine, combustion, cooling system, dry sump system, numerical simulation, power, torque, mechanical supercharger.

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Authors: Tariq Aljuneidi, Akif Asil Bulgak

Abstract:

An efficient remanufacturing network lead to an efficient design of sustainable manufacturing enterprise. In remanufacturing network, products are collected from the customer zone, disassembled and remanufactured at a suitable remanufacturing facility. In this respect, another issue to consider is how the returned product to be remanufactured, in other words, what is the best layout for such facility. In order to achieve a sustainable manufacturing system, Cellular Manufacturing System (CMS) designs are highly recommended, CMSs combine high throughput rates of line layouts with the flexibility offered by functional layouts (job shop). Introducing the CMS while designing a remanufacturing network will benefit the utilization of such a network. This paper presents and analyzes a comprehensive mathematical model for the design of Dynamic Cellular Remanufacturing Systems (DCRSs). In this paper, the proposed model is the first one to date that considers CMS and remanufacturing system simultaneously. The proposed DCRS model considers several manufacturing attributes such as multi period production planning, dynamic system reconfiguration, duplicate machines, machine capacity, available time for workers, worker assignments, and machine procurement, where the demand is totally satisfied from a returned product. A numerical example is presented to illustrate the proposed model.

Keywords: Cellular Manufacturing System, Remanufacturing, Mathematical Programming, Sustainability.

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Authors: Sandhya Dixit, Tilak Raj

Abstract:

Flexible Manufacturing System (FMS) is seen as an option for industries which want to boost productivity as well as respond quickly to an increasingly changing marketplace. FMS produces in mid variety, mid volume range and can meet the changing market demands very quickly. But still the impact of adoption of FMS on the productivity of any industry is not very clear. In this paper an attempt has been made to model the various factors affecting the productivity of FMS installation using Total Interpretive Structural Modelling (TISM) Technique.

Keywords: Flexible manufacturing system, productivity, total interpretive structural modelling.

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Authors: H. Bentarzi, A. Zitouni

Abstract:

The reliability of the power grid depends on the successful operation of thousands of protective relays. The failure of one relay to operate as intended may lead the entire power grid to blackout. In fact, major power system failures during transient disturbances may be caused by unnecessary protective relay tripping rather than by the failure of a relay to operate. Adequate relay testing provides a first defense against false trips of the relay and hence improves power grid stability and prevents catastrophic bulk power system failures. The goal of this research project is to design and enhance the relay tester using a technology such as Field Programmable Gate Array (FPGA) card NI 7851. A PC based tester framework has been developed using Simulink power system model for generating signals under different conditions (faults or transient disturbances) and LabVIEW for developing the graphical user interface and configuring the FPGA. Besides, the interface system has been developed for outputting and amplifying the signals without distortion. These signals should be like the generated ones by the real power system and large enough for testing the relay’s functionality. The signals generated that have been displayed on the scope are satisfactory. Furthermore, the proposed testing system can be used for improving the performance of protective relay.

Keywords: Amplifier class D, FPGA, protective relay, tester.

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Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

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This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: Power system, Transient stability, Critical trajectory method, Energy function method.

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Authors: N. Hatraf, N. Moummi

Abstract:

The interest in air conditioning using renewable energies is increasing. The thermal energy produced from the solar energy can be converted to useful cooling and heating through the thermochemical or thermophysical processes by using thermally activated energy conversion systems. The ambient air contains so much water that very high dehumidification rates are required. For a continuous dehumidification of the process air, the water adsorbed on the desiccant material has to be removed, which is done by allowing hot air to flow through the desiccant material (regeneration). A solid desiccant cooling system transfers moisture from the inlet air to the silica gel by using two processes: Absorption process and the regeneration process. The main aim of this paper is to study how the dehumidification rate, the generation temperature and many other factors influence the efficiency of a solid desiccant system by using TRNSYS software. The results show that the desiccant system could be used to decrease the humidity rate of the entering air.

Keywords: Dehumidification, efficiency, humidity, TRNSYS.

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Authors: T. Hussein

Abstract:

In this paper, determining the optimal proportionalintegral- derivative (PID) controller gains of an single-area load frequency control (LFC) system using genetic algorithm (GA) is presented. The LFC is notoriously difficult to control optimally using conventionally tuning a PID controller because the system parameters are constantly changing. It is for this reason the GA as tuning strategy was applied. The simulation has been conducted in MATLAB Simulink package for single area power system. the simulation results shows the effectiveness performance of under various disturbance.

Keywords: Load Frequency Control (LFC), PID controller and Genetic Algorithm (GA).

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Authors: Fernando Pérez, Humberto Sossa, Rigoberto Martínez, Daniel Lorias, Arturo Minor

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This paper presents a system for tracking the movement of laparoscopic instruments which is based on an orthogonal system of webcams and video image processing. The movements are captured with two webcams placed orthogonally inside of the physical trainer. On the image, the instruments were detected by using color markers placed on the distal tip of each instrument. The 3D position of the tip of the instrument within the work space was obtained by linear triangulation method. Preliminary results showed linearity and repeatability in the motion tracking with a resolution of 0.616 mm in each axis; the accuracy of the system showed a 3D instrument positioning error of 1.009 ± 0.101 mm. This tool is a portable and low-cost alternative to traditional tracking devices and a trustable method for the objective evaluation of the surgeon’s surgical skills.

Keywords: Laparoscopic Surgery, Orthogonal Vision, Tracking Instruments, Triangulation.

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Authors: Satoru Fukuta, Masaki Ito, Takao Kawamura, Kazunori Sugahara

Abstract:

Recently, many web services to provide information for public transport are developed and released. They are optimized for mobile devices such a smartphone. We are also developing better path planning system for route buses and trains called “Bus-Net"[1]. However these systems only provide paths and related information before the user start moving. So we propose a context aware navigation to change the way to support public transport users. If we go to somewhere using many kinds of public transport, we have to know how to use them. In addition, public transport is dynamic system, and these have different characteristic by type. So we need information at real-time. Therefore we suggest the system that can support on user-s state. It has a variety of ways to help public transport users by each state, like turn-by-turn navigation. Context aware navigation will be able to reduce anxiety for using public transport.

Keywords: Navigation, Public Transport, Smartphone, User Experience.

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Authors: Ahmad Rouhani

Abstract:

Iran has several potential for using renewable energies, so use them could significantly contribute to energy supply. The purpose of this paper is to identify the potential of the country and select the appropriate DG technologies with consideration the potential and primary energy resources in the regions. In this context, hybrid energy systems proportionate with the potential of different regions will be determined based on technical, economic, and environmental aspect. In the following the proposed structure will be optimized in terms of size and cost. DG technologies used in this project include photovoltaic system, wind turbine, diesel generator and battery bank. The HOMER software is applied for choosing the appropriate structure and the optimization of system sizing. The results have been analyzed in terms of technical and economic. The performance and the cost of each project demonstrate the appropriate structure of hybrid energy system in that region.

Keywords: Feasibility, Hybrid Energy System, Iran, Renewable Energy.

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Authors: H. S. Huang, J. C. Jao, K. L. Yen, C. T. Tsai

Abstract:

The purpose of this article applies the monthly final energy yield and failure data of 202 PV systems installed in Taiwan to analyze the PV operational performance and system availability. This data is collected by Industrial Technology Research Institute through manual records. Bad data detection and failure data estimation approaches are proposed to guarantee the quality of the received information. The performance ratio value and system availability are then calculated and compared with those of other countries. It is indicated that the average performance ratio of Taiwan-s PV systems is 0.74 and the availability is 95.7%. These results are similar with those of Germany, Switzerland, Italy and Japan.

Keywords: availability, performance ratio, PV system, Taiwan

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Authors: Cesar Eduardo Hernández Curiel, Victor Hugo Benítez Baltazar, Jesús Horacio Pacheco Ramírez

Abstract:

This paper is devoted to present the advances in the design of a prototype that is able to supervise the complex behavior of water quality parameters such as pH and temperature, via a real-time monitoring system. The current water quality tests that are performed in government water quality institutions in Mexico are carried out in problematic locations and they require taking manual samples. The water samples are then taken to the institution laboratory for examination. In order to automate this process, a water quality monitoring system based on wireless sensor networks is proposed. The system consists of a sensor node which contains one pH sensor, one temperature sensor, a microcontroller, and a ZigBee radio, and a base station composed by a ZigBee radio and a PC. The progress in this investigation shows the development of a water quality monitoring system. Due to recent events that affected water quality in Mexico, the main motivation of this study is to address water quality monitoring systems, so in the near future, a more robust, affordable, and reliable system can be deployed.

Keywords: pH measurement, water quality monitoring, wireless sensor networks, ZigBee.

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Authors: Hong-Bing Wang, Zhi-Hua Fan, Chun-Dong She

Abstract:

Open Agent System platform based on High Level Architecture is firstly proposed to support the application involving heterogeneous agents. The basic idea is to develop different wrappers for different agent systems, which are wrapped as federates to join a federation. The platform is based on High Level Architecture and the advantages for this open standard are naturally inherited, such as system interoperability and reuse. Especially, the federal architecture allows different federates to be heterogeneous so as to support the integration of different agent systems. Furthermore, both implicit communication and explicit communication between agents can be supported. Then, as the wrapper RTI_JADE an example, the components are discussed. Finally, the performance of RTI_JADE is analyzed. The results show that RTI_JADE works very efficiently.

Keywords: Open Agent System, High Level Architecture, Heterogeneous Agents, Wrapper.

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Authors: Haydar Teymourlouei

Abstract:

Cybersecurity is one of the greatest challenges society faces in an age revolving around technological development. With cyber-attacks on the continuous rise, the nation needs to understand and learn ways that can prevent such attacks. A major contribution that can change the education system is to implement laboratories and competitions into academia. This method can improve and educate students with more hands-on exercises in a highly motivating setting. Considering the fact that students are the next generation of the nation’s workforce, it is important for students to understand concepts not only through books, but also through actual hands-on experiences in order for them to be prepared for the workforce. An effective cybersecurity education system is critical for creating a strong cyber secure workforce today and for the future. This paper emphasizes the need for awareness and the need for competitions and cybersecurity laboratories to be implemented into the education system.

Keywords: Awareness, competition, cybersecurity, laboratories, workforce.

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Authors: Ioannis P. Panapakidis, Marios N. Moschakis

Abstract:

The Greek Energy Market is structured as a mandatory pool where the producers make their bid offers in day-ahead basis. The System Operator solves an optimization routine aiming at the minimization of the cost of produced electricity. The solution of the optimization problem leads to the calculation of the System Marginal Price (SMP). Accurate forecasts of the SMP can lead to increased profits and more efficient portfolio management from the producer`s perspective. Aim of this study is to provide a comparative analysis of various machine learning models such as artificial neural networks and neuro-fuzzy models for the prediction of the SMP of the Greek market. Machine learning algorithms are favored in predictions problems since they can capture and simulate the volatilities of complex time series.

Keywords: Deregulated energy market, forecasting, machine learning, system marginal price, energy efficiency and quality.

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Authors: M. Saleh, H. Bevrani

Abstract:

This paper quantifies the impact of providing a shortterm excess active power support of a variable speed wind turbine (VSWT) and effect of super magnetic energy storage (SMES) unit on frequency control, particularly temporary minimum frequency (TMF) term. To demonstrate the effect of these factors on the power system frequency, a three-area power system is considered as a test system.

Keywords: Frequency regulation, inertia, primary frequencycontrol, rotational energy, variable speed wind turbine.

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Authors: S. Khosravi, A. Afshar, F. Barazandeh

Abstract:

In this study we propose a novel monitor hydraulic automatic gauge control (HAGC) system based on fuzzy feedforward controller. This is used in the development of cold rolling mill automation system to improve the quality of cold strip. According to features/ properties of entry steel strip like its average yield stress, width of strip, and desired exit thickness, this controller realizes the compensation for the exit thickness error. The traditional methods of adjusting the roller position, can-t tolerate the variance in the entry steel strip. The proposed method uses a mathematical model of the system together with the expert knowledge to perform this adjustment while minimizing the effect of the stated problem. In order to improve the speed of the controller in rejecting disturbances introduced by entry strip thickness variations, expert knowledge is added as a feed-forward term to the HAGC system. Simulation results for the application of the proposed controller to a real cold mill show that the exit strip quality is highly improved.

Keywords: Fuzzy feed-forward controller, monitor HAGC system, dynamic mathematical model, entry strip thickness deviation compensation

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Authors: Ali Asadian, Behzad Moshiri, Ali Khaki Sedigh, Caro Lucas

Abstract:

Most integrated inertial navigation systems (INS) and global positioning systems (GPS) have been implemented using the Kalman filtering technique with its drawbacks related to the need for predefined INS error model and observability of at least four satellites. Most recently, a method using a hybrid-adaptive network based fuzzy inference system (ANFIS) has been proposed which is trained during the availability of GPS signal to map the error between the GPS and the INS. Then it will be used to predict the error of the INS position components during GPS signal blockage. This paper introduces a genetic optimization algorithm that is used to update the ANFIS parameters with respect to the INS/GPS error function used as the objective function to be minimized. The results demonstrate the advantages of the genetically optimized ANFIS for INS/GPS integration in comparison with conventional ANFIS specially in the cases of satellites- outages. Coping with this problem plays an important role in assessment of the fusion approach in land navigation.

Keywords: Adaptive Network based Fuzzy Inference System (ANFIS), Genetic optimization, Global Positioning System (GPS), Inertial Navigation System (INS).

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Authors: Jihan Abdulazeez Ahmed, Adnan Mohsin Abdulazeez Brifcani

Abstract:

This paper suggests a new internal architecture of holon based on feature selection model using the combination of Bees Algorithm (BA) and Artificial Neural Network (ANN). BA is used to generate features while ANN is used as a classifier to evaluate the produced features. Proposed system is applied on the Wine dataset, the statistical result proves that the proposed system is effective and has the ability to choose informative features with high accuracy.

Keywords: Artificial Neural Networks, Holonic Approach, Feature Selection, Bee Algorithm.

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Authors: Ghada Abdelmouez M., Fathy S. Helail, Abdellatif A. Elkouny

Abstract:

It is known that symmetric encryption algorithms are fast and easy to implement in hardware. Also elliptic curves have proved to be a good choice for building encryption system. Although most of the symmetric systems have been broken, we can create a hybrid system that has the same properties of the symmetric encryption systems and in the same time, it has the strength of elliptic curves in encryption. As DES algorithm is considered the core of all successive symmetric encryption systems, we modified DES using elliptic curves and built a new DES algorithm that is hard to be broken and will be the core for all other symmetric systems.

Keywords: DES, Elliptic Curves, hybrid system, symmetricencryption.

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Authors: Amel Grissa-Touzi, Habib Ounally, Aissa Boulila

Abstract:

The utility of expert system generators has been widely recognized in many applications. Several generators based on concept of the paradigm object, have been recently proposed. The generator of oriented object expert system (GSEOO) offers languages that are often complex and difficult to use. We propose in this paper an extension of the expert system generator, JESS, which permits a friendly use of this expert system. The new tool, called VISUAL JESS, bring two main improvements to JESS. The first improvement concerns the easiness of its utilization while giving back transparency to the syntax and semantic aspects of the JESS programming language. The second improvement permits an easy access and modification of the JESS knowledge basis. The implementation of VISUAL JESS is made so that it is extensible and portable.

Keywords: Generator of Systems Expert, Programming oriented object classifies, object, inheritance, polymorphism.

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Authors: HangRok Lee, DoWon Hong

Abstract:

Since communications between tag and reader in RFID system are by radio, anyone can access the tag and obtain its any information. And a tag always replies with the same ID so that it is hard to distinguish between a real and a fake tag. Thus, there are many security problems in today-s RFID System. Firstly, unauthorized reader can easily read the ID information of any Tag. Secondly, Adversary can easily cheat the legitimate reader using the collected Tag ID information, such as the any legitimate Tag. These security problems can be typically solved by encryption of messages transmitted between Tag and Reader and by authentication for Tag. In this paper, to solve these security problems on RFID system, we propose the Tag Authentication Scheme based on self shrinking generator (SSG). SSG Algorithm using in our scheme is proposed by W.Meier and O.Staffelbach in EUROCRYPT-94. This Algorithm is organized that only one LFSR and selection logic in order to generate random stream. Thus it is optimized to implement the hardware logic on devices with extremely limited resource, and the output generating from SSG at each time do role as random stream so that it is allow our to design the light-weight authentication scheme with security against some network attacks. Therefore, we propose the novel tag authentication scheme which use SSG to encrypt the Tag-ID transmitted from tag to reader and achieve authentication of tag.

Keywords: RFID system, RFID security, self shrinkinggeneratior, authentication, protocol.

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Authors: Patil Ashwini, Archana Thosar

Abstract:

This paper addresses the mathematical model of wind energy system useful for designing fault tolerant control. To serve the demand of power, large capacity wind energy systems are vital. These systems are installed offshore where non planned service is very costly. Whenever there is a fault in between two planned services, the system may stop working abruptly. This might even lead to the complete failure of the system. To enhance the reliability, the availability and reduce the cost of maintenance of wind turbines, the fault tolerant control systems are very essential. For designing any control system, an appropriate mathematical model is always needed. In this paper, the two-mass model is modified by considering the frequent mechanical faults like misalignments in the drive train, gears and bearings faults. These faults are subject to a wear process and cause frictional losses. This paper addresses these faults in the mathematics of the wind energy system. Further, the work is extended to study the variations of the parameters namely generator inertia constant, spring constant, viscous friction coefficient and gear ratio; on the pole-zero plot which is related with the physical design of the wind turbine. Behavior of the wind turbine during drive train faults are simulated and briefly discussed.

Keywords: Mathematical model of wind energy system, stability analysis, shaft stiffness, viscous friction coefficient, gear ratio, generator inertia, fault tolerant control.

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Authors: Tarathorn Podcharathitikull, Jirarat Teeravaraprug

Abstract:

Transportation cost is the highest cost in logistics cost of Thailand, and truck transportation is counted as about 90% of the overall transportation cost. The main problem of truck transportation is backhauling. Backhauling has become an attractive cost-saving approach in logistics. To explore such opportunities, this paper investigated the current backhauling systems in Thailand. It was found that the backhauling problem is attracted to both governmental agencies and private sector. They gave attempts to build backhauling systems. This paper investigated two systems built by governmental agencies and one by private sector. Moreover, based on the interviews with the system representatives and users, pros and cons of the systems were found. The obstacles and challenges were obtained. This paper finally proposed a conceptual model of to-be backhauling system in Thailand.

Keywords: Backhauling system, Backhauls, interview, Thailand.

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Authors: Pham Luu Trung Duong, Moonyong Lee

Abstract:

To increase precision and reliability of automatic control systems, we have to take into account of random factors affecting the control system. Thus, operational matrix technique is used for statistical analysis of first order plus time delay system with uniform random parameter. Examples with deterministic and stochastic disturbance are considered to demonstrate the validity of the method. Comparison with Monte Carlo method is made to show the computational effectiveness of the method.

Keywords: First order plus dead-time, Operational matrix, Statistical analysis, Walsh function.

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Authors: Şt. Creangâ, V. Maciuc, A.V. Bâlteanu, S.S. Chelmu

Abstract:

The paper presents a part of the results obtained in a complex research project on Romanian Grey Steppe breed, owner of some remarkable qualities such as hardiness, longevity, adaptability, special resistance to ban weather and diseases and included in the genetic fund (G.D. no. 822/2008.) from Romania. Following the researches effectuated, we identified alleles of six loci, codifying the six types of major milk proteins: alpha-casein S1 (α S1-cz); beta-casein (β-cz); kappa-casein (K-cz); beta-lactoglobulin (β-lg); alpha-lactalbumin (α-la) and alpha-casein S2 (α S2-cz). In system αS1-cz allele αs1-Cn B has the highest frequency (0.700), in system β-cz allele β-Cn A2 ( 0.550 ), in system K-cz allele k-CnA2 ( 0.583 ) and heterozygote genotype AB ( 0.416 ) and BB (0.375), in system β-lg allele β-lgA1 has the highest frequency (0.542 ) and heterozygote genotype AB ( 0.500 ), in system α-la there is monomorphism for allele α-la B and similarly in system αS2-cz for allele αs2-Cn A. The milk analysis by the isoelectric focalization technique (I.E.F.) allowed the identification of a new allele for locus αS1-casein, for two of the individuals under analysis, namely allele called αS1-casein IRV. When experiments were repeated, we noticed that this is not a proteolysis band and it really was a new allele that has not been registered in the specialized literature so far. We identified two heterozygote individuals, carriers of this allele, namely: BIRV and CIRV. This discovery is extremely important if focus is laid on the national genetic patrimony.

Keywords: allele, breed, genetic preservation, lactoproteins, Romanian Grey Steppe

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Authors: Mohd Agos Salim Nasir, Ahmad Izani Md. Ismail

Abstract:

Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.

Keywords: Goursat problem, partial differential equation, finite difference scheme, compact finite difference

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