Search results for: multi electrode

Authors: Yelena Chaiko

Abstract:

This paper presents a developed method for controlling multi-renewable energy generators. The control system depends basically on three sensors (wind anemometer, solar sensor, and voltage sensor). These sensors represent PLC-s analogue inputs. Controlling the output voltage supply can be achieved by an enhanced method of interlocking between the renewable energy generators, depending on those sensors and output contactors.

Keywords: Renewable, energy, control, model, generator.

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Authors: Mohammad Syed Ali Molla, Mohammed Azim, Mohammad Esharuzzaman

Abstract:

Centrifugal-casting machine is used in manufacturing special machine components like multi-layer journal bearing used in all internal combustion engine, steam, gas turbine and air craft turboengine where isotropic properties and high precisions are desired. Moreover, this machine can be used in manufacturing thin wall hightech machine components like cylinder liners and piston rings of IC engine and other machine parts like sleeves, and bushes. Heavy-duty machine component like railway wheel can also be prepared by centrifugal casting. A lot of technological developments are required in casting process for production of good casted machine body and machine parts. Usually defects like blowholes, surface roughness, chilled surface etc. are found in sand casted machine parts. But these can be removed by centrifugal casting machine using rotating metallic die. Moreover, die rotation, its temperature control, and good pouring practice can contribute to the quality of casting because of the fact that the soundness of a casting in large part depends upon how the metal enters into the mold or dies and solidifies. Poor pouring practice leads to variety of casting defects such as temperature loss, low quality casting, excessive turbulence, over pouring etc. Besides these, handling of molten metal is very unsecured and dangerous for the workers. In order to get rid of all these problems, the need of an automatic pouring device arises. In this research work, a robot assisted pouring device and a centrifugal casting machine are designed, developed constructed and tested experimentally which are found to work satisfactorily. The robot assisted pouring device is further modified and developed for using it in actual metal casting process. Lot of settings and tests are required to control the system and ultimately it can be used in automation of centrifugal casting machine to produce high-tech machine parts with desired precision.

Keywords: Casting, cylinder liners, journal bearing, robot.

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Authors: Su-Hyun Jung, Chang-Bin Ha, Hyoung-Kyu Song

Abstract:

Recently, increasing the quality of experience (QoE) is an important issue. Since performance degradation at cell edge extremely reduces the QoE, several techniques are defined at LTE/LTE-A standard to remove inter-cell interference (ICI). However, the conventional techniques have disadvantage because there is a trade-off between resource allocation and reliable communication. The proposed scheme reduces the ICI more efficiently by using channel state information (CSI) smartly. It is shown that the proposed scheme can reduce the ICI with fewer resources.

Keywords: Adaptive beam forming, CoMP, LTE-A, ICI reduction.

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Authors: Pierre Abou-Haila, Richard Hall, Mark Dawes

Abstract:

Instead of representing individual cognition only, population cognition is represented using artificial neural networks whilst maintaining individuality. This population network trains continuously, simulating adaptation. An implementation of two coexisting populations is compared to the Lotka-Volterra model of predator-prey interaction. Applications include multi-agent systems such as artificial life or computer games.

Keywords: Collective unconsciousness, neural networks, adaptation, predator-prey simulation.

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Authors: Mylena McCoggle, Shyra Wilson, Andrea Rivera, Rocio Alba-Flores, Valentin Soloiu

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This work describes a system that uses electromyography (EMG) signals obtained from muscle sensors and an Artificial Neural Network (ANN) for signal classification and pattern recognition that is used to control a small unmanned aerial vehicle using specific arm movements. The main objective of this endeavor is the development of an intelligent interface that allows the user to control the flight of a drone beyond direct manual control. The sensor used were the MyoWare Muscle sensor which contains two EMG electrodes used to collect signals from the posterior (extensor) and anterior (flexor) forearm, and the bicep. The collection of the raw signals from each sensor was performed using an Arduino Uno. Data processing algorithms were developed with the purpose of classifying the signals generated by the arm’s muscles when performing specific movements, namely: flexing, resting, and motion of the arm. With these arm motions roll control of the drone was achieved. MATLAB software was utilized to condition the signals and prepare them for the classification. To generate the input vector for the ANN and perform the classification, the root mean square and the standard deviation were processed for the signals from each electrode. The neuromuscular information was trained using an ANN with a single 10 neurons hidden layer to categorize the four targets. The result of the classification shows that an accuracy of 97.5% was obtained. Afterwards, classification results are used to generate the appropriate control signals from the computer to the drone through a Wi-Fi network connection. These procedures were successfully tested, where the drone responded successfully in real time to the commanded inputs.

Keywords: Biosensors, electromyography, Artificial Neural Network, Arduino, drone flight control, machine learning.

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Authors: Teresa Coffman, Mary Beth Klinger

Abstract:

Multi User Virtual Worlds are becoming a valuable educational tool. Learning experiences within these worlds focus on discovery and active experiences that both engage students and motivate them to explore new concepts. As educators, we need to explore these environments to determine how they can most effectively be used in our instructional practices. This paper explores the current application of virtual worlds to identify meaningful educational strategies that are being used to engage students and enhance teaching and learning.

Keywords: Virtual Environments, MUVEs, Constructivist, Distance Learning, Learner Centered.

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Authors: R. Arulmurugan, P. Sengottuvelan

Abstract:

Object detection using Wavelet Neural Network (WNN) plays a major contribution in the analysis of image processing. Existing cluster-based algorithm for co-saliency object detection performs the work on the multiple images. The co-saliency detection results are not desirable to handle the multi scale image objects in WNN. Existing Super Resolution (SR) scheme for landmark images identifies the corresponding regions in the images and reduces the mismatching rate. But the Structure-aware matching criterion is not paying attention to detect multiple regions in SR images and fail to enhance the result percentage of object detection. To detect the objects in the high-resolution remote sensing images, Tagged Grid Matching (TGM) technique is proposed in this paper. TGM technique consists of the three main components such as object determination, object searching and object verification in WNN. Initially, object determination in TGM technique specifies the position and size of objects in the current image. The specification of the position and size using the hierarchical grid easily determines the multiple objects. Second component, object searching in TGM technique is carried out using the cross-point searching. The cross out searching point of the objects is selected to faster the searching process and reduces the detection time. Final component performs the object verification process in TGM technique for identifying (i.e.,) detecting the dissimilarity of objects in the current frame. The verification process matches the search result grid points with the stored grid points to easily detect the objects using the Gabor wavelet Transform. The implementation of TGM technique offers a significant improvement on the multi-object detection rate, processing time, precision factor and detection accuracy level.

Keywords: Object Detection, Cross-point Searching, Wavelet Neural Network, Object Determination, Gabor Wavelet Transform, Tagged Grid Matching.

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Authors: Farzad Abdous

Abstract:

Fuel cell's system requires regulating circuit for voltage and current in order to control power in case of connecting to other generative devices or load. In this paper Fuel cell system and convertor, which is a multi-variable system, are controlled using sliding mode method. Use of weighting matrix in design procedure made it possible to regulate speed of control. Simulation results show the robustness and accuracy of proposed controller for controlling desired of outputs.

Keywords: DC-DC converter, Fuel cell, PEM, Slides mode control.

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Authors: John Kabuba, Antoine Mulaba-Bafubiandi

Abstract:

The elution process for the removal of Co and Cu from clinoptilolite as an ion-exchanger was investigated using three parameters: bed volume, pH and contact time. The present paper study has shown quantitatively that acid concentration has a significant effect on the elution process. The favorable eluant concentration was found to be 2 M HCl and 2 M H2SO4, respectively. The multi-component equilibrium relationship in the process can be very complex, and perhaps ill-defined. In such circumstances, it is preferable to use a non-parametric technique such as Neural Network to represent such an equilibrium relationship.

Keywords: Clinoptilolite, elution, modeling, neural network.

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Authors: Rekha V. Dundur , M.V.Latte, S.Y. Kulkarni, M.K.Venkatesha

Abstract:

The advent of multi-million gate Field Programmable Gate Arrays (FPGAs) with hardware support for multiplication opens an opportunity to recreate a significant portion of the front end of a human cochlea using this technology. In this paper we describe the implementation of the cochlear filter and show that it is entirely suited to a single device XC3S500 FPGA implementation .The filter gave a good fit to real time data with efficiency of hardware usage.

Keywords: Cochlea, FPGA, IIR (Infinite Impulse Response), Multiplier.

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Authors: Mohammad Reza Pirestani, Hamid Reza Vosoghifar, Pegah Jazayeri

Abstract:

In designing river intakes and diversion structures, it is paramount that the sediments entering the intake are minimized or, if possible, completely separated. Due to high water velocity, sediments can significantly damage hydraulic structures especially when mechanical equipment like pumps and turbines are used. This subsequently results in wasting water, electricity and further costs. Therefore, it is prudent to investigate and analyze the performance of lateral intakes affected by sediment control structures. Laboratory experiments, despite their vast potential and benefits, can face certain limitations and challenges. Some of these include: limitations in equipment and facilities, space constraints, equipment errors including lack of adequate precision or mal-operation, and finally, human error. Research has shown that in order to achieve the ultimate goal of intake structure design – which is to design longlasting and proficient structures – the best combination of sediment control structures (such as sill and submerged vanes) along with parameters that increase their performance (such as diversion angle and location) should be determined. Cost, difficulty of execution and environmental impacts should also be included in evaluating the optimal design. This solution can then be applied to similar problems in the future. Subsequently, the model used to arrive at the optimal design requires high level of accuracy and precision in order to avoid improper design and execution of projects. Process of creating and executing the design should be as comprehensive and applicable as possible. Therefore, it is important that influential parameters and vital criteria is fully understood and applied at all stages of choosing the optimal design. In this article, influential parameters on optimal performance of the intake, advantages and disadvantages, and efficiency of a given design are studied. Then, a multi-criterion decision matrix is utilized to choose the optimal model that can be used to determine the proper parameters in constructing the intake.

Keywords: Diversion structures lateral intake, multi criteria decision making, optimal design, sediment control.

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Authors: Kandarpa Kumar Sarma

Abstract:

The key to the continued success of ANN depends, considerably, on the use of hybrid structures implemented on cooperative frame-works. Hybrid architectures provide the ability to the ANN to validate heterogeneous learning paradigms. This work describes the implementation of a set of Distributed and Hybrid ANN models for Character Recognition applied to Anglo-Assamese scripts. The objective is to describe the effectiveness of Hybrid ANN setups as innovative means of neural learning for an application like multilingual handwritten character and numeral recognition.

Keywords: Assamese, Feature, Recurrent.

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Authors: Seongykyoon Jeong, Sungki Lee, Jaeyun Kim, Seunghun Oh, Kiho Kwak

Abstract:

The purpose of this article is to identify the practical strategies of R&D (research and development) entities for developing converging technology in organizational context. Based on the multi-assignation technological domains of patents derived from entire government-supported R&D projects for 13 years, we find that technology convergence is likely to occur when a university solely develops technology or when university develops technology as one of the collaborators. These results reflect the important role of universities in developing converging technology

Keywords: Interdisciplinary, Research and development strategy, Technology convergence

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Authors: Hassan Haghighi, Seyedeh Zahra Hosseini, Seyedeh Elahe Jalambadani

Abstract:

ERP systems are often supposed to be implemented and deployed in multi-national companies. On the other hand, an ERP developer may plan to market and sale its product in various countries. Therefore, an EPR system should have the ability to communicate with its users, who usually have different languages and cultures, in a suitable way. EPR support of Multilanguage capability is a solution to achieve this objective. In this paper, an agent oriented architecture including several independent but cooperative agents has been suggested that helps to implement Multilanguage EPR systems.

Keywords: enterprise resource planning, Multilanguage, software architecture, agent oriented architecture, intelligence, learning, translation.

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Authors: Costin Badica, Maria Ganzha, Marcin Paprzycki

Abstract:

Recently, a model multi-agent e-commerce system based on mobile buyer agents and transfer of strategy modules was proposed. In this paper a different approach to code mobility is introduced, where agent mobility is replaced by local agent creation supplemented by similar code mobility as in the original proposal. UML diagrams of agents involved in the new approach to mobility and the augmented system activity diagram are presented and discussed.

Keywords: Agent system, agent mobility, code mobility, e-commerce, UML formalization.

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Authors: C. Slim

Abstract:

This paper presents an integrated model, which hybridized data envelopment analysis (DEA) and support vector machine (SVM) together, to class countries according to their efficiency and performance. This model takes into account aspects of multi-dimensional indicators, decision-making hierarchy and relativity of measurement. Starting from a set of indicators of performance as exhaustive as possible, a process of successive aggregations has been developed to attain an overall evaluation of a country’s competitiveness.

Keywords: Artificial neural networks, support vector machine, data envelopment analysis, aggregations, indicators of performance.

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Authors: D. Boutana, B. Barkat , F. Marir

Abstract:

In this paper, we propose a novel time-frequency distribution (TFD) for the analysis of multi-component signals. In particular, we use synthetic as well as real-life speech signals to prove the superiority of the proposed TFD in comparison to some existing ones. In the comparison, we consider the cross-terms suppression and the high energy concentration of the signal around its instantaneous frequency (IF).

Keywords: Cohen's Class, Multicomponent signal, SeparableKernel, Speech signal, Time- frequency resolution.

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Authors: Ki-Young Kim, Jae-Ho Lim, Deok-Min Kim, Seok-Yoon Kim

Abstract:

Average current analysis checking the impact of current flow is very important to guarantee the reliability of semiconductor systems. As semiconductor process technologies improve, the coupling capacitance often become bigger than self capacitances. In this paper, we propose an analytic technique for analyzing average current on interconnects in multi-conductor structures. The proposed technique has shown to yield the acceptable errors compared to HSPICE results while providing computational efficiency.

Keywords: current moment, interconnect modeling, reliability analysis, worst-case switching

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Authors: Elsheikh Asser

Abstract:

Time and cost are the main goals of the construction project management. The first schedule developed may not be a suitable schedule for beginning or completing the project to achieve the target completion time at a minimum total cost. In general, there are trade-offs between time and cost (TCT) to complete the activities of a project. This research presents genetic algorithms (GAs) multiobjective model for project scheduling considering different scenarios such as least cost, least time, and target time.

Keywords: Genetic algorithms, Time-cost trade-off.

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Authors: Sheroz Khan, A. F. Salami, W. A. Lawal, AHM Zahirul Alam, Shihab Abdel Hameed, M. J. E.Salami

Abstract:

In this paper, a multi-branch power line is modeled using ABCD matrix to show its worth as a communication channel. The model is simulated using MATLAB in an effort to investigate the effects of multiple loading, multipath, and those as a result of load mismatching. The channel transfer function is obtained and investigated using different cable lengths, and different number of bridge taps under given loading conditions.

Keywords: Power line Communication, Transfer Function, Channel Modeling, Signal Transmission.

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Authors: Ekkaluk Eksook, Chutima Prommak

Abstract:

This paper address the network reliability optimization problem in the optical access network design for the 3G cellular systems. We presents a novel 0-1 integer programming model for designing optical access network topologies comprised of multi-rings with common-edge in order to guarantee always-on services. The results show that the proposed model yields access network topologies with the optimal reliablity and satisfies both network cost limitations and traffic demand requirements.

Keywords: Network Reliability, Topological Network Design, 3G Cellular Networks.

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Authors: W. K. Yap, V. Karri

Abstract:

This paper presents a hybrid electric scooter model developed and simulated using Matlab/Simulink. This hybrid scooter modeled has a parallel hybrid structure. The main propulsion units consist of a two stroke internal combustion engine and a hub motor attached to the front wheel of the scooter. The methodology used to optimize the energy and fuel consumption of the hybrid electric scooter is the multi-mode approach. Various case studies were presented to check the model and were compared to the literatures. Results shown that the model developed was feasible and valuable.

Keywords: Hybrid electric scooters, modeling and simulation, hybrid scooter energy management.

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Authors: Amin Hajizadeh, Ehsan Hajizadeh

Abstract:

This paper presents a multi-objective formulation for optimal siting and sizing of distributed generation (DG) resources in distribution systems in order to minimize the cost of power losses and energy not supplied. The implemented technique is based on particle swarm optimization (PSO) and weight method that employed to obtain the best compromise between these costs. Simulation results on 33-bus distribution test system are presented to demonstrate the effectiveness of the proposed procedure.

Keywords: Distributed generation, distribution networks, particle swarm optimization, reliability, weight method

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Authors: Abdelrahman Ahmed Mohamed Osman

Abstract:

Over the past few years, a number of efforts have been exerted to build parallel processing systems that utilize the idle power of LAN-s and PC-s available in many homes and corporations. The main advantage of these approaches is that they provide cheap parallel processing environments for those who cannot afford the expenses of supercomputers and parallel processing hardware. However, most of the solutions provided are not very flexible in the use of available resources and very difficult to install and setup. In this paper, a multi-level web-based parallel processing system (MWPS) is designed (appendix). MWPS is based on the idea of volunteer computing, very flexible, easy to setup and easy to use. MWPS allows three types of subscribers: simple volunteers (single computers), super volunteers (full networks) and end users. All of these entities are coordinated transparently through a secure web site. Volunteer nodes provide the required processing power needed by the system end users. There is no limit on the number of volunteer nodes, and accordingly the system can grow indefinitely. Both volunteer and system users must register and subscribe. Once, they subscribe, each entity is provided with the appropriate MWPS components. These components are very easy to install. Super volunteer nodes are provided with special components that make it possible to delegate some of the load to their inner nodes. These inner nodes may also delegate some of the load to some other lower level inner nodes .... and so on. It is the responsibility of the parent super nodes to coordinate the delegation process and deliver the results back to the user. MWPS uses a simple behavior-based scheduler that takes into consideration the current load and previous behavior of processing nodes. Nodes that fulfill their contracts within the expected time get a high degree of trust. Nodes that fail to satisfy their contract get a lower degree of trust. MWPS is based on the .NET framework and provides the minimal level of security expected in distributed processing environments. Users and processing nodes are fully authenticated. Communications and messages between nodes are very secure. The system has been implemented using C#. MWPS may be used by any group of people or companies to establish a parallel processing or grid environment.

Keywords: Volunteer computing, Parallel Processing, XMLWebServices, .NET Remoting, Tuplespace.

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Authors: G. Balakayeva, A. Aktymbayeva

Abstract:

In this paper, we consider components of discrete event imitating model, implementing a simulation model by using JAVA and performing an input analysis of the data and an output analysis of the simulation results. Was lead development of imitating model of mass service system with n (n≥1) devices of service. On the basis of the developed process of a multithreading simulated the distributed processes with presence of synchronization. Was developed the algorithm of event-oriented simulation, was received results of system functioning with n devices of service.

Keywords: Imitating modeling, Mass service system, Multi agentsystem.

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Authors: Nadia El Alami El Hassani, Soukaina Motia, Benachir Bouchikhi, Nezha El Bari

Abstract:

Doxycycline (DXy) is a cycline antibiotic, most frequently prescribed to treat bacterial infections in veterinary medicine. However, its broad antimicrobial activity and low cost, lead to an intensive use, which can seriously affect human health. Therefore, its spread in the food products has to be monitored. The scope of this work was to synthetize a sensitive and very selective molecularly imprinted polymer (MIP) for DXy detection in honey samples. Firstly, the synthesis of this biosensor was performed by casting a layer of carboxylate polyvinyl chloride (PVC-COOH) on the working surface of a gold screen-printed electrode (Au-SPE) in order to bind covalently the analyte under mild conditions. Secondly, DXy as a template molecule was bounded to the activated carboxylic groups, and the formation of MIP was performed by a biocompatible polymer by the mean of polyacrylamide matrix. Then, DXy was detected by measurements of differential pulse voltammetry (DPV). A non-imprinted polymer (NIP) prepared in the same conditions and without the use of template molecule was also performed. We have noticed that the elaborated biosensor exhibits a high sensitivity and a linear behavior between the regenerated current and the logarithmic concentrations of DXy from 0.1 pg.mL⁻¹ to 1000 pg.mL⁻¹. This technic was successfully applied to determine DXy residues in honey samples with a limit of detection (LOD) of 0.1 pg.mL⁻¹ and an excellent selectivity when compared to the results of oxytetracycline (OXy) as analogous interfering compound. The proposed method is cheap, sensitive, selective, simple, and is applied successfully to detect DXy in honey with the recoveries of 87% and 95%. Considering these advantages, this system provides a further perspective for food quality control in industrial fields.

Keywords: Electrochemical sensor, molecular imprinted polymer, doxycycline, food control.

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Authors: Tamara Grujic, Mirjana Bonkovic

Abstract:

Measurements and quantitative analysis of kinematic parameters of human hand movements have an important role in different areas such as hand function rehabilitation, modeling of multi-digits robotic hands, and the development of machine-man interfaces. In this paper the assessment and evaluation of the reachto- grasp movement by using computerized and robot-assisted method is described. Experiment involved the measurements of hand positions of seven healthy subjects during grasping three objects of different shapes and sizes. Results showed that three dominant phases of reach-to-grasp movements could be clearly identified.

Keywords: Human hand, kinematics, reach-to-grasp movement.

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Authors: Bello Abdullahi, Yahaya M. Ibrahim, Ahmed D. Ibrahim, Kabir Bala

Abstract:

Public sector tendering has traditionally been conducted using manual paper-based processes which are known to be inefficient, less transparent and more prone to manipulations and errors. The advent of the Internet and the World Wide Web has led to the development of numerous e-Tendering systems that addressed some of the problems associated with the manual paper-based tendering system. However, most of these systems rarely support the evaluation of tenders and where they do it is mostly based on the single decision maker which is not suitable in public sector tendering, where for the sake of objectivity, transparency, and fairness, it is required that the evaluation is conducted through a tender evaluation committee. Currently, in Nigeria, the public tendering process in general and the evaluation of tenders, in particular, are largely conducted using manual paper-based processes. Automating these manual-based processes to digital-based processes can help in enhancing the proficiency of public sector tendering in Nigeria. This paper is part of a larger study to develop an electronic tendering system that supports the whole tendering lifecycle based on Nigerian procurement law. Specifically, this paper presents the design and implementation of part of the system that supports group evaluation of tenders based on a technique called fuzzy multi-attributes group decision making. The system was developed using Object-Oriented methodologies and Unified Modelling Language and hypothetically applied in the evaluation of technical and financial proposals submitted by bidders. The system was validated by professionals with extensive experiences in public sector procurement. The results of the validation showed that the system called NPS-eTender has an average rating of 74% with respect to correct and accurate modelling of the existing manual tendering domain and an average rating of 67.6% with respect to its potential to enhance the proficiency of public sector tendering in Nigeria. Thus, based on the results of the validation, the automation of the evaluation process to support tender evaluation committee is achievable and can lead to a more proficient public sector tendering system.

Keywords: e-Tendering, e-Procurement, public tendering, tender evaluation, tender evaluation committee, web-based group decision support system.

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Authors: Payman Davoodi-Nasab, Ahmad Rahbar-Kelishami, Jaber Safdari, Hossein Abolghasemi

Abstract:

The high purity rare earth elements (REEs) have been vastly used in the field of chemical engineering, metallurgy, nuclear energy, optical, magnetic, luminescence and laser materials, superconductors, ceramics, alloys, catalysts, and etc. Neodymium is one of the most abundant rare earths. By development of a neodymium–iron–boron (Nd–Fe–B) permanent magnet, the importance of neodymium has dramatically increased. Solvent extraction processes have many operational limitations such as large inventory of extractants, loss of solvent due to the organic solubility in aqueous solutions, volatilization of diluents, etc. One of the promising methods of liquid membrane processes is emulsion liquid membrane (ELM) which offers an alternative method to the solvent extraction processes. In this work, a study on Nd extraction through multi-walled carbon nanotubes (MWCNTs) assisted ELM using response surface methodology (RSM) has been performed. The ELM composed of diisooctylphosphinic acid (CYANEX 272) as carrier, MWCNTs as nanoparticles, Span-85 (sorbitan triooleate) as surfactant, kerosene as organic diluent and nitric acid as internal phase. The effects of important operating variables namely, surfactant concentration, MWCNTs concentration, and treatment ratio were investigated. Results were optimized using a central composite design (CCD) and a regression model for extraction percentage was developed. The 3D response surfaces of Nd(III) extraction efficiency were achieved and significance of three important variables and their interactions on the Nd extraction efficiency were found out. Results indicated that introducing the MWCNTs to the ELM process led to increasing the Nd extraction due to higher stability of membrane and mass transfer enhancement. MWCNTs concentration of 407 ppm, Span-85 concentration of 2.1 (%v/v) and treatment ratio of 10 were achieved as the optimum conditions. At the optimum condition, the extraction of Nd(III) reached the maximum of 99.03%.

Keywords: Emulsion liquid membrane, extraction of neodymium, multi-walled carbon nanotubes, response surface method.

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Authors: Guang Zeng, Jin Huang, Zicai Li

Abstract:

In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.

Keywords: Finite-difference equation, computational stability, hirt method.

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