Search results for: Gaussian process model

Authors: A. Youseef, F. Liu

Abstract:

The existing information system (IS) developments methods are not met the requirements to resolve the security related IS problems and they fail to provide a successful integration of security and systems engineering during all development process stages. Hence, the security should be considered during the whole software development process and identified with the requirements specification. This paper aims to propose an integrated security and IS engineering approach in all software development process stages by using i* language. This proposed framework categorizes into three separate parts: modelling business environment part, modelling information technology system part and modelling IS security part. The results show that considering security IS goals in the whole system development process can have a positive influence on system implementation and better meet business expectations.

Keywords: Business Process Modelling (BPM), Information System Security, Software Development Process, Requirement Engineering.

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Authors: Richard Pircher, Lukas Zenk, Hanna Risku

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Using activity theory, organisational theory and didactics as theoretical foundations, a comprehensive model of the organisational dimensions relevant for learning and knowledge transfer will be developed. In a second step, a Learning Assessment Guideline will be elaborated. This guideline will be designed to permit a targeted analysis of organisations to identify the status quo in those areas crucial to the implementation of learning and knowledge transfer. In addition, this self-analysis tool will enable learning managers to select adequate didactic models for e- and blended learning. As part of the European Integrated Project "Process-oriented Learning and Information Exchange" (PROLIX), this model of organisational prerequisites for learning and knowledge transfer will be empirically tested in four profit and non-profit organisations in Great Britain, Germany and France (to be finalized in autumn 2006). The findings concern not only the capability of the model of organisational dimensions, but also the predominant perceptions of and obstacles to learning in organisations.

Keywords: Activity theory, knowledge management organisational theory, "Process-oriented Learning and Information Exchange" (PROLIX).

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Authors: M. Tridi, N. Nacereddine, N. Oucief

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This paper describes a novel method for automatic estimation of the contours of weld defect in radiography images. Generally, the contour detection is the first operation which we apply in the visual recognition system. Our approach can be described as a region based maximum likelihood formulation of parametric deformable contours. This formulation provides robustness against the poor image quality, and allows simultaneous estimation of the contour parameters together with other parameters of the model. Implementation is performed by a deterministic iterative algorithm with minimal user intervention. Results testify for the very good performance of the approach especially in synthetic weld defect images.

Keywords: Contour, gaussian, likelihood, rayleigh.

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Authors: Saeed Vaneshani, Hooshang Jazayeri-Rad

Abstract:

Fuzzy logic control (FLC) systems have been tested in many technical and industrial applications as a useful modeling tool that can handle the uncertainties and nonlinearities of modern control systems. The main drawback of the FLC methodologies in the industrial environment is challenging for selecting the number of optimum tuning parameters. In this paper, a method has been proposed for finding the optimum membership functions of a fuzzy system using particle swarm optimization (PSO) algorithm. A synthetic algorithm combined from fuzzy logic control and PSO algorithm is used to design a controller for a continuous stirred tank reactor (CSTR) with the aim of achieving the accurate and acceptable desired results. To exhibit the effectiveness of proposed algorithm, it is used to optimize the Gaussian membership functions of the fuzzy model of a nonlinear CSTR system as a case study. It is clearly proved that the optimized membership functions (MFs) provided better performance than a fuzzy model for the same system, when the MFs were heuristically defined.

Keywords: continuous stirred tank reactor (CSTR), fuzzy logiccontrol (FLC), membership function(MF), particle swarmoptimization (PSO)

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Authors: Jānis Zuters

Abstract:

There are a lot of extensions made to the classic model of multi-layer perceptron (MLP). A notable amount of them has been designed to hasten the learning process without considering the quality of generalization. The paper proposes a new MLP extension based on exploiting topology of the input layer of the network. Experimental results show the extended model to improve upon generalization capability in certain cases. The new model requires additional computational resources to compare to the classic model, nevertheless the loss in efficiency isn-t regarded to be significant.

Keywords: Learning algorithm, multi-layer perceptron, topology.

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Authors: Reinhold Decker, Christian Holsing, Sascha Lerke

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This paper presents a new growing neural network for cluster analysis and market segmentation, which optimizes the size and structure of clusters by iteratively checking them for multivariate normality. We combine the recently published SGNN approach [8] with the basic principle underlying the Gaussian-means algorithm [13] and the Mardia test for multivariate normality [18, 19]. The new approach distinguishes from existing ones by its holistic design and its great autonomy regarding the clustering process as a whole. Its performance is demonstrated by means of synthetic 2D data and by real lifestyle survey data usable for market segmentation.

Keywords: Artificial neural network, clustering, multivariatenormality, market segmentation, self-organization

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Authors: Sujoy Das, M. M. Ghosh

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The thermal conductivity of a fluid can be significantly enhanced by dispersing nano-sized particles in it, and the resultant fluid is termed as "nanofluid". A theoretical model for estimating the thermal conductivity of a nanofluid has been proposed here. It is based on the mechanism that evenly dispersed nanoparticles within a nanofluid undergo Brownian motion in course of which the nanoparticles repeatedly collide with the heat source. During each collision a rapid heat transfer occurs owing to the solidsolid contact. Molecular dynamics (MD) simulation of the collision of nanoparticles with the heat source has shown that there is a pulselike pick up of heat by the nanoparticles within 20-100 ps, the extent of which depends not only on thermal conductivity of the nanoparticles, but also on the elastic and other physical properties of the nanoparticle. After the collision the nanoparticles undergo Brownian motion in the base fluid and release the excess heat to the surrounding base fluid within 2-10 ms. The Brownian motion and associated temperature variation of the nanoparticles have been modeled by stochastic analysis. Repeated occurrence of these events by the suspended nanoparticles significantly contributes to the characteristic thermal conductivity of the nanofluids, which has been estimated by the present model for a ethylene glycol based nanofluid containing Cu-nanoparticles of size ranging from 8 to 20 nm, with Gaussian size distribution. The prediction of the present model has shown a reasonable agreement with the experimental data available in literature.

Keywords: Brownian dynamics, Molecular dynamics, Nanofluid, Thermal conductivity.

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Authors: Mikhail Vladimirovich Deryabin, Morten Willatzen

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In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k . p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom.

Keywords: cylindrical quantum dots, electronic eigen energies, red and white Gaussian noise, ensemble averaging effects.

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Authors: Teerapun Saeheaw, Nivit Charoenchai, Wichai Chattinnawat

Abstract:

This paper proposes a meta-heuristic called Ant Colony Optimization to solve multi-objective production problems. The multi-objective function is to minimize lead time and work in process. The problem is related to the decision variables, i.e.; distance and process time. According to decision criteria, the mathematical model is formulated. In order to solve the model an ant colony optimization approach has been developed. The proposed algorithm is parameterized by the number of ant colonies and the number of pheromone trails. One example is given to illustrate the effectiveness of the proposed model. The proposed formulations; Max-Min Ant system are then used to solve the problem and the results evaluate the performance and efficiency of the proposed algorithm using simulation.

Keywords: Ant colony optimization, multi-objective problems.

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Authors: D. Pérez, M. M. E. Alemany

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In this work, a framework to model the Supply Chain (SC) Collaborative Planning (CP) process is proposed. The main contributions of this framework concern 1) the presentation of the decision view, the most important one due to the characteristics of the process, jointly within the physical, organisation and information views, and 2) the simultaneous consideration of the spatial and temporal integration among the different supply chain decision centres. This framework provides the basis for a realistic and integrated perspective of the supply chain collaborative planning process and also the analytical modeling of each of its decisional activities.

Keywords: Collaborative Planning, Decision View, Distributed Decision-Making, Framework.

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Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis, Leila Jafari

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In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed, illustrated by a numerical example.

Keywords: Partially observable system, hidden Markov model, competing risks, multivariate Bayesian control.

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Authors: Amit Kohli, Aashim Wadhwa, Tapan Virmani, Ujjwal Jain

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The objective of present work is to stimulate the machining of material by electrical discharge machining (EDM) to give effect of input parameters like discharge current (Ip), pulse on time (Ton), pulse off time (Toff) which can bring about changes in the output parameter, i.e. material removal rate. Experimental data was gathered from die sinking EDM process using copper electrode and Medium Carbon Steel (AISI 1040) as work-piece. The rules of membership function (MF) and the degree of closeness to the optimum value of the MMR are within the upper and lower range of the process parameters. It was found that proposed fuzzy model is in close agreement with the experimental results. By Intelligent, model based design and control of EDM process parameters in this study will help to enable dramatically decreased product and process development cycle times.

Keywords: Electrical discharge Machining (EDM), Fuzzy Logic, Material removal rate (MRR), Membership functions (MF).

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Authors: M. Zeydan, G. Toğa

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This study deals with a multi-criteria optimization problem which has been transformed into a single objective optimization problem using Response Surface Methodology (RSM), Artificial Neural Network (ANN) and Grey Relational Analyses (GRA) approach. Grey-RSM and Grey-ANN are hybrid techniques which can be used for solving multi-criteria optimization problem. There have been two main purposes of this research as follows. 1. To determine optimum and robust fiber dyeing process conditions by using RSM and ANN based on GRA, 2. To obtain the best suitable model by comparing models developed by different methodologies. The design variables for fiber dyeing process in textile are temperature, time, softener, anti-static, material quantity, pH, retarder, and dispergator. The quality characteristics to be evaluated are nominal color consistency of fiber, maximum strength of fiber, minimum color of dyeing solution. GRA-RSM with exact level value, GRA-RSM with interval level value and GRA-ANN models were compared based on GRA output value and MSE (Mean Square Error) performance measurement of outputs with each other. As a result, GRA-ANN with interval value model seems to be suitable reducing the variation of dyeing process for GRA output value of the model.

Keywords: Artificial Neural Network, Grey Relational Analysis, Optimization, Response Surface Methodology

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Authors: Sachin Man Bajimaya, SangChul Park, Gi-Nam Wang

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The objective of this paper is to estimate realistic principal extrusion process parameters by means of artificial neural network. Conventionally, finite element analysis is used to derive process parameters. However, the finite element analysis of the extrusion model does not consider the manufacturing process constraints in its modeling. Therefore, the process parameters obtained through such an analysis remains highly theoretical. Alternatively, process development in industrial extrusion is to a great extent based on trial and error and often involves full-size experiments, which are both expensive and time-consuming. The artificial neural network-based estimation of the extrusion process parameters prior to plant execution helps to make the actual extrusion operation more efficient because more realistic parameters may be obtained. And so, it bridges the gap between simulation and real manufacturing execution system. In this work, a suitable neural network is designed which is trained using an appropriate learning algorithm. The network so trained is used to predict the manufacturing process parameters.

Keywords: Artificial Neural Network (ANN), Indirect Extrusion, Finite Element Analysis, MES.

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Authors: A. Nuchitprasittichai, N. Lerdritsirikoon, T. Khamsing

Abstract:

Simulation modeling can be used to solve real world problems. It provides an understanding of a complex system. To develop a simplified model of process simulation, a suitable experimental design is required to be able to capture surface characteristics. This paper presents the experimental design and algorithm used to model the process simulation for optimization problem. The CO₂ liquefaction based on external refrigeration with two refrigeration circuits was used as a simulation case study. Latin Hypercube Sampling (LHS) was purposed to combine with existing Central Composite Design (CCD) samples to improve the performance of CCD in generating the second order model of the system. The second order model was then used as the objective function of the optimization problem. The results showed that adding LHS samples to CCD samples can help capture surface curvature characteristics. Suitable number of LHS sample points should be considered in order to get an accurate nonlinear model with minimum number of simulation experiments.

Keywords: Central composite design, CO2 liquefaction, Latin Hypercube Sampling, simulation – based optimization.

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Authors: Andrés Carrión García, Aura López de Murillo, José Jabaloyes Vivas, Angela Grisales del Río

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Some quality control tools use non metric subjective information coming from experts, who qualify the intensity of relations existing inside processes, but without quantifying them. In this paper we have developed a quality control analytic tool, measuring the impact or strength of the relationship between process operations and product characteristics. The tool includes two models: a qualitative model, allowing relationships description and analysis; and a formal quantitative model, by means of which relationship quantification is achieved. In the first one, concepts from the Graphs Theory were applied to identify those process elements which can be sources of variation, that is, those quality characteristics or operations that have some sort of prelacy over the others and that should become control items. Also the most dependent elements can be identified, that is those elements receiving the effects of elements identified as variation sources. If controls are focused in those dependent elements, efficiency of control is compromised by the fact that we are controlling effects, not causes. The second model applied adapts the multivariate statistical technique of Covariance Structural Analysis. This approach allowed us to quantify the relationships. The computer package LISREL was used to obtain statistics and to validate the model.

Keywords: Characteristics matrix, covariance structure analysis, LISREL.

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Authors: Jin-Bao Zhao, Wei Deng

Abstract:

This paper aims at developing a multilevel fuzzy decision support model for urban rail transit planning schemes in China under the background that China is presently experiencing an unprecedented construction of urban rail transit. In this study, an appropriate model using multilevel fuzzy comprehensive evaluation method is developed. In the decision process, the followings are considered as the influential objectives: traveler attraction, environment protection, project feasibility and operation. In addition, consistent matrix analysis method is used to determine the weights between objectives and the weights between the objectives- sub-indictors, which reduces the work caused by repeated establishment of the decision matrix on the basis of ensuring the consistency of decision matrix. The application results show that multilevel fuzzy decision model can perfectly deal with the multivariable and multilevel decision process, which is particularly useful in the resolution of multilevel decision-making problem of urban rail transit planning schemes.

Keywords: Urban rail transit, planning schemes, multilevel fuzzy decision support model, consistent matrix analysis

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Authors: Serena Alvino, Paola Forcheri, Maria Grazia Ierardi, Luigi Sarti

Abstract:

One of the main advantages of the LO paradigm is to allow the availability of good quality, shareable learning material through the Web. The effectiveness of the retrieval process requires a formal description of the resources (metadata) that closely fits the user-s search criteria; in spite of the huge international efforts in this field, educational metadata schemata often fail to fulfil this requirement. This work aims to improve the situation, by the definition of a metadata model capturing specific didactic features of shareable learning resources. It classifies LOs into “teacher-oriented" and “student-oriented" categories, in order to describe the role a LO is to play when it is integrated into the educational process. This article describes the model and a first experimental validation process that has been carried out in a controlled environment.

Keywords: Learning object, pedagogical metadata, experimental validation.

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Authors: M. K. Pradhan, C. K. Biswas,

Abstract:

In the current research, neuro-fuzzy model and regression model was developed to predict Material Removal Rate in Electrical Discharge Machining process for AISI D2 tool steel with copper electrode. Extensive experiments were conducted with various levels of discharge current, pulse duration and duty cycle. The experimental data are split into two sets, one for training and the other for validation of the model. The training data were used to develop the above models and the test data, which was not used earlier to develop these models were used for validation the models. Subsequently, the models are compared. It was found that the predicted and experimental results were in good agreement and the coefficients of correlation were found to be 0.999 and 0.974 for neuro fuzzy and regression model respectively

Keywords: Electrical discharge machining, material removal rate, neuro-fuzzy model, regression model, mountain clustering.

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Authors: Kai Jin, Hyder Abdul-Razzak, Yousri Elkassabgi, Hong Zhou, Aaron Herrera

Abstract:

Six Sigma is a well known discipline that reduces variation using complex statistical tools and the DMAIC model. By integrating Goldratts-s Theory of Constraints, the Five Focusing Points and System Thinking tools, Six Sigma projects can be selected where it can cause more impact in the company. This research defines an integrated model of six sigma and constraint management that shows a step-by-step guide using the original methodologies from each discipline and is evaluated in a case study from the production line of a Automobile engine monoblock V8, resulting in an increase in the line capacity from 18.7 pieces per hour to 22.4 pieces per hour, a reduction of 60% of Work-In-Process and a variation decrease of 0.73%.

Keywords: Constraint Management, Manufacturing Process Improvement, Six Sigma, System Thinking.

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Authors: Hassan Haleh, Amin Ghaffari, Parisa Farahpour

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Need for an appropriate system of evaluating students- educational developments is a key problem to achieve the predefined educational goals. Intensity of the related papers in the last years; that tries to proof or disproof the necessity and adequacy of the students assessment; is the corroborator of this matter. Some of these studies tried to increase the precision of determining question weights in scientific examinations. But in all of them there has been an attempt to adjust the initial question weights while the accuracy and precision of those initial question weights are still under question. Thus In order to increase the precision of the assessment process of students- educational development, the present study tries to propose a new method for determining the initial question weights by considering the factors of questions like: difficulty, importance and complexity; and implementing a combined method of PROMETHEE and fuzzy analytic network process using a data mining approach to improve the model-s inputs. The result of the implemented case study proves the development of performance and precision of the proposed model.

Keywords: Assessing students, Analytic network process, Clustering, Data mining, Fuzzy sets, Multi-criteria decision making, and Preference function.

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Authors: H. Baseri, G. Alinejad

Abstract:

The objective of this study is to design an adaptive neuro-fuzzy inference system (ANFIS) for estimation of surface roughness in grinding process. The Used data have been generated from experimental observations when the wheel has been dressed using a rotary diamond disc dresser. The input parameters of model are dressing speed ratio, dressing depth and dresser cross-feed rate and output parameter is surface roughness. In the experimental procedure the grinding conditions are constant and only the dressing conditions are varied. The comparison of the predicted values and the experimental data indicates that the ANFIS model has a better performance with respect to back-propagation neural network (BPNN) model which has been presented by the authors in previous work for estimation of the surface roughness.

Keywords: Grinding, ANFIS, Neural network, Disc dressing.

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Authors: Abdulsalam A. Al-Sudairi

Abstract:

Object-oriented simulation is considered one of the most sophisticated techniques that has been widely used in planning, designing, executing and maintaining construction projects. This technique enables the modeler to focus on objects which is extremely important for thorough understanding of a system. Thus, identifying an object is an essential point of building a successful simulation model. In a maintenance process an object is a maintenance work order (MWO). This study demonstrates a maintenance simulation model for the building maintenance division of Saudi Consolidated Electric Company (SCECO) in Dammam, Saudi Arabia. The model focused on both types of maintenance processes namely: (1) preventive maintenance (PM) and (2) corrective maintenance (CM). It is apparent from the findings that object-oriented simulation is a good diagnostic and experimental tool. This is because problems, limitations, bottlenecks and so forth are easily identified. These features are very difficult to obtain when using other tools.

Keywords: Object oriented, simulation, maintenance, process, work orders

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Authors: Beata Czarnacka-Chrobot

Abstract:

Unsatisfactory effectiveness of software systems development and enhancement projects is one of the main reasons why in software engineering there are attempts being made to use experiences coming from other engineering disciplines. In spite of specificity of software product and process a belief had come out that the execution of software could be more effective if these objects were subject to measurement – as it is true in other engineering disciplines for which measurement is an immanent feature. Thus objective and reliable approaches to the measurement of software processes and products have been sought in software engineering for several dozens of years already. This may be proved, among others, by the current version of CMMI for Development model. This paper is aimed at analyzing the approach to the software processes and products measurement proposed in the latest version of this very model, indicating growing acceptance for this issue in software engineering.

Keywords: CMMI for Development (1.3), ISO/IEC standards, measurement and analysis process area, software process measurement, software product measurement.

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Authors: Dariush Jafari, Seyed Ali Jafari

Abstract:

The recommended limit for cadmium concentration in potable water is less than 0.005 mg/L. A continuous biosorption process using indigenous red seaweed, Gracilaria corticata, was performed to remove cadmium from the potable water. The process was conducted under fixed conditions and the breakthrough curves were achieved for three consecutive sorption-desorption cycles. A modeling based on Artificial Neural Network (ANN) was employed to fit the experimental breakthrough data. In addition, a simplified semi empirical model, Thomas, was employed for this purpose. It was found that ANN well described the experimental data (R2>0.99) while the Thomas prediction were a bit less successful with R2>0.97. The adjusted design parameters using the nonlinear form of Thomas model was in a good agreement with the experimentally obtained ones. The results approve the capability of ANN to predict the cadmium concentration in potable water.

Keywords: ANN, biosorption, cadmium, packed-bed, potable water.

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Authors: Aussadavut Dumrongsiri

Abstract:

Web-based technologies have created numerous opportunities for electronic word-of-mouth (eWOM) communication. There are many factors that affect customer adoption and decisionmaking process. However, only a few researches focus on some factors such as the membership time of forum and propensity to trust. Using a discrete-time event simulation to simulate a diffusion model along with a consumer decision model, the study shows the effect of each factor on adoption of opinions on on-line discussion forum. The purpose of this study is to examine the effect of factor affecting information adoption and decision making process. The model is constructed to test quantitative aspects of each factor. The simulation study shows the membership time and the propensity to trust has an effect on information adoption and purchasing decision. The result of simulation shows that the longer the membership time in the communities and the higher propensity to trust could lead to the higher demand rates because consumers find it easier and faster to trust the person in the community and then adopt the eWOM. Other implications for both researchers and practitioners are provided.

Keywords: word of mouth, simulation, consumer behavior, ebusiness, marketing, diffusion process.

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Authors: Ε. Giovanis

Abstract:

The purpose of this paper is to present two different approaches of financial distress pre-warning models appropriate for risk supervisors, investors and policy makers. We examine a sample of the financial institutions and electronic companies of Taiwan Security Exchange (TSE) market from 2002 through 2008. We present a binary logistic regression with paned data analysis. With the pooled binary logistic regression we build a model including more variables in the regression than with random effects, while the in-sample and out-sample forecasting performance is higher in random effects estimation than in pooled regression. On the other hand we estimate an Adaptive Neuro-Fuzzy Inference System (ANFIS) with Gaussian and Generalized Bell (Gbell) functions and we find that ANFIS outperforms significant Logit regressions in both in-sample and out-of-sample periods, indicating that ANFIS is a more appropriate tool for financial risk managers and for the economic policy makers in central banks and national statistical services.

Keywords: ANFIS, Binary logistic regression, Financialdistress, Panel data

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Authors: Akbar Zamaniyan, Alireza Behroozsarand, Hadi Ebrahimi

Abstract:

Partial oxidation (POX) of light hydrocarbons (e.g. methane) is occurred in the first part of the autothermal reformer (ATR). The results of the detailed modeling of the reformer based on the thermodynamic model of the POX and 1D heterogeneous catalytic model for the fixed bed section are considered here. According to the results, the overall performance of the ATR can be improved by changing the important feed parameters.

Keywords: Autothermal Reformer, Partial Oxidation, Mathematical Modeling, Process Simulation, Syngas.

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Authors: Mohammad H. Fattahi

Abstract:

Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. Noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: Chaotic behavior, wavelet, noise reduction, river flow.

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Authors: Asadollah Boshra, Ahmad Seif, Mehran Aghaei

Abstract:

A model of (4, 4) single-walled boron-nitride nanotube as a representative of armchair boron-nitride nanotubes studied. At first the structure optimization performed and then Nuclear Magnetic Resonance parameters (NMR) by Density Functional Theory (DFT) method at 11B and 15N nuclei calculated. Resulted parameters evaluation presents electrostatic environment heterogeneity along the nanotube and especially at the ends but the nuclei in a layer feel the same electrostatic environment. All of calculations carried out using Gaussian 98 Software package.

Keywords: Boron-nitride nanotube, Density Functional Theory, Nuclear Magnetic Resonance (NMR).

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