Search results for: Virtual prototyping (VP) models.

Authors: Chil-Chyuan Kuo, Chen-Hsuan Tsai

Abstract:

This study presents a cost-effective approach for rapid fabricating modeling platforms utilized in fused deposition modeling system. A small-batch production of modeling platforms about 20 pieces can be obtained economically through silicone rubber mold using vacuum casting without applying the plastic injection molding. The air venting systems is crucial for fabricating modeling platform using vacuum casting. Modeling platforms fabricated can be used for building rapid prototyping model after sandblasting. This study offers industrial value because it has both time-effectiveness and cost-effectiveness.

Keywords: Vacuum casting, fused deposition modeling, modeling platform, sandblasting, surface roughness.

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Authors: Yanshuang Zhang, Byungho Jeong

Abstract:

In many cases, there are some time lag between the consumption of inputs and the production of outputs. This time lag effect should be considered in evaluating the performance of organizations. Recently, a couple of DEA models were developed for considering time lag effect in efficiency evaluation of research activities. Multi-periods input(MpI) and Multi-periods output(MpO) models are integrate models to calculate simple efficiency considering time lag effect. However, these models can’t discriminate efficient DMUs because of the nature of basic DEA model in which efficiency scores are limited to ‘1’. That is, efficient DMUs can’t be discriminated because their efficiency scores are same. Thus, this paper suggests a super-efficiency model for efficiency evaluation under the consideration of time lag effect based on the MpO model. A case example using a long term research project is given to compare the suggested model with the MpO model.

Keywords: DEA, Super-efficiency, Time Lag.

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Authors: Shewit Tsegaye, Kinde A. Fante

Abstract:

This paper presents the comparison and performance evaluation of synchronous machine excitation models. The two models, DC1A and AC4A, are among the IEEE standardized model structures for representing the wide variety of synchronous machine excitation systems. The performance evaluation of these models is done using SIMULINK simulation software. The simulation results obtained using transient analysis show that the DC1A excitation system is more reliable and stable than AC4A excitation system.

Keywords: Excitation system, synchronous machines, AC and DC regulators.

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Authors: Verónica Diaz Quezada

Abstract:

This research examines the teaching models used by secondary math teachers when teaching logarithmic, quadratic and exponential functions. For this, descriptive case studies have been carried out on 5 secondary teachers. These teachers have been chosen from 3 scientific-humanistic and technical schools, in Chile. Data have been obtained through non-participant class observation and the application of a questionnaire and a rubric to teachers. According to the results, the didactic model that prevails is the one that starts with an interactive strategy, moves to a more content-based structure, and ends with a reinforcement stage. Nonetheless, there is always influence from teachers, their methods, and the group of students.

Keywords: Teaching models, math teachers, functions, secondary education.

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Authors: Dalila Hamami, Baghdad Atmani

Abstract:

Modelling is a widely used tool to facilitate the evaluation of disease management. The interest of epidemiological models lies in their ability to explore hypothetical scenarios and provide decision makers with evidence to anticipate the consequences of disease incursion and impact of intervention strategies.

All models are, by nature, simplification of more complex systems. Models that involve diseases can be classified into different categories depending on how they treat the variability, time, space, and structure of the population. Approaches may be different from simple deterministic mathematical models, to complex stochastic simulations spatially explicit.

Thus, epidemiological modelling is now a necessity for epidemiological investigations, surveillance, testing hypotheses and generating follow-up activities necessary to perform complete and appropriate analysis.

The state of the art presented in the following, allows us to position itself to the most appropriate approaches in the epidemiological study.

Keywords: Bio-PEPA, Cellular automata, Epidemiological modelling, multi agent system, ordinary differential equations, PEPA, Process Algebra, Tuberculosis.

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Authors: Majid Tolouei-Rad, Anurag Dhull

Abstract:

This paper describes various stages of design and prototyping of a modular robot for use in various industrial applications. The major goal of current research has been to design and make different robotic joints at low cost capable of being assembled together in any given order for achieving various robot configurations. Five different types of joins were designed and manufactured where extensive research has been carried out on the design of each joint in order to achieve optimal strength, size, modularity, and price. This paper presents various stages of research and development undertaken to engineer these joints that include material selection, manufacturing, and strength analysis. The outcome of this research addresses the birth of a new generation of modular industrial robots with a wider range of applications and greater efficiency.

Keywords: Actuator, control system, configuration, robot.

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Authors: Thomas I. Kounitis

Abstract:

The purpose of this paper is to investigate the influence of a number of variables on the conditional mean and conditional variance of credit spread changes. The empirical analysis in this paper is conducted within the context of bivariate GARCH-in- Mean models, using the so-called BEKK parameterization. We show that credit spread changes are determined by interest-rate and equityreturn variables, which is in line with theory as provided by the structural models of default. We also identify the credit spread change volatility as an important determinant of credit spread changes, and provide evidence on the transmission of volatility between the variables under study.

Keywords: Credit spread changes, GARCH-in-Mean models, structural framework, volatility transmission.

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Authors: Muñoz-Sanchez, Victor Manuel, Perez-Flores, Antonio Manuel

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The main objective of this paper is to establish the relationship between models of state organization and the various types of collective identity expressed by the Spanish. The question of nationalism and identity ascription in Spain has always been a topic of special importance due to the presence in that country of territories where the population emits very different opinions of nationalist sentiment than the rest of Spain. The current situation of sovereignty challenge of Catalonia to the central government exemplifies the importance of the subject matter. In order to analyze this process of interrelation, we use a secondary data mining by applying the multiple correspondence analysis technique (MCA). As a main result a typology of four types of expression of collective identity based on models of State organization are shown, which are connected with the party position on this issue.

Keywords: Models of organization of the state, nationalism, collective identity, Spain, political parties.

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Authors: Zöhre Kara Kayikci, Günther Palm

Abstract:

A word recognition architecture based on a network of neural associative memories and hidden Markov models has been developed. The input stream, composed of subword-units like wordinternal triphones consisting of diphones and triphones, is provided to the network of neural associative memories by hidden Markov models. The word recognition network derives words from this input stream. The architecture has the ability to handle ambiguities on subword-unit level and is also able to add new words to the vocabulary during performance. The architecture is implemented to perform the word recognition task in a language processing system for understanding simple command sentences like “bot show apple".

Keywords: Hebbian learning, hidden Markov models, neuralassociative memories, word recognition.

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Authors: D. I. De Souza, G. P. Azevedo, R. Rocha

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In this paper we will develop a sequential life test approach applied to a modified low alloy-high strength steel part used in highway overpasses in Brazil.We will consider two possible underlying sampling distributions: the Normal and theInverse Weibull models. The minimum life will be considered equal to zero. We will use the two underlying models to analyze a fatigue life test situation, comparing the results obtained from both.Since a major chemical component of this low alloy-high strength steel part has been changed, there is little information available about the possible values that the parameters of the corresponding Normal and Inverse Weibull underlying sampling distributions could have. To estimate the shape and the scale parameters of these two sampling models we will use a maximum likelihood approach for censored failure data. We will also develop a truncation mechanism for the Inverse Weibull and Normal models. We will provide rules to truncate a sequential life testing situation making one of the two possible decisions at the moment of truncation; that is, accept or reject the null hypothesis H0. An example will develop the proposed truncated sequential life testing approach for the Inverse Weibull and Normal models.

Keywords: Sequential life testing, normal and inverse Weibull models, maximum likelihood approach, truncation mechanism.

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Authors: Greeshma Sharma, Sushil Chandra, Vijander Singh, Alok Prakash Mittal

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Navigational ability requires spatial representation, planning, and memory. It covers three interdependent domains, i.e. cognitive and perceptual factors, neural information processing, and variability in brain microstructure. Many attempts have been made to see the role of spatial representation in the navigational ability, and the individual differences have been identified in the neural substrate. But, there is also a need to address the influence of planning, memory on navigational ability. The present study aims to evaluate relations of aforementioned factors in the navigational ability. Total 30 participants volunteered in the study of a virtual shopping complex and subsequently were classified into good and bad navigators based on their performances. The result showed that planning ability was the most correlated factor for the navigational ability and also the discriminating factor between the good and bad navigators. There was also found the correlations between spatial memory recall and navigational ability. However, non-verbal episodic memory and spatial memory recall were also found to be correlated with the learning variable. This study attempts to identify differences between people with more and less navigational ability on the basis of planning and memory.

Keywords: Memory, planning navigational ability, virtual reality.

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Authors: Yogesh D. Bansod, Jiri Bursa

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The quantitative study of cell mechanics is of paramount interest, since it regulates the behaviour of the living cells in response to the myriad of extracellular and intracellular mechanical stimuli. The novel experimental techniques together with robust computational approaches have given rise to new theories and models, which describe cell mechanics as combination of biomechanical and biochemical processes. This review paper encapsulates the existing continuum-based computational approaches that have been developed for interpreting the mechanical responses of living cells under different loading and boundary conditions. The salient features and drawbacks of each model are discussed from both structural and biological points of view. This discussion can contribute to the development of even more precise and realistic computational models of cell mechanics based on continuum approaches or on their combination with microstructural approaches, which in turn may provide a better understanding of mechanotransduction in living cells.

Keywords: Cell mechanics, computational models, continuum approach, mechanical models.

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Authors: V. Phupha, T. Lantharthong, N. Rugthaicharoencheep

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The problem of generation expansion planning (GEP) has been extensively studied for many years. This paper presents three topics in GEP as follow: statistical model, models for generation expansion, and expansion problem. In the topic of statistical model, the main stages of the statistical modeling are briefly explained. Some works on models for GEP are reviewed in the topic of models for generation expansion. Finally for the topic of expansion problem, the major issues in the development of a longterm expansion plan are summarized.

Keywords: Generation expansion planning, strategies, power system

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Authors: O. Mauroner, L. Le, S. Best

Abstract:

Digital technologies offer many opportunities in the design and implementation of brand communication and advertising. Augmented reality (AR) is an innovative technology in marketing communication that focuses on the fact that virtual interaction with a product ad offers additional value to consumers. AR enables consumers to obtain (almost) real product experiences by the way of virtual information even before the purchase of a certain product. Aim of AR applications in relation with advertising is in-depth examination of product characteristics to enhance product knowledge as well as brand knowledge. Interactive design of advertising provides observers with an intense examination of a specific advertising message and therefore leads to better brand knowledge. The elaboration likelihood model and the central route to persuasion strongly support this argumentation. Nevertheless, AR in brand communication is still in an initial stage and therefore scientific findings about the impact of AR on information processing and brand attitude are rare. The aim of this paper is to empirically investigate the potential of AR applications in combination with traditional print advertising. To that effect an experimental design with different levels of interactivity is built to measure the impact of interactivity of an ad on different variables o advertising effectiveness.

Keywords: Advertising effectiveness, augmented reality, brand communication, brand recall, interactivity.

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Authors: Kristjan Kuhi, Kati K. Kaare, Ott Koppel

Abstract:

Modern management in most fields is performance based; both planning and implementation of maintenance and operational activities are driven by appropriately defined performance indicators. Continuous real-time data collection for management is becoming feasible due to technological advancements. Outdated and insufficient input data may result in incorrect decisions. When using deterministic models the uncertainty of the object state is not visible thus applying the deterministic models are more likely to give false diagnosis. Constructing structured probabilistic models of the performance indicators taking into consideration the surrounding indicator environment enables to estimate the trustworthiness of the indicator values. It also assists to fill gaps in data to improve the quality of the performance analysis and management decisions. In this paper authors discuss the application of probabilistic graphical models in the road performance measurement and propose a high-level conceptual model that enables analyzing and predicting more precisely future pavement deterioration based on road utilization.

Keywords: Probabilistic graphical models, performance indicators, road performance management, data collection

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Authors: Afshin Ahmadi Nadooshan, Ebrahim Shirani

Abstract:

Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.

Keywords: Volume-of-Fluid, Bubble Rising, SGIP model, CSS model, CSF model, PCIL model, interface, surface tension force.

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Authors: J. Zamastil, V. Patkos

Abstract:

Recent progress in calculation of the one-loop selfenergy of the electron bound in the Coulomb field is summarized. The relativistic multipole expansion is introduced. This expansion is based on a single assumption: except for the part of the time component of the electron four-momentum corresponding to the electron rest mass, the exchange of four-momentum between the virtual electron and photon can be treated perturbatively. For non Sstates and normalized difference n3
En −
E1 of the S-states this itself yields very accurate results after taking the method to the third order. For the ground state the perturbation treatment of the electron virtual states with very high three-momentum is to be avoided. For these states one can always rearrange the pertinent expression in such a way that free-particle approximation is allowed. Combination of the relativistic multipole expansion and free-particle approximation yields very accurate result after taking the method to the ninth order. These results are in very good agreement with the previous results obtained by the partial wave expansion and definitely exclude the possibility that the uncertainity in determination of the proton radius comes from the uncertainity in the calculation of the one-loop selfenergy.

Keywords: Hydrogen-like atoms, self-energy.

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Authors: Werner Sandmann, Verena Wolf

Abstract:

Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.

Keywords: Computational Modeling, Biological Networks, Stochastic Models, Markov Chains, Transition Class Models.

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Authors: Hina Gull, Farooque Azam, Wasi Haider Butt, Sardar Zafar Iqbal

Abstract:

The software system goes through a number of stages during its life and a software process model gives a standard format for planning, organizing and running a project. The article presents a new software development process model named as “Divide and Conquer Process Model", based on the idea first it divides the things to make them simple and then gathered them to get the whole work done. The article begins with the backgrounds of different software process models and problems in these models. This is followed by a new divide and conquer process model, explanation of its different stages and at the end edge over other models is shown.

Keywords: Process Model, Waterfall, divide and conquer, Requirements.

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Authors: Ganetsou Evanthia, Koutsikos Emmanouil, Austin Anna Maria

Abstract:

Information technology has long served the needs of individuals for learning and entertainment, but much less for children in sickness. The aim of the proposed online video game is to provide immersive learning opportunities as well as essential social and emotional scenarios for hospital-bound children with long-term illness. Online self-paced courses on chosen school subjects, including specialized software and multisensory assessments, aim at enhancing children’s academic achievement and sense of inclusion, while doctor minigames familiarize and educate young patients on their medical conditions. Online ethical dilemmas will offer children opportunities to contemplate on the importance of medical procedures and following assigned medication, often challenging for young patients; they will therefore reflect on their condition, re-evaluate their perceptions about hospitalization, and assume greater personal responsibility for their progress. Children’s emotional and psychosocial needs are addressed by engaging in social conventions, such as interactive, daily, collaborative mini games with other hospitalized peers, like virtual competitive sports games, weekly group psychodrama sessions, and online birthday parties or sleepovers. Social bonding is also fostered by having a virtual pet to interact with and take care of, as well as a virtual nurse to discuss and reflect on the mood of the day, engage in constructive dialogue and perspective-taking, and offer reminders. Access to the platform will be available throughout the day depending on the patient’s health status. The program is designed to minimize escapism and feelings of exclusion and can flexibly be adapted to offer post-treatment and a support online system at home.

Keywords: Hospitalized children, interactive games, long-term illness, cognitive enhancement, socioemotional development.

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Y. H. Tsai, Y. W. Chen

Abstract:

Facial features are frequently used to represent local properties of a human face image in computer vision applications. In this paper, we present a fast algorithm that can extract the facial features online such that they can give a satisfying representation of a face image. It includes one step for a coarse detection of each facial feature by AdaBoost and another one to increase the accuracy of the found points by Active Shape Models (ASM) in the regions of interest. The resulted facial features are evaluated by matching with artificial face models in the applications of physiognomy. The distance measure between the features and those in the fate models from the database is carried out by means of the Hausdorff distance. In the experiment, the proposed method shows the efficient performance in facial feature extractions and online system of physiognomy.

Keywords: Facial feature extraction, AdaBoost, Active shapemodel, Hausdorff distance

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Authors: Mimi Hafizah Abdullah, Hanani Farhah Harun, Nik Ruzni Nik Idris

Abstract:

With the implied volatility as an important factor in financial decision-making, in particular in option pricing valuation, and also the given fact that the pricing biases of Leland option pricing models and the implied volatility structure for the options are related, this study considers examining the implied adjusted volatility smile patterns and term structures in the S&P/ASX 200 index options using the different Leland option pricing models. The examination of the implied adjusted volatility smiles and term structures in the Australian index options market covers the global financial crisis in the mid-2007. The implied adjusted volatility was found to escalate approximately triple the rate prior the crisis.

Keywords: Implied adjusted volatility, Financial crisis, Leland option pricing models.

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Authors: Hai Ming Wong, Kuen Wai Ma, Lavender Yu Xin Yang, Yanqi Yang

Abstract:

Objectives: In recent years, the Faculty of Dentistry of the University of Hong Kong have extended the implementation of 3D electronic models (e-models) into problem-based learning (PBL) of the Bachelor of Dental Surgery (BDS) curriculum, aiming at mutual enhancement of PBL teaching quality and the students’ skills in using e-models. This study focuses on the effectiveness of e-models serving as a tool to enhance the students’ skills and competences in PBL. Methods: The questionnaire surveys are conducted to measure 50 fourth-year BDS students’ attitude change between beginning and end of blended PBL tutorials. The response rate of this survey is 100%. Results: The results of this study show the students’ agreement on enhancement of their learning experience after e-model implementation and their expectation to have more blended PBL courses in the future. The potential of e-models in cultivating students’ self-learning skills reduces their dependence on others, while improving their communication skills to argue about pros and cons of different treatment options. The students’ independent thinking ability and problem solving skills are promoted by e-model implementation, resulting in better decision making in treatment planning. Conclusion: It is important for future dental education curriculum planning to cope with the students’ needs, and offer support in the form of software, hardware and facilitators’ assistance for better e-model implementation.

Keywords: Problem-Based learning, curriculum, dental education, 3-D electronic models.

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Authors: I. Alberdi, H. Iribas, A. Martin, N. Aginako

Abstract:

This paper describes a platform that faces the main research areas for e-learning educational contents. Reusability tackles the possibility to use contents in different courses reducing costs and exploiting available data from repositories. In our approach the production of educational material is based on templates to reuse learning objects. In terms of interoperability the main challenge lays on reaching the audience through different platforms. E-learning solution must track social consumption evolution where nowadays lots of multimedia contents are accessed through the social networks. Our work faces it by implementing a platform for generation of multimedia presentations focused on the new paradigm related to social media. The system produces videos-courses on top of web standard SMIL (Synchronized Multimedia Integration Language) ready to be published and shared. Regarding interfaces it is mandatory to satisfy user needs and ease communication. To overcome it the platform deploys virtual teachers that provide natural interfaces while multimodal features remove barriers to pupils with disabilities.

Keywords: Collaborative, multimedia e-learning, reusability, SMIL, virtual teacher

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Authors: Khaoula Hidouri, Ali Benhmidene, Bechir Chouachi

Abstract:

The purification of brackish seawater becomes a necessity and not a choice against demographic and industrial growth especially in third world countries. Two models can be used in this work: simple solar still and simple solar still coupled with a heat pump. In this research, the productivity of water by Simple Solar Distiller (SSD) and Simple Solar Distiller Hybrid Heat Pump (SSDHP) was determined by the orientation, the use of heat pump, the simple or double glass cover. The productivity can exceed 1.2 L/m²h for the SSDHP and 0.5 L/m²h for SSD model. The result of the global efficiency is determined for two models SSD and SSDHP give respectively 30%, 50%. The internal efficiency attained 35% for SSD and 60% of the SSDHP models. Convective heat coefficient can be determined by attained 2.5 W/m²°C and 0.5 W/m²°C respectively for SSDHP and SSD models.

Keywords: Productivity, efficiency, convective heat coefficient, SSD model, SSDHP model.

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Authors: Hussein A. Kazem, Abdulhakeem Abdullah Albaloshi, Ali Said Ali Al-Jabri, Khamis Humaid AlSaidi

Abstract:

This paper proposes different methods for estimation of the harmonic currents of the single-phase diode bridge rectifier. Both simple and advanced methods are compared and the models are put into a context of practical use for calculating the harmonic distortion in a typical application. Finally, the different models are compared to measurements of a real application and convincing results are achieved.

Keywords: Single-phase rectifier, line side Harmonics

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Authors: Farhad Asgari Mehrabadi, Mohammad Reza Khoshravan

Abstract:

In the present study, fracture behavior of woven fabric-reinforced glass/epoxy composite laminates under mode III crack growth was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance calibration (CC) method and the Virtual Crack Closure Technique (VCCT). To achieve this aim ECT (Edge Crack Torsion) was used to evaluate fracture toughness in mode III loading (out of plane-shear) at different crack lengths. Load–displacement and associated energy release rates were obtained for various case of interest. To calculate fracture toughness JIII, two criteria were considered including non-linearity and maximum points in load-displacement curve and it is observed that JIII increases with the crack length increase. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of woven glass/epoxy laminates in mode III.

Keywords: Mode III, Fracture, Composite, Crack growth Finite Element.

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Authors: Karim Heidari

Abstract:

Semantic Web Technologies enable machines to interpret data published in a machine-interpretable form on the web. At the present time, only human beings are able to understand the product information published online. The emerging semantic Web technologies have the potential to deeply influence the further development of the Internet Economy. In this paper we propose a scenario based research approach to predict the effects of these new technologies on electronic markets and business models of traders and intermediaries and customers. Over 300 million searches are conducted everyday on the Internet by people trying to find what they need. A majority of these searches are in the domain of consumer ecommerce, where a web user is looking for something to buy. This represents a huge cost in terms of people hours and an enormous drain of resources. Agent enabled semantic search will have a dramatic impact on the precision of these searches. It will reduce and possibly eliminate information asymmetry where a better informed buyer gets the best value. By impacting this key determinant of market prices semantic web will foster the evolution of different business and economic models. We submit that there is a need for developing these futuristic models based on our current understanding of e-commerce models and nascent semantic web technologies. We believe these business models will encourage mainstream web developers and businesses to join the “semantic web revolution."

Keywords: E-Commerce, E-Business, Semantic Web, XML.

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Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we mainly analyze an automated parking system where the storage and retrieval requests are performed by a tower crane. In this parking system, the S/R crane which is located at the middle of the bottom of the cylinder parking area can rotate in both clockwise and counterclockwise and three kinds of movements can be done simultaneously. We develop some mathematical travel time models for the single command cycle under the random storage assignment using the characteristics of this system. Finally, we compare these travel models with discrete case and it is shown that these travel models display a good satisfactory performance.

Keywords: Parking system, travel time model, tower crane.

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