Search results for: Average Mean Distance function

Authors: Suresh S. Salankar, Balasaheb M. Patre

Abstract:

Research into the problem of classification of sonar signals has been taken up as a challenging task for the neural networks. This paper investigates the design of an optimal classifier using a Multi layer Perceptron Neural Network (MLP NN) and Support Vector Machines (SVM). Results obtained using sonar data sets suggest that SVM classifier perform well in comparison with well-known MLP NN classifier. An average classification accuracy of 91.974% is achieved with SVM classifier and 90.3609% with MLP NN classifier, on the test instances. The area under the Receiver Operating Characteristics (ROC) curve for the proposed SVM classifier on test data set is found as 0.981183, which is very close to unity and this clearly confirms the excellent quality of the proposed classifier. The SVM classifier employed in this paper is implemented using kernel Adatron algorithm is seen to be robust and relatively insensitive to the parameter initialization in comparison to MLP NN.

Keywords: Classification, MLP NN, backpropagation algorithm, SVM, Receiver Operating Characteristics.

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Authors: Robert E. Hursig, Jane X. Zhang

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A robust still image face localization algorithm capable of operating in an unconstrained visual environment is proposed. First, construction of a robust skin classifier within a shifted HSV color space is described. Then various filtering operations are performed to better isolate face candidates and mitigate the effect of substantial non-skin regions. Finally, a novel Bhattacharyya-based face detection algorithm is used to compare candidate regions of interest with a unique illumination-dependent face model probability distribution function approximation. Experimental results show a 90% face detection success rate despite the demands of the visually noisy environment.

Keywords: Audio-visual speech recognition, Bhattacharyyacoefficient, face detection,

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Authors: Wen-Bao Qiao, Jean-Charles Créput

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To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: Doubly linked list, parallel 2-opt, tour division, GPU.

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Authors: Young-Seok Choi

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This paper presents a subband adaptive filter (SAF) for a system identification where an impulse response is sparse and disturbed with an impulsive noise. Benefiting from the uses of l1-norm optimization and l0-norm penalty of the weight vector in the cost function, the proposed l0-norm sign SAF (l0-SSAF) achieves both robustness against impulsive noise and much improved convergence behavior than the classical adaptive filters. Simulation results in the system identification scenario confirm that the proposed l0-norm SSAF is not only more robust but also faster and more accurate than its counterparts in the sparse system identification in the presence of impulsive noise.

Keywords: Subband adaptive filter, l0-norm, sparse system, robustness, impulsive interference.

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Authors: A. Hortacsu, A. Tektas

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This paper aims to develop a model that assists the international retailer in selecting the country that maximizes the degree of fit between the retailer-s goals and the country characteristics in his initial internationalization move. A two-stage multi criteria decision model is designed integrating the Analytic Hierarchy Process (AHP) and Goal Programming. Ethical, cultural, geographic and economic proximity are identified as the relevant constructs of the internationalization decision. The constructs are further structured into sub-factors within analytic hierarchy. The model helps the retailer to integrate, rank and weigh a number of hard and soft factors and prioritize the countries accordingly. The model has been implemented on a Turkish luxury goods retailer who was planning to internationalize. Actual entry of the specific retailer in the selected country is a support for the model. Implementation on a single retailer limits the generalizability of the results; however, the emphasis of the paper is on construct identification and model development. The paper enriches the existing literature by proposing a hybrid multi objective decision model which introduces new soft dimensions i.e. perceived distance, ethical proximity, humane orientation to the decision process and facilitates effective decision making.

Keywords: Analytic hierarchy process, culture, ethics, goal programming, retail foreign market selection.

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Authors: Tianyi Qin

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Along with the acceleration of Chinese urbanization, the expansion, renovation and demolition of old buildings is on the stage together with the design and construction of new buildings every day in downtown of the old city area. The coordinative symbiosis between new and old buildings is an important problem which needs to be solved in the process of urban development. By studying and analyzing the case of Shanghai Citic Plaza and surroundings, this paper contributes to discussing the concept, value and problems to be solved of the coordination of new and old buildings, meanwhile, striking the balance between new and old buildings from the aspects of architectural form, space, function and local context. As a result, the strategy of the coordinative symbiosis between new and old buildings is summarized, which can offer some guiding principles to urban development from now on.

Keywords: Coordinative symbiosis, new and old buildings, Shanghai Citic Plaza, strategy.

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Authors: Abd Elrahman Elgamala, N. Darwish, I. Bondouk, Sh. Hamada

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Available experimental angular distributions for ⁶Li elastically scattered from ¹⁶O nucleus in the energy range 13.0–50.0 MeV are investigated and reanalyzed using optical model of the conventional phenomenological potential and also using double folding optical model of different interaction models: DDM3Y1, CDM3Y1, CDM3Y2, and CDM3Y3. All the involved models of interaction are of M3Y Paris except DDM3Y1 which is of M3Y Reid and the main difference between them lies in the different values for the parameters of the incorporated density distribution function F(ρ). We have extracted the renormalization factor N_R for ⁶Li+¹⁶O nuclear system in the energy range 13.0–50.0 MeV using the aforementioned interaction models.

Keywords: Elastic scattering, optical model, folding potential, density distribution.

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Authors: Arash Azizi-Mazreah, Mohammad T. Manzuri Shalmani, Hamid Barati, Ali Barati

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The energy consumption and delay in read/write operation of conventional SRAM is investigated analytically as well as by simulation. Explicit analytical expressions for the energy consumption and delay in read and write operation as a function of device parameters and supply voltage are derived. The expressions are useful in predicting the effect of parameter changes on the energy consumption and speed as well as in optimizing the design of conventional SRAM. HSPICE simulation in standard 0.25μm CMOS technology confirms precision of analytical expressions derived from this paper.

Keywords: Read energy consumption, write energy consumption, read delay, write delay.

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Authors: J. E. Mendes, L.Abrunhosa, J. A. Teixeira, E. R. de Camargo, C. P. de Souza, J. D. C. Pessoa

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Among the many promising nanomaterials with antifungal properties, metal nanoparticles (silver nanoparticles) stand out due to their high chemical activity. Therefore, the aim of this study was to evaluate the effect of silver nanoparticles (AgNPs) against Phomopsis sp. AgNPs were synthesized by silver nitrate reduction with sodium citrate and stabilized with ammonia. The synthesized AgNPs have further been characterized by UV/Visible spectroscopy, Biophysical techniques like Dynamic light scattering (DLS) and Scanning Electron Microscopy (SEM). The average diameter of the prepared silver colloidal nanoparticles was about 52 nm. Absolute inhibitions (100%) were observed on treated with a 270 and 540 µg ml^-1 concentration of AgNPs. The results from the study of the AgNPs antifungal effect are significant and suggest that the synthesized silver nanoparticles may have an advantage compared with conventional fungicides.

Keywords: Antifungal activity, Phomopsis sp., Seeds, Silver Nanoparticles, Soybean.

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Authors: H. Gholami, M. Jalali Azizpour

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Stress Corrosion Crack (SCC) in pipeline is a type of environmentally assisted cracking (EAC), since its discovery in 1965 as a possible cause of failure in pipeline, SCC has caused, on average, one of two failures per year in the U.S, According to the NACE SCC DA a pipe line segment is considered susceptible to SCC if all of the following factors are met: The operating stress exceeds 60% of specified minimum yield strength (SMYS), the operating temperature exceeds 38°C, the segment is less than 32 km downstream from a compressor station, the age of the pipeline is greater than 10 years and the coating type is other than Fusion Bonded Epoxy(FBE). In this paper as a practical experience in NISOC, Direct Assessment (DA) Method is used for identification SCC defect in unpiggable pipeline located downstream of compressor station.

Keywords: Stress Corrosion Crack, Direct Assessment, Disbondment, Transgranular SCC, Compressor Station.

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Authors: M. Orefice, V. Di Vito

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This paper provides a description of a Collision Avoidance algorithm that has been developed starting from the mathematical modeling of the flight of insects, in terms of spirals and conchospirals geometric paths. It is able to calculate a proper avoidance manoeuver aimed to prevent the infringement of a predefined distance threshold between ownship and the considered intruder, while minimizing the ownship trajectory deviation from the original path and in compliance with the aircraft performance limitations and dynamic constraints. The algorithm is designed in order to be suitable for real-time applications, so that it can be considered for the implementation in the most recent airborne automatic collision avoidance systems using the traffic data received through an ADS-B IN device. The presented approach is able to take into account the rules-of-the-air, due to the possibility to select, through specifically designed decision making logic based on the consideration of the encounter geometry, the direction of the calculated collision avoidance manoeuver that allows complying with the rules-of-the-air, as for instance the fundamental right of way rule. In the paper, the proposed collision avoidance algorithm is presented and its preliminary design and software implementation is described. The applicability of this method has been proved through preliminary simulation tests performed in a 2D environment considering single intruder encounter geometries, as reported and discussed in the paper.

Keywords: collision avoidance, RPAS, spiral geometry, ADS-B based application

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Authors: Shengqi Yu, Jinwei Zhao

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This paper presents a kind of analog circuit based temperature control system, which is mainly composed by threshold control signal circuit, synchronization signal circuit and trigger pulse circuit. Firstly, the temperature feedback signal function is realized by temperature sensor TS503F3950E. Secondly, the main control circuit forms the cycle controlled pulse signal to control the thyristor switching model. Finally two reverse paralleled thyristors regulate the output power by their switching state. In the consequence, this is a modernized and energy-saving domestic electric heating system.

Keywords: Time base circuit, automatic control, zero-crossing trigger, temperature control.

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Authors: Viriyavudh Sim, WooYoung Jung

Abstract:

Window system in high rise building is occasionally subjected to an excessive wind intensity, particularly during typhoon. The failure of window system did not affect overall safety of structural performance; however, it could endanger the safety of the residents. In this paper, comparison of fragility curves for window system of two residential buildings was studied. The probability of failure for individual window was determined with Monte Carlo Simulation method. Then, lognormal cumulative distribution function was used to represent the fragility. The results showed that windows located on the edge of leeward wall were more susceptible to wind load and the probability of failure for each window panel increased at higher floors.

Keywords: Wind fragility, window system, high rise building.

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Authors: C. Ardil

Abstract:

The purpose of this paper is to present fuzzy TOPSIS in an entropic fuzzy environment. Due to the ambiguous concepts often represented in decision data, exact values are insufficient to model real-life situations. In this paper, the rating of each alternative is defined in fuzzy linguistic terms, which can be expressed with triangular fuzzy numbers. The weight of each criterion is then derived from the decision matrix using the entropy weighting method. Next, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the TOPSIS concept, a closeness coefficient is defined to determine the ranking order of all alternatives by simultaneously calculating the distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). Finally, an illustrative example of selecting stealth fighter aircraft is shown at the end of this article to highlight the procedure of the proposed method. Correlation analysis and validation analysis using TOPSIS, WSM, and WPM methods were performed to compare the ranking order of the alternatives.

Keywords: stealth fighter aircraft selection, fuzzy uncertainty theory (FUT), fuzzy entropic decision (FED), fuzzy linguistic variables, triangular fuzzy numbers, multiple criteria decision making analysis, MCDMA, TOPSIS, WSM, WPM

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Authors: Chen Zhang, Bernhard Schwarz-Röhr, Alexander Härting

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To acquire accurate ship motions at the center of gravity, a single low-cost inertial sensor is utilized and applied on board to measure ship oscillating motions. As observations, the three axes accelerations and three axes rotational rates provided by the sensor are used. The mathematical model of processing the observation data includes determination of the distance vector between the sensor and the center of gravity in x, y, and z directions. After setting up the transfer matrix from sensor’s own coordinate system to the ship’s body frame, an extended Kalman filter is applied to deal with nonlinearities between the ship motion in the body frame and the observation information in the sensor’s frame. As a side effect, the method eliminates sensor noise and other unwanted errors. Results are not only roll and pitch, but also linear motions, in particular heave and surge at the center of gravity. For testing, we resort to measurements recorded on a small vessel in a well-defined sea state. With response amplitude operators computed numerically by a commercial software (Seaway), motion characteristics are estimated. These agree well with the measurements after processing with the suggested method.

Keywords: Extended Kalman filter, nonlinear estimation, sea trial, ship motion estimation.

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Authors: Tomas Cechura, Michal Simon

Abstract:

This paper describes a proposal for cost calculation of warehouse processes and its usage for setting standards for performance evaluation. One of the most common options of monitoring process performance is benchmarking. The typical outcome is whether the monitored object is better or worse than an average or standard. Traditional approaches, however, cannot find any specific opportunities to improve performance or eliminate inefficiencies in processes. Higher process efficiency can be achieved for example by cost reduction assuming that the same output is generated. However, costs can be reduced only if we know their structure and we are able to calculate them accurately. In the warehouse process area it is rather difficult because in most cases we have available only aggregated values with low explanatory ability. The aim of this paper is to create a suitable method for calculating the storage costs. At the end is shown a practical example of process calculation.

Keywords: Calculation, Costs, Performance, Process, Warehouse.

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Authors: Frank Emmert Streib, Matthias Dehmer, Jing Liu, Max Mühlhauser

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In this paper we present a method for gene ranking from DNA microarray data. More precisely, we calculate the correlation networks, which are unweighted and undirected graphs, from microarray data of cervical cancer whereas each network represents a tissue of a certain tumor stage and each node in the network represents a gene. From these networks we extract one tree for each gene by a local decomposition of the correlation network. The interpretation of a tree is that it represents the n-nearest neighbor genes on the n-th level of a tree, measured by the Dijkstra distance, and, hence, gives the local embedding of a gene within the correlation network. For the obtained trees we measure the pairwise similarity between trees rooted by the same gene from normal to cancerous tissues. This evaluates the modification of the tree topology due to progression of the tumor. Finally, we rank the obtained similarity values from all tissue comparisons and select the top ranked genes. For these genes the local neighborhood in the correlation networks changes most between normal and cancerous tissues. As a result we find that the top ranked genes are candidates suspected to be involved in tumor growth and, hence, indicates that our method captures essential information from the underlying DNA microarray data of cervical cancer.

Keywords: Graph similarity, DNA microarray data, cancer.

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Authors: Adarsh Venkataraman Ganesan, Sundaram Swaminathan, Rama Jayaraj

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Human middle-ear is the key component of the auditory system. Its function is to transfer the sound waves through the ear canal to provide sufficient stimulus to the fluids of the inner ear. Degradation of the ossicles that transmit these sound waves from the eardrum to the inner ear leads to hearing loss. This problem can be overcome by replacing one or more of these ossicles by middleear prosthesis. Designing such prosthesis requires a comprehensive knowledge of the biomechanics of the middle-ear. There are many finite element modeling approaches developed to understand the biomechanics of the middle ear. The available models in the literature, involve high computation time. In this paper, we propose a simplified model which provides a reasonably accurate result with much less computational time. Simulation results indicate a maximum sound pressure gain of 10 dB at 5500 Hz.

Keywords: Ear, Ossicles, COMSOL, Stapes.

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: Non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two- dimensional Schrodinger equation.

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Authors: Petr Šimek, Kamil Kostruk

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This paper deals with the problem of testing the Electronic Control Unit (ECU) for the specified function validation. Modern ECUs have many functions which need to be tested. This process requires tracking between the test and the specification. The technique discussed in this paper explores the system for automating this process. The paper focuses on the introduction to the problem in general, then it describes the proposed test system concept and its principle. It looks at how the process of the ECU interface specification file for automated interface testing and test tracking works. In the end, the future possible development of the project is discussed.

Keywords: Electronic control unit testing, embedded system, test generate, test automation, process automation, CAN bus, Ethernet.

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Authors: Lorenzo Daghini, Andreas Archenti, Cornel Mihai Nicolescu

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This paper introduces a novel design for boring bar with enhanced damping capability. The principle followed in the design phase was to enhance the damping capability minimizing the loss in static stiffness through implementation of composite material interfaces. The newly designed tool has been compared to a conventional tool. The evaluation criteria were the dynamic characteristics, frequency and damping ratio, of the machining system, as well as the surface roughness of the machined workpieces. The use of composite material in the design of damped tool has been demonstrated effective. Furthermore, the autoregressive moving average (ARMA) models presented in this paper take into consideration the interaction between the elastic structure of the machine tool and the cutting process and can therefore be used to characterize the machining system in operational conditions.

Keywords: ARMA, cutting stability, damped tool, machining.

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Authors: Joon Ho Kim, Tae Kwon Ha

Abstract:

Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by differential speed rolling (DSR) process were studied by electron back scattered diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100^oC with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400^oC for 30 to 120min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.

Keywords: Aluminum/Copper clad sheet, differential speed rolling, interface layer, microstructure, annealing, electron back scattered diffraction.

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Authors: K. Varesi, A. Radan

Abstract:

In this paper, a new Genetic Algorithm (GA) based methodology is proposed to optimize the Degree of Hybridization (DOH) in a passenger parallel hybrid car. At first step, target parameters for the vehicle are decided and then using ADvanced VehIcle SimulatOR (ADVISOR) software, the variation pattern of these target parameters, across the different DOHs, is extracted. At the next step, a suitable cost function is defined and is optimized using GA. In this paper, also a new technique has been proposed for deciding the number of battery modules for each DOH, which leads to a great improvement in the vehicle performance. The proposed methodology is so simple, fast and at the same time, so efficient.

Keywords: Degree of Hybridization (DOH), Electric Motor, Emissions, Fuel Economy, Genetic Algorithm (GA), Hybrid ElectricVehicle (HEV), Vehicle Performance

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Authors: Masahiro Takahashi, Kosuke Harada, Shihomi Nakao, Mitsuhiro Higashihata, Hiroshi Ikenoue, Daisuke Nakamura, Tatsuo Okada

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Zinc oxide (ZnO) is one of the light emitting materials in ultraviolet (UV) region. In addition, ZnO nanostructures are also attracting increasing research interest as buildingblocks for UV optoelectronic applications. We have succeeded in synthesizing vertically-aligned ZnO nanostructures by laser interference patterning, which is catalyst-free and non-contact technique. In this study, vertically-aligned ZnO nanowall arrays were synthesized using two-beam interference. The maximum height and average thickness of the ZnO nanowalls were about 4.5µm and 200 nm, respectively.UV lasing from a piece of the ZnO nanowall was obtained under the third harmonic of a Q-switched Nd:YAG laser excitation, and the estimated threshold power density for lasing was about 150 kW/cm². Furthermore, UV lasing from the vertically-aligned ZnO nanowall was also achieved. The results indicate that ZnO nanowalls can be applied to random laser.

Keywords: Zinc Oxide, nanowall, interference laser, UV lasing.

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Authors: Petra Balla, Gabor Manhertz, Akos Antal

Abstract:

Nowadays spinal deformities are very frequent problems among teenagers. Scheuermann disease is a one dimensional deformity of the spine, but it has prevalence over 11% of the children. A traditional technology, the moiré method was used by us for screening and diagnosing this type of spinal deformity. A LabVIEW program has been developed to evaluate the moiré pictures of patients with Scheuermann disease. Two different solutions were tested in this computer program, the extreme and the inflexion point calculation methods. Effects using these methods were compared and according to the results both solutions seemed to be appropriate. Statistical results showed better efficiency in case of the extreme search method where the average difference was only 6,09⁰.

Keywords: Spinal deformity, picture evaluation, moiré method, Scheuermann disease, curve detection, moiré topography.

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Authors: Shan Gao

Abstract:

This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer-s observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

Keywords: Discrete-time, finite buffer, single working vacation, batch arrival, partial rejection.

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Authors: C. Ardil

Abstract:

In this paper, we introduce an e-collaborative learning circles methodology which utilizes the information and communication technologies (ICTs) in e-educational processes. In e-collaborative learning circles methodology, the teachers and students announce their research projects on various mailing lists and discussion boards using available ICTs. The teachers & moderators and students who are already members of the e-forums, discuss the project proposals in their classrooms sent out by the potential global partner schools and return the requested feed back to the proposing school(s) about their level of the participation and contribution in the research. In general, an e-collaborative learning circle project is implemented with a small and diverse group (usually 8-10 participants) from around the world. The students meet regularly over a period of weeks/months through the ICTs during the ecollaborative learning process. When the project is completed, a project product (e-book / DVD) is prepared and sent to the circle members. In this research, when taking into account the interests and motivation of the participating students with the facilitating role of the teacher(s), the students in each circle do research to obtain new data and information, thus enabling them to have the opportunity to meet both different cultures and international understandings across the globe. However, while the participants communicate along with the members in the circle they also practice and develop their communication language skills. Finally, teachers and students find the possibility to develop their skills in using the ICTs as well.

Keywords: Distance Education, Online Learning, Web BasedLearning, Learning Circles, e-Collaborative Learning Circles

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Authors: Farid Moshgelani, Dhamin Al-Khalili, Côme Rozon

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In this paper, FinFET devices are analyzed with emphasis on sub-threshold leakage current control. This is achieved through proper biasing of the back gate, and through the use of asymmetric work functions for the four terminal FinFET devices. We are also examining different configurations of multiplexers and XOR gates using transistors of symmetric and asymmetric work functions. Based on extensive characterization data for MUX circuits, our proposed configuration using symmetric devices lead to leakage current and delay improvements of 65% and 47% respectively compared to results in the literature. For XOR gates, a 90% improvement in the average leakage current is achieved by using asymmetric devices. All simulations are based on a 25nm FinFET technology using the University of Florida UFDG model.

Keywords: FinFET, logic functions, asymmetric workfunction devices, back gate biasing, sub-threshold leakage current.

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Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

In this study, thermal fatigue properties of 400 series ferritic stainless steels have been evaluated in the temperature ranges of 200-800oC and 200-900oC. Systematic methods for control of temperatures within the predetermined range and measurement of load applied to specimens as a function of temperature during thermal cycles have been established. Thermal fatigue tests were conducted under fully constrained condition, where both ends of specimens were completely fixed. It has been revealed that load relaxation behavior at the temperatures of thermal cycle was closely related with the thermal fatigue property. Thermal fatigue resistance of 430J1L stainless steel is found to be superior to the other steels.

Keywords: Ferritic stainless steel, automotive exhaust, thermal fatigue, microstructure, load relaxation.

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Authors: N. M. Kamoh, D. G. Gyemang, M. C. Soomiyol

Abstract:

This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.

Keywords: Collocation shifted Legendre polynomials, Simpson’s rule and Volterra integro-differential equations.

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