Search results for: innovative method and tools.

Authors: A. S. Kipcak, P. Gurses, K. Kunt, E. Moroydor Derun, S. Piskin

Abstract:

There are many kinds of metal borates found not only in nature but also synthesized in the laboratory such as magnesium borates. Due to its excellent properties, as remarkable ceramic materials, they have also application areas in anti-wear and friction reducing additives as well as electro-conductive treating agents. The synthesis of magnesium borate powders can be fulfilled simply with two different methods, hydrothermal and thermal synthesis. Microwave assisted method, also another way of producing magnesium borate, can be classified into thermal synthesis because of using the principles of solid state synthesis. It also contributes producing particles with small size and high purity in nano-size material synthesize. In this study the production of magnesium borates, are aimed using MgCl2.6H2O and H3BO3. The identification of both starting materials and products were made by the equipments of, X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). After several synthesis steps magnesium borates were synthesized and characterized by XRD and FT-IR, as well.

Keywords: FT-IR, magnesium borates, microwave method, XRD.

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Authors: Peyman Shadman Heidari, Mohammad Khorasani

Abstract:

The principal purpose of this article is to present a new method based on Adaptive Neural Network Fuzzy Inference System (ANFIS) to generate additional artificial earthquake accelerograms from presented data, which are compatible with specified response spectra. The proposed method uses the learning abilities of ANFIS to develop the knowledge of the inverse mapping from response spectrum to earthquake records. In addition, wavelet packet transform is used to decompose specified earthquake records and then ANFISs are trained to relate the response spectrum of records to their wavelet packet coefficients. Finally, an interpretive example is presented which uses an ensemble of recorded accelerograms to demonstrate the effectiveness of the proposed method.

Keywords: Adaptive Neural Network Fuzzy Inference System, Wavelet Packet Transform, Response Spectrum.

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Authors: A. K. Al-Othman, K. M. EL-Nagger

Abstract:

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED). Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using one system. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED).

Keywords: Security Constrained Economic Dispatch, Direct Search method, optimization.

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Authors: T. Hacib, M. R. Mekideche, N. Ferkha

Abstract:

This paper presents an approach which is based on the use of supervised feed forward neural network, namely multilayer perceptron (MLP) neural network and finite element method (FEM) to solve the inverse problem of parameters identification. The approach is used to identify unknown parameters of ferromagnetic materials. The methodology used in this study consists in the simulation of a large number of parameters in a material under test, using the finite element method (FEM). Both variations in relative magnetic permeability and electrical conductivity of the material under test are considered. Then, the obtained results are used to generate a set of vectors for the training of MLP neural network. Finally, the obtained neural network is used to evaluate a group of new materials, simulated by the FEM, but not belonging to the original dataset. Noisy data, added to the probe measurements is used to enhance the robustness of the method. The reached results demonstrate the efficiency of the proposed approach, and encourage future works on this subject.

Keywords: Inverse problem, MLP neural network, parametersidentification, FEM.

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Authors: A. Zerarka, A. Soukeur, N. Khelil

Abstract:

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

Keywords: Integral equation, particle swarm optimization, Runge's phenomenon.

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Authors: H. B. Darbandi, M. R. Ito, J. Little

Abstract:

This paper describes a probabilistic method for three-dimensional object recognition using a shared pool of surface signatures. This technique uses flatness, orientation, and convexity signatures that encode the surface of a free-form object into three discriminative vectors, and then creates a shared pool of data by clustering the signatures using a distance function. This method applies the Bayes-s rule for recognition process, and it is extensible to a large collection of three-dimensional objects.

Keywords: Object recognition, modeling, classification, computer vision.

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Authors: S. A. Naeini, A. Khalili

Abstract:

Nowadays, tunnels with different applications are developed, and most of them are related to subway tunnels. The excavation of shallow tunnels that pass under municipal utilities is very important, and the surface settlement control is an important factor in the design. The study sought to analyze the settlement and also to find an appropriate model in order to predict the behavior of the tunnel in Tehran subway line-3. The displacement in these sections is also determined by using numerical analyses and numerical modeling. In addition, the Adaptive Neuro-Fuzzy Inference System (ANFIS) method is utilized by Hybrid training algorithm. The database pertinent to the optimum network was obtained from 46 subway tunnels in Iran and Turkey which have been constructed by the new Austrian tunneling method (NATM) with similar parameters based on type of their soil. The surface settlement was measured, and the acquired results were compared to the predicted values. The results disclosed that computing intelligence is a good substitute for numerical modeling.

Keywords: Settlement, subway line, FLAC3D, ANFIS method.

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Authors: Afrooz Moatari Kazerouni

Abstract:

In a competitive production environment, critical decision making are based on data resulted by random sampling of product units. Efficiency of these decisions depends on data quality and also their reliability scale. This point leads to the necessity of a reliable measurement system. Therefore, the conjecture process and analysing the errors contributes to a measurement system known as Measurement System Analysis (MSA). The aim of this research is on determining the necessity and assurance of extensive development in analysing measurement systems, particularly with the use of Repeatability and Reproducibility Gages (GR&R) to improve physical measurements. Nowadays in productive industries, repeatability and reproducibility gages released so well but they are not applicable as well as other measurement system analysis methods. To get familiar with this method and gain a feedback in improving measurement systems, this survey would be on “ANOVA" method as the most widespread way of calculating Repeatability and Reproducibility (R&R).

Keywords: Analysis of Variance (ANOVA), MeasurementSystem Analysis (MSA), Part-Operator interaction effect, Repeatability and Reproducibility.

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Authors: F. Noto, G. Costa, L. Celona, F. Chines, G. Ciavola, G. Cuttone, S. Gammino, O. Leonardi, S. Marletta, G. Torrisi

Abstract:

At Istituto Nazionale di Fisica Nucleare – Laboratorio Nazionale del Sud (INFN-LNS), a broad experience in the design, construction and commissioning of ECR and microwave ion sources is available. The AISHa ion source has been designed by taking into account the typical requirements of hospital-based facilities, where the minimization of the mean time between failures (MTBF) is a key point together with the maintenance operations, which should be fast and easy. It is intended to be a multipurpose device, operating at 18 GHz, in order to achieve higher plasma densities. It should provide enough versatility for future needs of the hadron therapy, including the ability to run at larger microwave power to produce different species and highly charged ion beams. The source is potentially interesting for any hadron therapy facility using heavy ions. In this paper, we analyzed the dimensional test and electrical test about an innovative solution for the containment chamber that allows us to solve our isolation and structural problems.

Keywords: FEM Analysis, ECR ion source, dielectrical measurement.

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Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

Abstract:

This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

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Authors: M. Ramachandra, G. Dilip Maruthi, R. Rashmi

Abstract:

This paper aims to study the corrosion property of aluminum matrix nanocomposite of an aluminum alloy (Al-6061) reinforced with zirconium dioxide (ZrO₂) particles. The zirconium dioxide particles are synthesized by solution combustion method. The nanocomposite materials are prepared by mechanical stir casting method, varying the percentage of n-ZrO₂ (2.5%, 5% and 7.5% by weight). The corrosion behavior of base metal (Al-6061) and Al/ZrO₂ nanocomposite in seawater (3.5% NaCl solution) is measured using the potential control method. The corrosion rate is evaluated by Tafel extrapolation technique. The corrosion potential increases with the increase in wt.% of n-ZrO₂ in the nanocomposite which means the decrease in corrosion rate. It is found that on addition of n-ZrO2 particles to the aluminum matrix, the corrosion rate has decreased compared to the base metal.

Keywords: Al6061 alloy, corrosion, solution combustion, stir casting, Potentiostat, Zirconium Dioxide.

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Authors: Tomáš Ludík, Josef Navrátil, Alena Langerová

Abstract:

Tackling emergency situations is performed based on emergency scenarios. These scenarios do not have a uniform form in the Czech Republic. They are unstructured and developed primarily in the text form. This does not allow solving emergency situations efficiently. For this reason, the paper aims at defining a Process Oriented Architecture to support and thus to improve tackling emergency situations in the Czech Republic. The innovative Process Oriented Architecture is based on the Workflow Reference Model while taking into account the options of Business Process Management Suites for the implementation of process oriented emergency scenarios. To verify the proposed architecture the Proof of Concept has been used which covers the reception of an emergency event at the district emergency operations centre. Within the particular implementation of the proposed architecture the Bonita Open Solution has been used. The architecture created in this way is suitable not only for emergency management, but also for educational purposes.

Keywords: Business Process Management Suite, Czech Republic, Emergency Scenarios, Process Execution, Process Oriented Architecture.

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Authors: A. Perolini

Abstract:

Feature and model selection are in the center of attention of many researches because of their impact on classifiers- performance. Both selections are usually performed separately but recent developments suggest using a combined GA-SVM approach to perform them simultaneously. This approach improves the performance of the classifier identifying the best subset of variables and the optimal parameters- values. Although GA-SVM is an effective method it is computationally expensive, thus a rough method can be considered. The paper investigates a joined approach of Genetic Algorithm and kernel matrix criteria to perform simultaneously feature and model selection for SVM classification problem. The purpose of this research is to improve the classification performance of SVM through an efficient approach, the Kernel Matrix Genetic Algorithm method (KMGA).

Keywords: Feature and model selection, Genetic Algorithms, Support Vector Machines, kernel matrix.

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Authors: S. Sfarni, E. Bellenger, J. Fortin, M. Guessasma

Abstract:

The use of the mechanical simulation (in particular the finite element analysis) requires the management of assumptions in order to analyse a real complex system. In finite element analysis (FEA), two modeling steps require assumptions to be able to carry out the computations and to obtain some results: the building of the physical model and the building of the simulation model. The simplification assumptions made on the analysed system in these two steps can generate two kinds of errors: the physical modeling errors (mathematical model, domain simplifications, materials properties, boundary conditions and loads) and the mesh discretization errors. This paper proposes a mesh adaptive method based on the use of an h-adaptive scheme in combination with an error estimator in order to choose the mesh of the simulation model. This method allows us to choose the mesh of the simulation model in order to control the cost and the quality of the finite element analysis.

Keywords: Finite element, discretization errors, adaptivity.

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Authors: Tanwarat Kajsongkram, Saowalux Rotamporn, Sirinat Limbunruang, Sirinan Thubthimthed

Abstract:

High Performance Liquid Chromatography (HPLC) method was developed and validated for simultaneous estimation of 6-Gingerol(6G) and 6-Shogaol(6S) in joint pain relief gel containing ginger extract. The chromatographic separation was achieved by using C18 column, 150 x 4.6mm i.d., 5μ Luna, mobile phase containing acetonitrile and water (gradient elution). The flow rate was 1.0 ml/min and the absorbance was monitored at 282 nm. The proposed method was validated in terms of the analytical parameters such as specificity, accuracy, precision, linearity, range, limit of detection (LOD), limit of quantification (LOQ), and determined based on the International Conference on Harmonization (ICH) guidelines. The linearity ranges of 6G and 6S were obtained over 20- 60 and 6-18 μg/ml respectively. Good linearity was observed over the above-mentioned range with linear regression equation Y= 11016x- 23778 for 6G and Y = 19276x-19604 for 6S (x is concentration of analytes in μg/ml and Y is peak area). The value of correlation coefficient was found to be 0.9994 for both markers. The limit of detection (LOD) and limit of quantification (LOQ) for 6G were 0.8567 and 2.8555 μg/ml and for 6S were 0.3672 and 1.2238 μg/ml respectively. The recovery range for 6G and 6S were found to be 91.57 to 102.36 % and 84.73 to 92.85 % for all three spiked levels. The RSD values from repeated extractions for 6G and 6S were 3.43 and 3.09% respectively. The validation of developed method on precision, accuracy, specificity, linearity, and range were also performed with well-accepted results.

Keywords: Ginger, 6-gingerol, HPLC, 6-shogaol.

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Authors: Mu-Yen Chen, Min-Hsuan Fan, Chia-Chen Chen, Siang-Yu Jhong

Abstract:

In recent years, real estate prediction or valuation has been a topic of discussion in many developed countries. Improper hype created by investors leads to fluctuating prices of real estate, affecting many consumers to purchase their own homes. Therefore, scholars from various countries have conducted research in real estate valuation and prediction. With the back-propagation neural network that has been popular in recent years and the orthogonal array in the Taguchi method, this study aimed to find the optimal parameter combination at different levels of orthogonal array after the system presented different parameter combinations, so that the artificial neural network obtained the most accurate results. The experimental results also demonstrated that the method presented in the study had a better result than traditional machine learning. Finally, it also showed that the model proposed in this study had the optimal predictive effect, and could significantly reduce the cost of time in simulation operation. The best predictive results could be found with a fewer number of experiments more efficiently. Thus users could predict a real estate transaction price that is not far from the current actual prices.

Keywords: Artificial Neural Network, Taguchi Method, Real Estate Valuation Model.

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Dylan Menzies, Ismail Shahin

Abstract:

This paper describes a new efficient blind source separation method; in this method we uses a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.

Keywords: Blind source separation (BSS), estimates, full-band, mixtures, Sub-band.

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Authors: A. Falsafain, S. M. Taheri, M. Mashinchi

Abstract:

Using a set of confidence intervals, we develop a common approach, to construct a fuzzy set as an estimator for unknown parameters in statistical models. We investigate a method to derive the explicit and unique membership function of such fuzzy estimators. The proposed method has been used to derive the fuzzy estimators of the parameters of a Normal distribution and some functions of parameters of two Normal distributions, as well as the parameters of the Exponential and Poisson distributions.

Keywords: Confidence interval. Fuzzy number. Fuzzy estimation.

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Authors: Yun-Yao Chi, Ya-Fen Lee

Abstract:

In this paper, a study of slope failures along the Alishan Highway is carried out. An innovative empirical model is developed based on 15-year records of rainfall-induced slope failures. The statistical models are intended for assessing the volume of landslide for slope failure along the Alishan Highway in the future. The rainfall data considered in the proposed models include the effective cumulative rainfall and the critical rainfall intensity. The effective cumulative rainfall is defined at the point when the curve of cumulative rainfall goes from steep to flat. Then, the rainfall thresholds of landslide are established for assessing the volume of landslide and issuing warning and/or closure for the Alishan Highway during a future extreme rainfall. Slope failures during Typhoon Saola in 2012 demonstrate that the new empirical model is effective and applicable to other cases with similar rainfall conditions.

Keywords: Slope failure, landslide, volume, model, rainfall thresholds.

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Authors: Elizabeth Downs, Judith Repman, Kenneth Clark

Abstract:

This paper describes the evolution of strategies to evaluate ePortfolios in an online Master-s of Education (M.Ed.) degree in Instructional Technology. The ePortfolios are required as a culminating activity for students in the program. By using Web 2.0 tools to develop the ePortfolios, students are able to showcase their technical skills, integrate national standards, demonstrate their professional understandings, and reflect on their individual learning. Faculty have created assessment strategies to evaluate student achievement of these skills. To further develop ePortfolios as a tool promoting authentic learning, faculty are moving toward integrating transparency as part of the evaluation process.

Keywords: e-learning evaluation, ePortfolios, transparency, Web 2.0

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Authors: Itgel Bayarsaikhan, Jimin Lee, Sejong Oh

Abstract:

Classification is one of the primary themes in computational biology. The accuracy of classification strongly depends on quality of a dataset, and we need some method to evaluate this quality. In this paper, we propose a new graphical analysis method using 'Membership-Deviation Graph (MDG)' for analyzing quality of a dataset. MDG represents degree of membership and deviations for instances of a class in the dataset. The result of MDG analysis is used for understanding specific feature and for selecting best feature for classification.

Keywords: feature, classification, machine learning algorithm.

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Authors: Hossein Mirzaee, Farhad Besharati

Abstract:

A combination of image fusion and quad tree decomposition method is used for detecting the sunspot trajectories in each month and computation of the latitudes of these trajectories in each solar hemisphere. Daily solar images taken with SOHO satellite are fused for each month and the result of fused image is decomposed with Quad Tree decomposition method in order to classifying the sunspot trajectories and then to achieve the precise information about latitudes of sunspot trajectories. Also with fusion we deduce some physical remarkable conclusions about sun magnetic fields behavior. Using quad tree decomposition we give information about the region on sun surface and the space angle that tremendous flares and hot plasma gases permeate interplanetary space and attack to satellites and human technical systems. Here sunspot images in June, July and August 2001 are used for studying and give a method to compute the latitude of sunspot trajectories in each month with sunspot images.

Keywords: Quad Tree Decomposition, Sunspot.

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

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Authors: A. Mojtaba Aghajani, B. Leila Shavakhi

Abstract:

Energy intensity(energy consumption intensity) is a global index which computes the required energy for producing a specific value of goods and services in each country. It is computed in terms of initial energy supply or final energy consumption. In this study (research) Divisia method is used to decompose energy consumption and energy intensity. This method decomposes consumption and energy intensity to production effects, structural and net intensity and could be done as time series or two-periodical. This study analytically investigates consumption changes and energy intensity on economical sectors of Iran and more specific on road transportation(rail road and road).Our results show that the contribution of structural effect (change in economical activities combination) is very low and the effect of net energy consumption has the higher contribution in consumption changes and energy intensity. In other words, the high consumption of energy is due to Intensity of energy consumption and is not to structural effect of transportation sector.

Keywords: Divisia Method, Energy Intensity, Net IntensityEffect, Road Transportation , Structural Effect.

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Authors: Bella Llego

Abstract:

This study aims to investigate the relationships between human resource management and entrepreneurship in the view of owner-managers and employees, and among employees with in the SME in Thailand. The research method used qualitative method to confirm the phenomenology interest with top management position which women are regarding their career path by using purposive sampling method. The results showed that human resources management has positive relate with the corporate entrepreneurship are including the recruitment process, training worker, professional career development and reward system impact to entrepreneur’s knowledge and innovation of corporate entrepreneurship in respectively to bring a very reliable way. Then, the key informant suggested that women’s career experiences predisposed them to find an alternative route for entrepreneurship, despite having achieved top management. The understanding factors that successfully contribute to the development of women entrepreneurs from career development perspective are critical endeavour for any type of organization as well.

Keywords: Entrepreneurship, firm performance, human resource management, work efficiency.

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Authors: J. Yang, Y. Ma, X. Zhang, S. Li, Y. Zhang

Abstract:

The traditional k-means algorithm has been widely used as a simple and efficient clustering method. However, the algorithm often converges to local minima for the reason that it is sensitive to the initial cluster centers. In this paper, an algorithm for selecting initial cluster centers on the basis of minimum spanning tree (MST) is presented. The set of vertices in MST with same degree are regarded as a whole which is used to find the skeleton data points. Furthermore, a distance measure between the skeleton data points with consideration of degree and Euclidean distance is presented. Finally, MST-based initialization method for the k-means algorithm is presented, and the corresponding time complexity is analyzed as well. The presented algorithm is tested on five data sets from the UCI Machine Learning Repository. The experimental results illustrate the effectiveness of the presented algorithm compared to three existing initialization methods.

Keywords: Degree, initial cluster center, k-means, minimum spanning tree.

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Authors: Yoichi Ishikawa, Yuichi Masukake, Yoshihisa Ishida

Abstract:

This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.

Keywords: Chaos, nonlinear plant, radial basis function network.

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Authors: A. Selmi

Abstract:

Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: Differential transformation method, functionally graded material, mode shape, natural frequency.

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