Search results for: matrix equation

Authors: A. M. Fudhail, N. A. C. Sidik, M. Z. M. Rody, H. M. Zahir, M.T. Musthafah

Abstract:

In this paper, fluid flow patterns of steady incompressible flow inside shear driven cavity are studied. The numerical simulations are conducted by using lattice Boltzmann method (LBM) for different Reynolds numbers. In order to simulate the flow, derivation of macroscopic hydrodynamics equations from the continuous Boltzmann equation need to be performed. Then, the numerical results of shear-driven flow inside square and triangular cavity are compared with results found in literature review. Present study found that flow patterns are affected by the geometry of the cavity and the Reynolds numbers used.

Keywords: Lattice Boltzmann method, shear driven cavity, square cavity, triangular cavity.

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Authors: Dylan M. Copeland

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We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Asish O. Mathew, Lewlyn L. R. Rodrigues

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The organizations in the knowledge economy era have recognized the importance of building knowledge assets for sustainable growth and development. In comparison to other industries, Information Technology (IT) enterprises, holds an edge in developing an effective Knowledge Management (KM) programmethanks to their in-house technological abilities. This paper tries to study the various knowledge based incentive programmes and its effect on Knowledge Sharing and Learning in the context of the Indian IT sector. A conceptual model is developed linking KM Incentives, Knowledge Sharing and Learning. A questionnaire study is conducted to collect primary data from the knowledge workers of the IT organizations located in India. The data was analysed using Structural Equation Modeling using Partial Least Square method. The results show a strong influence of knowledge management incentives on knowledge sharing and an indirect influence on learning.

Keywords: Knowledge Management, Knowledge Management Incentives, Knowledge Sharing, Learning.

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Authors: David W.S. Tai, Ren-Cheng Zhang, Sheng-Hung Chang, Chin-Pin Chen, Jia-Ling Chen

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This study reports results of a meta-analytic path analysis e-learning Acceptance Model with k = 27 studies, Databases searched included Information Sciences Institute (ISI) website. Variables recorded included perceived usefulness, perceived ease of use, attitude toward behavior, and behavioral intention to use e-learning. A correlation matrix of these variables was derived from meta-analytic data and then analyzed by using structural path analysis to test the fitness of the e-learning acceptance model to the observed aggregated data. Results showed the revised hypothesized model to be a reasonable, good fit to aggregated data. Furthermore, discussions and implications are given in this article.

Keywords: E-learning, Meta Analytic Path Analysis, Technology Acceptance Model

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Authors: N. M. Ahmad, J. Abdullah, N. I. Ramli, S. Abd Rahman, N. E. Azmi, Z. Hamzah, A. Saat, N. H. Rahman

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A biosensor based on glucose oxidase (GOx) immobilized onto nanoparticles zirconium oxide with polyethylene nanocomposite for glucose monitoring has been designed. The CTAB/PEG/ZrO2/GOx nanocomposite was deposited onto screen printed carbon paste (SPCE) electrode via spin coating technique. The properties of CTAB/PEG/ZrO2/GOx were study using scanning electron microscopy (SEM). The SPE modified with the CTAB/PEG/ZrO2/GOx showed electrocatalytical response to the oxidation of glucose when ferrocene carboxaldehyde was used as an artificial redox mediator, which was studied by cyclic voltammetry (CV). Several parameters such as working potential, effect of pH and effect of ZrO2/PEG layers that governed the analytical performance of the biosensor, have been studied. The biosensor was applied to detect glucose with a linear range of 0.4 to 2.0 mmol L−1 with good repetability and reproducibility.

Keywords: Nanocomposite, Nanoparticles, Modified SPE, Ferrocenecarboxaldehyde.

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Authors: Ali Hajiha, Farhad Ghaffari, Nooshin Gholamali Tehrani

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This study aims at investigating the empirical relationships between risk preference, internet preference, and internet knowledge which are known as user characteristics, in addition to perceived risk of the customers on the internet purchase intention. In order to test the relationships between the variables of model 174, a questionnaire was collected from the students with previous online experience. For the purpose of data analysis, confirmatory factor analysis (CFA) and structural equation model (SEM) was used. Test results show that the perceived risk affects the internet purchase intention, and increase or decrease of perceived risk influences the purchase intention when the customer does the internet shopping. Other factors such as internet preference, knowledge of the internet, and risk preference affect the internet purchase intention.

Keywords: Perceived risk, Internet preference, Internetknowledge, Risk preference, Internet purchase intention

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Authors: Yun Jong Choi, Nam Woong, PooGyeon Park

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Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.

Keywords: Input saturation, linear-growth bounded disturbances, linear matrix inequality (LMI), variable structure control

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Authors: Z. Jannoo, B. W. Yap, N. Auchoybur, M. A. Lazim

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The two common approaches to Structural Equation Modeling (SEM) are the Covariance-Based SEM (CB-SEM) and Partial Least Squares SEM (PLS-SEM). There is much debate on the performance of CB-SEM and PLS-SEM for small sample size and when distributions are nonnormal. This study evaluates the performance of CB-SEM and PLS-SEM under normality and nonnormality conditions via a simulation. Monte Carlo Simulation in R programming language was employed to generate data based on the theoretical model with one endogenous and four exogenous variables. Each latent variable has three indicators. For normal distributions, CB-SEM estimates were found to be inaccurate for small sample size while PLS-SEM could produce the path estimates. Meanwhile, for a larger sample size, CB-SEM estimates have lower variability compared to PLS-SEM. Under nonnormality, CB-SEM path estimates were inaccurate for small sample size. However, CB-SEM estimates are more accurate than those of PLS-SEM for sample size of 50 and above. The PLS-SEM estimates are not accurate unless sample size is very large.  

Keywords: CB-SEM, Monte Carlo simulation, Normality conditions, Nonnormality, PLS-SEM.

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Authors: A. O. Oladele

Abstract:

The purpose of this study was to find out the effectiveness of neurological impress method and repeated reading technique on reading fluency of children with learning disabilities. Thirty primary four pupils in three public primary schools participated in the study. There were two experimental groups and a control. This research employed a 3 by 2 factorial matrix and the participants were taught for one session. Two hypotheses were formulated to guide the research. T-test was used to analyse the data gathered, and data analysis revealed that pupils exposed to the two treatment strategies had improvement in their reading fluency. It was recommended that the two strategies used in the study can be used to intervene in reading fluency problems in children with learning disabilities.

Keywords: Learning disabilities, neurological impress method, repeated reading, reading fluency.

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Authors: Djalal Eddine Khodja, Aissa Kheldoun

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In this work we present the modelling of the induction machine, taking into consideration the stator defects of the induction machine. It is based on the theory of electromagnetic coupling of electrical circuits. In fact, for the modelling of stationary defects such as short circuit between turns in the same phase, we introduce only in the matrix the coefficients of resistance and inductance of stator and in the mutual inductance stator-rotor. These coefficients take account the number of turns in short-circuit deducted from the total number of turns in the same phase; in this way we obtain the number of useful turns. In addition, all these faults involved, will be used for the creation of the database that will be used to develop an automated system failures of the induction machine.

Keywords: Asynchronous machine, Indicatory Values Statorfaults, Multi-turns Model, Three-phases Model.

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Authors: Vitalice K. Oduol

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The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

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Authors: Phu-Cuong Nguyen, Seung-Eock Kim

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This paper presents nonlinear elastic dynamic analysis of 3-D semi-rigid steel frames including geometric and connection nonlinearities. The geometric nonlinearity is considered by using stability functions and updating geometric stiffness matrix. The nonlinear behavior of the steel beam-to-column connection is considered by using a zero-length independent connection element comprising of six translational and rotational springs. The nonlinear dynamic equilibrium equations are solved by the Newmark numerical integration method. The nonlinear time-history analysis results are compared with those of previous studies and commercial SAP2000 software to verify the accuracy and efficiency of the proposed procedure.

Keywords: Geometric nonlinearity, nonlinear time-historyanalysis, semi-rigid connection, stability functions.

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Authors: S. A. Eftekhari

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In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Keywords: Dam-reservoir system, Differential quadrature method, Fluid-structure interaction, Galerkin method, Integral quadrature method.

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

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In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: Do Phuc, Nguyen Thi Kim Phung

Abstract:

In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

Keywords: Eigenvalues, m-tree, graph database, protein structure, spectra graph theory.

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Authors: B. J. Sandesh, Saurabha Jirgi, S. Vidya, Prakash Eljer, Gowri Srinivasa

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In this paper, we propose a framework to help users to search and retrieve the portions in the lecture video of their interest. This is achieved by temporally segmenting and indexing the lecture video using the topic keywords. We use transcribed text from the video and documents relevant to the video topic extracted from the web for this purpose. The keywords for indexing are found by applying the non-negative matrix factorization (NMF) topic modeling techniques on the web documents. Our proposed technique first creates indices on the transcribed documents using the topic keywords, and these are mapped to the video to find the start and end time of the portions of the video for a particular topic. This time information is stored in the index table along with the topic keyword which is used to retrieve the specific portions of the video for the query provided by the users.

Keywords: Video indexing and retrieval, lecture videos, content based video search, multimodal indexing.

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Authors: Kaltima Phichai, Pornchanoke Pragrobpondee, Thaweesak Khumpart, Samorn Hirunpraditkoon

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The paper provides biomasses characteristics by proximate analysis (volatile matter, fixed carbon and ash) and ultimate analysis (carbon, hydrogen, nitrogen and oxygen) for the prediction of the heating value equations. The heating value estimation of various biomasses can be used as an energy evaluation. Thirteen types of biomass were studied. Proximate analysis was investigated by mass loss method and infrared moisture analyzer. Ultimate analysis was analyzed by CHNO analyzer. The heating values varied from 15 to 22.4MJ kg-1. Correlations of the calculated heating value with proximate and ultimate analyses were undertaken using multiple regression analysis and summarized into three and two equations, respectively. Correlations based on proximate analysis illustrated that deviation of calculated heating values from experimental heating values was higher than the correlations based on ultimate analysis.

Keywords: Heating value equation, Proximate analysis, Ultimate analysis.

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Authors: Ashutosh Kumar Singh, Anand Mohan

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This paper deals with efficient computation of probability coefficients which offers computational simplicity as compared to spectral coefficients. It eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function. The method for computation of probability coefficients using transform matrix, fast transform method and using BDD is given. Theoretical relations for achievable computational advantage in terms of required additions in computing all 2n probability coefficients of n variable function have been developed. It is shown that for n ≥ 5, only 50% additions are needed to compute all probability coefficients as compared to spectral coefficients. The fault detection techniques based on spectral signature can be used with probability signature also to offer computational advantage.

Keywords: Binary Decision Diagrams, Spectral Coefficients, Fault detection

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Authors: E. Hajizadeh, H. Garmabi

Abstract:

Toughening of polyamide 6 (PA6)/ Nanoclay (NC) nanocomposites with styrene-ethylene/butadiene-styrene copolymer (SEBS) using maleated styrene-ethylene/butadiene-styrene copolymer (mSEBS)/ as a compatibilizer were investigated by blending them in a co-rotating twin-screw extruder. Response surface method of experimental design was used for optimizing the material and processing parameters. Effect of four factors, including SEBS, mSEBS and NC contents as material variables and order of mixing as a processing factor, on toughness of hybrid nanocomposites were studied. All the prepared samples showed ductile behavior and low temperature Izod impact toughness of some of the hybrid nanocomposites demonstrated 900% improvement compared to the PA6 matrix while the modulus showed maximum enhancement of 20% compared to the pristine PA6 resin.

Keywords: Hybrid nanocomposites, PA6, SEBS rubber, toughness.

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Authors: H. M. Mobarak, Helen Wu, Keqin Xiao

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In this work, a three-dimensional finite element model was developed to investigate the crack breathing behavior at different crack locations considering the effect of unbalance force. A two-disk rotor with a crack is simulated using ABAQUS. The duration of each crack status (open, closed and partially open/closed) during a full shaft rotation was examined to analyse the crack breathing behavior. Unbalanced shaft crack breathing behavior was found to be different at different crack locations. The breathing behavior of crack along the shaft length is divided into different regions depending on the unbalance force and crack location. The simulated results in this work can be further utilised to obtain the time-varying stiffness matrix of the cracked shaft element under the influence of unbalance force.

Keywords: Crack breathing, crack location, slant crack, unbalance force, rotating shaft.

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Authors: Z. Ishak, F.P Chew

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School experiences, family bonding and self-concept had always been a crucial factor in influencing all aspects of a student-s development. The purpose of this study is to develop and to validate a priori model of self-concept among students. The study was tested empirically using Structural Equation Modeling (SEM) and Confirmatory Factor Analysis (CFA) to validate the structural model. To address these concerns, 1167 students were randomly selected and utilized the Cognitive Psycho-Social University of Malaya instrument (2009).Resulted demonstrated there is indirect effect from family bonding to self-concept through school experiences among secondary school students as a mediator. Besides school experiences, there is a direct effect from family bonding to self-concept and family bonding to school experiences among students.

Keywords: Confirmatory Factor Analysis, self-concept, family bonding, and school experience

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Authors: Lina Fernandes, G. N. Nayak, D. Ilangovan

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Two short sediment cores collected from mangrove areas of Manori and Thane creeks along Mumbai coast were analysed for sediment composition and metals (Fe, Mn, Cu, Pb, Co, Ni, Zn, Cr and V). The statistical analysis of Pearson correlation matrix proved that there is a significant relationship between metal concentration and finer grain size in Manori creek while poor correlation was observed in Thane creek. Based on the enrichment factor, the present metal to background metal ratios clearly reflected maximum enrichment of Cu and Pb in Manori creek and Mn in Thane creek. Geoaccumulation index calculated indicate that the study area is unpolluted with respect to Fe, Mn, Co, Ni, Zn and Cr in both the cores while moderately polluted with Cu and Pb in Manori creek. Based on contamination degree, both the core sediments were found to be considerably contaminated with metals.

Keywords: Creek, Igeo, Mumbai, trace metals

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Authors: B.Tavakoly Sany, A.H .Sulaiman, GH. Monazami, A. Salleh

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Eight heavy metals (Cu, Cr, Zn, Hg, Pb, Cd, Ni and As) were analyzed in sediment samples in the dry and wet seasons from November 2009 to October 2010 in West Port of Peninsular Malaysia. The heavy metal concentrations (mg/kg dry weight) were ranged from 23.4 to 98.3 for Zn, 22.3 to 80 for Pb, 7.4 to 27.6 Cu, 0.244 to 3.53 for Cd, 7.2 to 22.2 for Ni, 20.2 to 162 for As, 0.11 to 0.409 for Hg and 11.5 to 61.5 for Cr. Metals concentrations in dry season were higher than the rainy season except in cupper and chromium. Analysis of variance with Statistical Analysis System (SAS) shows that the mean concentration of metals in the two seasons (α level=0.05) are not significantly different which shows that the metals were held firmly in the matrix of sediment. Also there are significant differences between control point station with other stations. According to the Interim Sediment Quality guidelines (ISQG), the metal concentrations are moderately polluted, except in arsenic which shows the highest level of pollution.

Keywords: Heavy metals, sediment quality guidelines, west port.

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Authors: M. E. Ali Mohsin, Agus Arsad, Othman Y. Alothman

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This study explains the influence of secondary filler on the dispersion of carbon nanotube (CNT) reinforced high density polyethylene (HDPE) nanocomposites (CNT/HDPE). In order to understand the mixed-fillers system, Montmorillonite (MMT) was added to CNT/HDPE nanocomposites. It was followed by investigating their effect on the thermal, mechanical and morphological properties of the aforesaid nanocomposite. Incorporation of 3 wt% each of MMT into CNT/HDPE nanocomposite resulted to the increased values for the tensile and flexural strength, as compared to the pure HDPE matrix. The thermal analysis result showed improved thermal stability of the formulated nanocomposites. Transmission electron microscopy (TEM) images revealed that larger aggregates of CNTs were disappeared upon addition of these two components leading to the enhancement of thermo-mechanical properties for such composites.

Keywords: Secondary filler, Montmorillonite, Carbon nanotube, nanocomposite.

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Authors: P. Gnanasekar, A. Nagappan, S. Sharavanan, O. Saravanan, D. Vinodkumar, T. Elayabharathi, G. Karthik

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In this paper we present the deep study about the Bio- Medical Images and tag it with some basic extracting features (e.g. color, pixel value etc). The classification is done by using a nearest neighbor classifier with various distance measures as well as the automatic combination of classifier results. This process selects a subset of relevant features from a group of features of the image. It also helps to acquire better understanding about the image by describing which the important features are. The accuracy can be improved by increasing the number of features selected. Various types of classifications were evolved for the medical images like Support Vector Machine (SVM) which is used for classifying the Bacterial types. Ant Colony Optimization method is used for optimal results. It has high approximation capability and much faster convergence, Texture feature extraction method based on Gabor wavelets etc..

Keywords: ACO Ant Colony Optimization, Correlogram, CCM Co-Occurrence Matrix, RTS Rough-Set theory

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: Sara A.Yones, Ahmed S. Moussa

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Quantitative measurements of tumor in general and tumor volume in particular, become more realistic with the use of Magnetic Resonance imaging, especially when the tumor morphological changes become irregular and difficult to assess by clinical examination. However, tumor volume estimation strongly depends on the image segmentation, which is fuzzy by nature. In this paper a fuzzy approach is presented for tumor volume segmentation based on the fuzzy connectedness algorithm. The fuzzy affinity matrix resulting from segmentation is then used to estimate a fuzzy volume based on a certainty parameter, an Alpha Cut, defined by the user. The proposed method was shown to highly affect treatment decisions. A statistical analysis was performed in this study to validate the results based on a manual method for volume estimation and the importance of using the Alpha Cut is further explained.

Keywords: Alpha Cut, Fuzzy Connectedness, Magnetic Resonance Imaging, Tumor volume estimation.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

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This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Vladimír Frišták, Martin Pipíška, Juraj Lesný

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Alginite has been evaluated as an efficient pollution control material. In this paper, alginite from maar Pinciná (SR) for removal of Cd²⁺ ions from aqueous solution was studied. The potential sorbent was characterized by X-ray fluorescence analysis (RFA) analysis, Fourier transform infrared spectral analysis (FT-IR) and specific surface area (SSA) was also determined. The sorption process was optimized from the point of initial cadmium concentration effect and effect of pH value. The Freundlich and Langmuir models were used to interpret the sorption behavior of Cd²⁺ ions, and the results showed that experimental data were well fitted by the Langmuir equation. Alginite maximal sorption capacity (Q_max) for Cd²⁺ ions calculated from Langmuir isotherm was 34 mg/g. Sorption process was significantly affected by initial pH value in the range from 4.0-7.0. Alginite is a comparable sorbent with other materials for toxic metals removal. 

Keywords: Alginites, Cd2+, sorption, Qmax

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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