Search results for: Generalized Chebyshev Collocation method
7878 Improvement of MLLR Speaker Adaptation Using a Novel Method
Authors: Ing-Jr Ding
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This paper presents a technical speaker adaptation method called WMLLR, which is based on maximum likelihood linear regression (MLLR). In MLLR, a linear regression-based transform which adapted the HMM mean vectors was calculated to maximize the likelihood of adaptation data. In this paper, the prior knowledge of the initial model is adequately incorporated into the adaptation. A series of speaker adaptation experiments are carried out at a 30 famous city names database to investigate the efficiency of the proposed method. Experimental results show that the WMLLR method outperforms the conventional MLLR method, especially when only few utterances from a new speaker are available for adaptation.Keywords: hidden Markov model, maximum likelihood linearregression, speech recognition, speaker adaptation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18417877 Homogeneous and Heterogeneous Catalysis: Teachings of the Thermal Energy and Power Engineering Course
Authors: Junjie Chen
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It is usually difficult for students to understand some basic theories in learning thermal energy and power engineering course. A new teaching method was proposed that we should introduce the comparison research method of those theories to help them being understood. “Homogeneous and heterogeneous catalysis” teaching is analyzed as an example by comparison research method.
Keywords: Homogeneous catalysis, heterogeneous catalysis, thermal energy and power engineering, teaching method, comparison research method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 55817876 A Fully Implicit Finite-Difference Solution to One Dimensional Coupled Nonlinear Burgers’ Equations
Authors: Vineet K. Srivastava, Mukesh K. Awasthi, Mohammad Tamsir
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A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.
Keywords: Burgers’ equation, Implicit Finite-difference method, Newton’s method, Gauss elimination with partial pivoting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 59407875 On a Pitch Duration Technique for Prosody Control
Authors: JongKuk Kim, HernSoo Hahn, Uei-Joong Yoo, MyungJin Bae
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In this paper, we propose a method of alter duration in frequency domain that control prosody in real time after pitch alteration. If there has a method to alteration duration freely among prosody information, that may used in several fields such as speech impediment person's pronunciation proof reading or language study. The pitch alteration method used control prosody altered by PSOLA synthesis method which is in time domain processing method. However, the duration of pitch alteration speech is changed by the frequency domain. In this paper, we altered the duration with the method of duration alteration by Fast Fourier Transformation in frequency domain. Consequently, the intelligibility of the pitch and duration are controlled has a slight decrease than the case when only pitch is changed, but the proposed algorithm obtained the higher MOS score about naturalness.Keywords: PSOLA, Pitch Alteration, Duration Control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16837874 On the Solution of Fully Fuzzy Linear Systems
Authors: Hsuan-Ku Liu
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A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
Keywords: Fully fuzzy linear equations, iterative method, homotopy perturbation method, approximate solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17457873 Continuity of Defuzzification and Its Application to Fuzzy Control
Authors: Takashi Mitsuishi, Kiyoshi Sawada, Yasunari Shidama
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The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discussed.
Keywords: Fuzzy approximate reasoning, defuzzification, area method, height method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16757872 Convergence and Comparison Theorems of the Modified Gauss-Seidel Method
Authors: Zhouji Chen
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In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M-matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented new preconditioner.
Keywords: Preconditioned linear system, M-matrix, Convergence, Comparison theorem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15037871 Method Development and Validation for the Determination of Cefixime in Pure and Commercial Dosage Forms by Specrophotometry
Authors: S. N. H. Azmi, B. Iqbal, J. K. Al Mamari, K. A. Al Hattali, W. N. Al Hadhrami
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A simple, accurate and precise direct spectrophotometric method has been developed for the determination of cefixime in tablets and capsules. The method is based on the reaction of cefixime with a mixture of potassium iodide and potassium iodate to form yellow coloured product in ethanol-distilled water medium at room temperature which absorbed maximally at 352 nm. The factors affecting the reaction product were carefully studied and optimized. The validation parameters based on International Conference on Harmonisation (ICH, USA) guidelines were followed. The effect of common excipients used as additives has been tested and the tolerance limit was calculated for the determination of cefixime. Beer’s law is obeyed in the concentration range of 4 – 24 ug mL-1 with apparent molar absorptivity of 1.52 × 104 L mol-1cm-1 and Sandell’s sensitivity of 0.033 ug/cm2/ 0.001 absorbance unit. The limits of detection and quantitation for the proposed method are 0.32 and 1.06 ug mL-1, respectively. The proposed method has been successfully applied for the determination of cefixime in pharmaceutical formulations. The results obtained by the proposed method were statistically compared with the reference method using t- and F- values and found no significant difference between the two methods. The proposed method can be used as an alternate method for routine quality control analysis of cefixime in pharmaceutical formulations.
Keywords: Spectrophotometry, cefixime, validation, pharmaceutical formulations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31607870 Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay
Authors: Liqiong Liu, Shouming Zhong
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In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.
Keywords: Finite-time stabilization, fractional-order system, Gronwall inequality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19017869 Density Estimation using Generalized Linear Model and a Linear Combination of Gaussians
Authors: Aly Farag, Ayman El-Baz, Refaat Mohamed
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In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.
Keywords: Logistic regression model, Expectationmaximization, Segmentation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17327868 Performance Evaluation of Refinement Method for Wideband Two-Beams Formation
Authors: C. Bunsanit
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This paper presents the refinement method for two beams formation of wideband smart antenna. The refinement method for weighting coefficients is based on Fully Spatial Signal Processing by taking Inverse Discrete Fourier Transform (IDFT), and its simulation results are presented using MATLAB. The radiation pattern is created by multiplying the incoming signal with real weights and then summing them together. These real weighting coefficients are computed by IDFT method; however, the range of weight values is relatively wide. Therefore, for reducing this range, the refinement method is used. The radiation pattern concerns with five input parameters to control. These parameters are maximum weighting coefficient, wideband signal, direction of mainbeam, beamwidth, and maximum of minor lobe level. Comparison of the obtained simulation results between using refinement method and taking only IDFT shows that the refinement method works well for wideband two beams formation.
Keywords: Fully spatial signal processing, beam forming, refinement method, smart antenna, weighting coefficient, wideband.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10777867 A Finite Element Method Simulation for Rocket Motor Material Selection
Authors: T. Kritsana, P. Sawitri, P. Teeratas
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This article aims to study the effect of pressure on rocket motor case by Finite Element Method simulation to select optimal material in rocket motor manufacturing process. In this study, cylindrical tubes with outside diameter of 122 mm and thickness of 3 mm are used for simulation. Defined rocket motor case materials are AISI4130, AISI1026, AISI1045, AL2024 and AL7075. Internal pressure used for the simulation is 22 MPa.
The result from Finite Element Method shows that at a pressure of 22 MPa rocket motor case produced by AISI4130, AISI1045 and AL7075 can be used. A comparison of the result between AISI4130, AISI1045 and AL7075 shows that AISI4130 has minimum principal stress and confirm the results of Finite Element Method by the used of calculation method found that, the results from Finite Element Method has good reliability.
Keywords: Rocket motor case, Finite Element Method, principal Stress.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25457866 An Improved Tie Force Method for Progressive Collapse Resistance of Precast Concrete Cross Wall Structures
Authors: M. Tohidi, J. Yang, C. Baniotopoulos
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Progressive collapse of buildings typically occurs when abnormal loading conditions cause local damages, which leads to a chain reaction of failure and ultimately catastrophic collapse. The tie force (TF) method is one of the main design approaches for progressive collapse. As the TF method is a simplified method, further investigations on the reliability of the method is necessary. This study aims to develop an improved TF method to design the cross wall structures for progressive collapse. To this end, the pullout behavior of strands in grout was firstly analyzed; and then, by considering the tie force-slip relationship in the friction stage together with the catenary action mechanism, a comprehensive analytical method was developed. The reliability of this approach is verified by the experimental results of concrete block pullout tests and full scale floor-to-floor joints tests undertaken by Portland Cement Association (PCA). Discrepancies in the tie force between the analytical results and codified specifications have suggested the deficiency of TF method, hence an improved model based on the analytical results has been proposed to address this concern.
Keywords: Cross wall, progressive collapse, ties force method, catenary, analytical.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36867865 Backstepping Design and Fractional Derivative Equation of Chaotic System
Authors: Ayub Khan, Net Ram Garg, Geeta Jain
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In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.
Keywords: Backstepping method, Fractional order, Synchronization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21427864 3D Face Modeling based on 3D Dense Morphable Face Shape Model
Authors: Yongsuk Jang Kim, Sun-Tae Chung, Boogyun Kim, Seongwon Cho
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Realistic 3D face model is more precise in representing pose, illumination, and expression of face than 2D face model so that it can be utilized usefully in various applications such as face recognition, games, avatars, animations, and etc. In this paper, we propose a 3D face modeling method based on 3D dense morphable shape model. The proposed 3D modeling method first constructs a 3D dense morphable shape model from 3D face scan data obtained using a 3D scanner. Next, the proposed method extracts and matches facial landmarks from 2D image sequence containing a face to be modeled, and then reconstructs 3D vertices coordinates of the landmarks using a factorization-based SfM technique. Then, the proposed method obtains a 3D dense shape model of the face to be modeled by fitting the constructed 3D dense morphable shape model into the reconstructed 3D vertices. Also, the proposed method makes a cylindrical texture map using 2D face image sequence. Finally, the proposed method generates a 3D face model by rendering the 3D dense face shape model using the cylindrical texture map. Through building processes of 3D face model by the proposed method, it is shown that the proposed method is relatively easy, fast and precise.Keywords: 3D Face Modeling, 3D Morphable Shape Model, 3DReconstruction, 3D Correspondence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24267863 The Principle Probabilities of Space-Distance Resolution for a Monostatic Radar and Realization in Cylindrical Array
Authors: Anatoly D. Pluzhnikov, Elena N. Pribludova, Alexander G. Ryndyk
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In conjunction with the problem of the target selection on a clutter background, the analysis of the scanning rate influence on the spatial-temporal signal structure, the generalized multivariate correlation function and the quality of the resolution with the increase pulse repetition frequency is made. The possibility of the object space-distance resolution, which is conditioned by the range-to-angle conversion with an increased scanning rate, is substantiated. The calculations for the real cylindrical array at high scanning rate are presented. The high scanning rate let to get the signal to noise improvement of the order of 10 dB for the space-time signal processing.Keywords: Antenna pattern, array, signal processing, spatial resolution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10737862 A Novel Estimation Method for Integer Frequency Offset in Wireless OFDM Systems
Authors: Taeung Yoon, Youngpo Lee, Chonghan Song, Na Young Ha, Seokho Yoon
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Ren et al. presented an efficient carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM), which has an estimation range as large as the bandwidth of the OFDM signal and achieves high accuracy without any constraint on the structure of the training sequence. However, its detection probability of the integer frequency offset (IFO) rapidly varies according to the fractional frequency offset (FFO) change. In this paper, we first analyze the Ren-s method and define two criteria suitable for detection of IFO. Then, we propose a novel method for the IFO estimation based on the maximum-likelihood (ML) principle and the detection criteria defined in this paper. The simulation results demonstrate that the proposed method outperforms the Ren-s method in terms of the IFO detection probability irrespective of a value of the FFO.Keywords: Orthogonal frequency division multiplexing, integer frequency offset, estimation, training symbol
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24517861 A New Method for Identifying Broken Rotor Bars in Squirrel Cage Induction Motor Based on Particle Swarm Optimization Method
Authors: V. Rashtchi, R. Aghmasheh
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Detection of squirrel cage induction motor (SCIM) broken bars has long been an important but difficult job in the detection area of motor faults. Early detection of this abnormality in the motor would help to avoid costly breakdowns. A new detection method based on particle swarm optimization (PSO) is presented in this paper. Stator current in an induction motor will be measured and characteristic frequency components of faylted rotor will be detected by minimizing a fitness function using pso. Supply frequency and side band frequencies and their amplitudes can be estimated by the proposed method. The proposed method is applied to a faulty motor with one and two broken bars in different loading condition. Experimental results prove that the proposed method is effective and applicable.
Keywords: broken bar, PSO, fault detection, SCIM
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17167860 A New Verified Method for Solving Nonlinear Equations
Authors: Taher Lotfi , Parisa Bakhtiari , Katayoun Mahdiani , Mehdi Salimi
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In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.
Keywords: Iinterval analysis, nonlinear equations, Ostrowski method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15097859 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials
Authors: N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, M. Hasan
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In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.
Keywords: Approximation, Galerkin method, Integral equations, Laguerre polynomial.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21807858 A Meshfree Solution of Tow-Dimensional Potential Flow Problems
Authors: I. V. Singh, A. Singh
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In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.
Keywords: Meshless, EFG method, potential flow, Lagrange multiplier method, penalty method, penalty parameter and scaling parameter
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15037857 Hybrid Coding for Animated Polygonal Meshes
Authors: Jinghua Zhang, Charles B. Owen, Jinsheng Xu
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A new hybrid coding method for compressing animated polygonal meshes is presented. This paper assumes the simplistic representation of the geometric data: a temporal sequence of polygonal meshes for each discrete frame of the animated sequence. The method utilizes a delta coding and an octree-based method. In this hybrid method, both the octree approach and the delta coding approach are applied to each single frame in the animation sequence in parallel. The approach that generates the smaller encoded file size is chosen to encode the current frame. Given the same quality requirement, the hybrid coding method can achieve much higher compression ratio than the octree-only method or the delta-only method. The hybrid approach can represent 3D animated sequences with higher compression factors while maintaining reasonable quality. It is easy to implement and have a low cost encoding process and a fast decoding process, which make it a better choice for real time application.Keywords: animated polygonal meshes, compression, deltacoding, octree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14677856 Linear Elasticity Problems Solved by Using the Fictitious Domain Method and Total - FETI Domain Decomposition
Authors: Lukas Mocek, Alexandros Markopoulos
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The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.
Keywords: Linear elasticity, fictitious domain method, Total-FETI, domain decomposition, saddle-point system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15807855 Some Computational Results on MPI Parallel Implementation of Dense Simplex Method
Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras
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There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20487854 MP-SMC-I Method for Slip Suppression of Electric Vehicles under Braking
Authors: Tohru Kawabe
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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.Keywords: Sliding Mode Control, Model Predictive Control, Integral Action, Electric Vehicle, Slip suppression.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22567853 Surveillance Video Summarization Based on Histogram Differencing and Sum Conditional Variance
Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass
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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.
Keywords: Temporal differencing, video summarization, histogram differencing, sum conditional variance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16927852 Solving a System of Nonlinear Functional Equations Using Revised New Iterative Method
Authors: Sachin Bhalekar, Varsha Daftardar-Gejji
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In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23357851 Assessment of Hargreaves Equation for Estimating Monthly Reference Evapotranspiration in the South of Iran
Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh
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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.Keywords: Evapotranspiration, Hargreaves equation, FAOPenman method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19097850 Local Error Control in the RK5GL3 Method
Authors: J.S.C. Prentice
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The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14847849 Restarted GMRES Method Augmented with the Combination of Harmonic Ritz Vectors and Error Approximations
Authors: Qiang Niu, Linzhang Lu
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Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.
Keywords: Arnoldi process, GMRES, Krylov subspace, systems of linear equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1936