Search results for: Sinc function
4891 An Application of Sinc Function to Approximate Quadrature Integrals in Generalized Linear Mixed Models
Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif
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This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function
Procedia PDF Downloads 3914890 Numerical Wave Solutions for Nonlinear Coupled Equations Using Sinc-Collocation Method
Authors: Kamel Al-Khaled
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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions
Procedia PDF Downloads 5194889 Convergence of Sinc Methods Applied to Kuramoto-Sivashinsky Equation
Authors: Kamel Al-Khaled
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A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point
Procedia PDF Downloads 4684888 Error Estimation for the Reconstruction Algorithm with Fan Beam Geometry
Authors: Nirmal Yadav, Tanuja Srivastava
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Shannon theory is an exact method to recover a band limited signals from its sampled values in discrete implementation, using sinc interpolators. But sinc based results are not much satisfactory for band-limited calculations so that convolution with window function, having compact support, has been introduced. Convolution Backprojection algorithm with window function is an approximation algorithm. In this paper, the error has been calculated, arises due to this approximation nature of reconstruction algorithm. This result will be defined for fan beam projection data which is more faster than parallel beam projection.Keywords: computed tomography, convolution backprojection, radon transform, fan beam
Procedia PDF Downloads 4814887 Design of Wide-Range Variable Fractional-Delay FIR Digital Filters
Authors: Jong-Jy Shyu, Soo-Chang Pei, Yun-Da Huang
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In this paper, design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters is proposed. With respect to the conventional VFD filter which is designed such that its delay is adjustable within one unit, the proposed VFD FIR filter is designed such that its delay can be tunable within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this paper, least-squares method is adopted to design WR-VFD FIR filter. Throughout this paper, several examples will be proposed to demonstrate the effectiveness of the presented methods.Keywords: digital filter, FIR filter, variable fractional-delay (VFD) filter, least-squares approximation
Procedia PDF Downloads 4874886 The Implementation of Secton Method for Finding the Root of Interpolation Function
Authors: Nur Rokhman
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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.Keywords: Secton method, interpolation, non linear function, numerical solution
Procedia PDF Downloads 3734885 Performance Analysis of New Types of Reference Targets Based on Spaceborne and Airborne SAR Data
Authors: Y. S. Zhou, C. R. Li, L. L. Tang, C. X. Gao, D. J. Wang, Y. Y. Guo
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Triangular trihedral corner reflector (CR) has been widely used as point target for synthetic aperture radar (SAR) calibration and image quality assessment. The additional “tip” of the triangular plate does not contribute to the reflector’s theoretical RCS and if it interacts with a perfectly reflecting ground plane, it will yield an increase of RCS at the radar bore-sight and decrease the accuracy of SAR calibration and image quality assessment. Regarding this problem, two types of CRs were manufactured. One was the hexagonal trihedral CR. It is a self-illuminating CR with relatively small plate edge length, while large edge length usually introduces unexpected edge diffraction error. The other was the triangular trihedral CR with extended bottom plate which considers the effect of ‘tip’ into the total RCS. In order to assess the performance of the two types of new CRs, flight campaign over the National Calibration and Validation Site for High Resolution Remote Sensors was carried out. Six hexagonal trihedral CRs and two bottom-extended trihedral CRs, as well as several traditional triangular trihedral CRs, were deployed. KOMPSAT-5 X-band SAR image was acquired for the performance analysis of the hexagonal trihedral CRs. C-band airborne SAR images were acquired for the performance analysis of the bottom-extended trihedral CRs. The analysis results showed that the impulse response function of both the hexagonal trihedral CRs and bottom-extended trihedral CRs were much closer to the ideal sinc-function than the traditional triangular trihedral CRs. The flight campaign results validated the advantages of new types of CRs and they might be useful in the future SAR calibration mission.Keywords: synthetic aperture radar, calibration, corner reflector, KOMPSAT-5
Procedia PDF Downloads 2654884 Throughput of Point Coordination Function (PCF)
Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb
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The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.Keywords: DCF, PCF, throughput, NS2
Procedia PDF Downloads 5704883 On a Univalent Function and the Integral Means of Its Derivative
Authors: Shatha S. Alhily
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The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.Keywords: derivative, integral means, self conformal maps, univalent function
Procedia PDF Downloads 6264882 Solution of the Nonrelativistic Radial Wave Equation of Hydrogen Atom Using the Green's Function Approach
Authors: F. U. Rahman, R. Q. Zhang
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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave
Procedia PDF Downloads 3894881 A Compressor Map Optimizing Tool for Prediction of Compressor Off-Design Performance
Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang
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A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.Keywords: beta function, compressor map, interpolation error, map optimization tool
Procedia PDF Downloads 2604880 Closed Forms of Trigonometric Series Interms of Riemann’s ζ Function and Dirichlet η, λ, β Functions or the Hurwitz Zeta Function and Harmonic Numbers
Authors: Slobodan B. Tričković
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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers
Procedia PDF Downloads 944879 Stability Analysis of SEIR Epidemic Model with Treatment Function
Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit
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The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function
Procedia PDF Downloads 5144878 Integration of Quality Function Deployment and Modular Function Deployment in Product Development
Authors: Naga Velamakuri, Jyothi K. Reddy
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Quality must be designed into a product and not inspected has become the main motto of all the companies globally. Due to the rapidly increasing technology in the past few decades, the nature of demands from the consumers has become more sophisticated. To sustain this global revolution of innovation in production systems, companies have to take steps to accommodate this technology growth. In this process of understanding the customers' expectations, all the firms globally take steps to deliver a perfect output. Most of these techniques also concentrate on the consistent development and optimization of the product to exceed the expectations. Quality Function Deployment(QFD) and Modular Function Deployment(MFD) are such techniques which rely on the voice of the customer and help deliver the needs. In this paper, Quality Function Deployment and Modular Function Deployment techniques which help in converting the quantitative descriptions to qualitative outcomes are discussed. The area of interest would be to understand the scope of each of the techniques and the application range in product development when these are applied together to any problem. The research question would be mainly aimed at comprehending the limitations using modularity in product development.Keywords: quality function deployment, modular function deployment, house of quality, methodology
Procedia PDF Downloads 3184877 A Transfer Function Representation of Thermo-Acoustic Dynamics for Combustors
Authors: Myunggon Yoon, Jung-Ho Moon
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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.Keywords: combustor, dynamics, thermoacoustics, transfer function
Procedia PDF Downloads 3734876 Geometric Properties of Some q-Bessel Functions
Authors: İbrahim Aktaş, Árpád Baricz
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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function
Procedia PDF Downloads 2714875 On the Fractional Integration of Generalized Mittag-Leffler Type Functions
Authors: Christian Lavault
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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function
Procedia PDF Downloads 4334874 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation
Authors: Diogo Silva, Fadul Rodor, Carlos Moraes
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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions
Procedia PDF Downloads 5754873 Characteristic Function in Estimation of Probability Distribution Moments
Authors: Vladimir S. Timofeev
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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation
Procedia PDF Downloads 4994872 Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function
Authors: Rogelio Luck, Yucheng Liu
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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix
Procedia PDF Downloads 1494871 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator
Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng
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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination
Procedia PDF Downloads 2844870 The Changes of Functions of Leishan Miao New-Year in Southeast Guizhou
Authors: Lanyan Peng, Ling Chen
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Leishan Miao New-Year is one of the grandest festivals in the southeastern of Guizhou Province in China. It was officially listed in the National Intangible Cultural Heritage List in 2008, as a traditional folk cultural activity organized by the local Miao people. With the rise of cultural tourism, after 19 years of exploration, the local government has successfully built Miao New-Year into a cultural card that is well-known at home and abroad. During the Miao New-Year period, it has attracted 3.8 million tourists and achieves a win-win situation in the economy and culture. However, tourism development has changed the living environment and living state of the local people. And it is accompanied by changes in the form of the festival, the content of the festival, and the local people’s needs and attitudes to the festival. This paper uses the field investigation method to achieve 410 questionnaires and 35 interviews, exploring the process and the reasons for changes of Leishan Miao New-Year’s cultural function. Among all the functions, the economic function, identity function, and entertainment function have been enhanced, and the marriage and love function has been extended. In the meanwhile, sacrificial function has been weakened. There are some trends in functions. The function of commemorating ancestor and self-entertainment has been changed to entertaining people and economic pursuit.Keywords: Miao New-Year, Miao nationality, festival function, changes
Procedia PDF Downloads 1164869 On Boundary Values of Hardy Space Banach Space-Valued Functions
Authors: Irina Peterburgsky
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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral
Procedia PDF Downloads 2424868 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra
Authors: Zuhier Altawallbeh
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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra
Procedia PDF Downloads 3984867 Multiple Relaxation Times in the Gibbs Ensemble Monte Carlo Simulation of Phase Separation
Authors: Bina Kumari, Subir K. Sarkar, Pradipta Bandyopadhyay
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The autocorrelation function of the density fluctuation is studied in each of the two phases in a Gibbs Ensemble Monte Carlo (GEMC) simulation of the problem of phase separation for a square well potential with various values of its range. We find that the normalized autocorrelation function is described very well as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of (α, τ₁, τ₂) on the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We also analyse the issue of how to choose the parameters of the GEMC simulation optimally.Keywords: autocorrelation function, density fluctuation, GEMC, simulation
Procedia PDF Downloads 1784866 A Practical and Efficient Evaluation Function for 3D Model Based Vehicle Matching
Authors: Yuan Zheng
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3D model-based vehicle matching provides a new way for vehicle recognition, localization and tracking. Its key is to construct an evaluation function, also called fitness function, to measure the degree of vehicle matching. The existing fitness functions often poorly perform when the clutter and occlusion exist in traffic scenarios. In this paper, we present a practical and efficient fitness function. Unlike the existing evaluation functions, the proposed fitness function is to study the vehicle matching problem from both local and global perspectives, which exploits the pixel gradient information as well as the silhouette information. In view of the discrepancy between 3D vehicle model and real vehicle, a weighting strategy is introduced to differently treat the fitting of the model’s wireframes. Additionally, a normalization operation for the model’s projection is performed to improve the accuracy of the matching. Experimental results on real traffic videos reveal that the proposed fitness function is efficient and robust to the cluttered background and partial occlusion.Keywords: 3D-2D matching, fitness function, 3D vehicle model, local image gradient, silhouette information
Procedia PDF Downloads 3924865 Modelling of the Linear Operator in the Representation of the Function of Wave of a Micro Particle
Authors: Mohammedi Ferhate
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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.Keywords: function, operator, simulation, wave
Procedia PDF Downloads 1394864 Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution
Authors: Md. Rashidul Hasan, Atikur Rahman Baizid
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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function
Procedia PDF Downloads 3804863 Remarks on the Lattice Green's Function for the Anisotropic Face Cantered Cubic Lattice
Authors: Jihad H. Asad
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An expression for the Green’s function (GF) of anisotropic face cantered cubic (IFCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.Keywords: lattice Green's function, elliptic integral, physics, cubic lattice
Procedia PDF Downloads 4614862 An Analytical Wall Function for 2-D Shock Wave/Turbulent Boundary Layer Interactions
Authors: X. Wang, T. J. Craft, H. Iacovides
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When handling the near-wall regions of turbulent flows, it is necessary to account for the viscous effects which are important over the thin near-wall layers. Low-Reynolds- number turbulence models do this by including explicit viscous and also damping terms which become active in the near-wall regions, and using very fine near-wall grids to properly resolve the steep gradients present. In order to overcome the cost associated with the low-Re turbulence models, a more advanced wall function approach has been implemented within OpenFoam and tested together with a standard log-law based wall function in the prediction of flows which involve 2-D shock wave/turbulent boundary layer interactions (SWTBLIs). On the whole, from the calculation of the impinging shock interaction, the three turbulence modelling strategies, the Lauder-Sharma k-ε model with Yap correction (LS), the high-Re k-ε model with standard wall function (SWF) and analytical wall function (AWF), display good predictions of wall-pressure. However, the SWF approach tends to underestimate the tendency of the flow to separate as a result of the SWTBLI. The analytical wall function, on the other hand, is able to reproduce the shock-induced flow separation and returns predictions similar to those of the low-Re model, using a much coarser mesh.Keywords: SWTBLIs, skin-friction, turbulence modeling, wall function
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