Search results for: Shifted Legendre polynomials

Authors: Mohammed A. Abutheraa, David Lester

Abstract:

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Keywords: Approximation Theory, Chebyshev Polynomial, Computable Functions, Computable Real Arithmetic, Integration, Numerical Analysis.

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Authors: Dimitris Varsamis, Nicholas Karampetakis

Abstract:

It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: Bivariate interpolation polynomial, Polynomial basis, Transformations.

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Authors: Chiou-Yng Lee, Wen-Yo Lee, Chieh-Tsai Wu, Cheng-Chen Yang

Abstract:

Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit level and digi -level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba schemes, and used that to derive a novel scalable multiplier architecture. Analytical results show that the proposed multiplier provides a trade-off between space and time complexities. Our proposed multiplier is modular, regular, and suitable for very large scale integration (VLSI) implementations. It involves less area complexity compared to the multipliers based on traditional decomposition methods. It is therefore, more suitable for efficient hardware implementation of pairing based cryptography and elliptic curve cryptography (ECC) in constraint driven applications.

Keywords: Digit-serial systolic multiplier, elliptic curve cryptography (ECC), Karatsuba algorithm (KA), shifted polynomial basis (SPB), pairing computation.

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Authors: Panos D. Kotsas, Tony Dodd

Abstract:

2D/3D registration is a special case of medical image registration which is of particular interest to surgeons. Applications of 2D/3D registration are [1] radiotherapy planning and treatment verification, spinal surgery, hip replacement, neurointerventions and aortic stenting. The purpose of this paper is to provide a literature review of the main methods for image registration for the 2D/3D case. At the end of the paper an algorithm is proposed for 2D/3D registration based on the Chebyssev polynomials iteration loop.

Keywords: Medical image registration, review, 2D/3D

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Authors: Joshi Manohar. V., Sujatha. P., Anjaneyulu K. S. R

Abstract:

The range of the output power is a very important and evident limitation of two-level inverters. In order to overcome this disadvantage, multilevel inverters are introduced. Recently, Cascade H-Bridge inverters have emerged as one of the popular converter topologies used in numerous industrial applications. The modulation switching strategies such as phase shifted carrier based Pulse Width Modulation (PWM) technique and Stair case modulation with Selective Harmonic Elimination (SHE) PWM technique are generally used. NR method is used to solve highly non linear transcendental equations which are formed by SHEPWM method. Generally NR method has a drawback of requiring good initial guess but in this paper a new approach is implemented for NR method with any random initial guess. A three phase CHB 11-level inverter is chosen for analysis. MATLAB/SIMULINK programming environment and harmonic profiles are compared. Finally this paper presents a method at fundamental switching frequency with least % THDV.

Keywords: Cascade H-bridge 11- level Inverter, NR method, Phase shifted carrier based pulse width modulation (PSCPWM), Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Total Harmonic Distortion (%THDv).

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Authors: Ahmad Zahran, Ahmed Herzallah, Ahmad Ahmad, Mahran Quraan

Abstract:

Generation of high DC voltages is necessary for testing the insulation material of high voltage AC transmission lines with long lengths. The harmonic and ripple contents of the output DC voltage supplied by high voltage DC circuits require the use of costly capacitors to smooth the output voltage after rectification. This paper proposes a new modular multiplier high voltage DC generator with embedded Cockcroft-Walton circuits that achieve a negligible harmonic and ripple contents of the output DC voltage without the need for costly filters to produce a nearly constant output voltage. In this new topology, Cockcroft-Walton modules are connected in series to produce a high DC output voltage. The modules are supplied by low input AC voltage sources that have the same magnitude and frequency and shifted from each other by a certain angle to eliminate the harmonics from the output voltage. The small ripple factor is provided by the smoothing column capacitors and the phase shifted input voltages of the cascaded modules. The constituent harmonics within each module are determined using Fourier analysis. The viability of the proposed DC generator for testing purposes and the effectiveness of the cascaded connection are confirmed by numerical simulations using MATLAB/Simulink.

Keywords: Cockcroft-Walton circuit, Harmonics, Ripple factor, HVDC generator.

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Authors: M. A. Koroma, S. Widatalla, A. F. Kamara, C. Zhang

Abstract:

Our aim in this piece of work is to demonstrate the power of the Laplace Adomian decomposition method (LADM) in approximating the solutions of nonlinear differential equations governing the two-dimensional viscous flow induced by a shrinking sheet.

Keywords: Adomian polynomials, Laplace Adomian decomposition method, Padé Approximant, Shrinking sheet.

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Authors: Inder K. Purohit, M. Nazrul Islam, K. Vijayan Asari, Mohammad A. Karim

Abstract:

A new target detection technique is presented in this paper for the identification of small boats in coastal surveillance. The proposed technique employs an adaptive progressive thresholding (APT) scheme to first process the given input scene to separate any objects present in the scene from the background. The preprocessing step results in an image having only the foreground objects, such as boats, trees and other cluttered regions, and hence reduces the search region for the correlation step significantly. The processed image is then fed to the shifted phase-encoded fringe-adjusted joint transform correlator (SPFJTC) technique which produces single and delta-like correlation peak for a potential target present in the input scene. A post-processing step involves using a peak-to-clutter ratio (PCR) to determine whether the boat in the input scene is authorized or unauthorized. Simulation results are presented to show that the proposed technique can successfully determine the presence of an authorized boat and identify any intruding boat present in the given input scene.

Keywords: Adaptive progressive thresholding, fringe adjusted filters, image segmentation, joint transform correlation, synthetic discriminant function

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

Abstract:

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.

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Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: R. Farkh, K. Laabidi, M. Ksouri

Abstract:

In this paper, we consider the control of time delay system by Proportional-Integral (PI) controller. By Using the Hermite- Biehler theorem, which is applicable to quasi-polynomials, we seek a stability region of the controller for first order delay systems. The essence of this work resides in the extension of this approach to second order delay system, in the determination of its stability region and the computation of the PI optimum parameters. We have used the genetic algorithms to lead the complexity of the optimization problem.

Keywords: Genetic algorithm, Hermit-Biehler theorem, optimization, PI controller, second order delay system, stability region.

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

Abstract:

The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Kouamana Bousson, Paulo Machado

Abstract:

The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the indirect or direct methods. The indirect methods are based on maximum principle of Pontryagin, on the other hand, in the direct methods it is necessary to transform into a nonlinear programming problem. We propose an approach based on direct methods with a pseudospectral integration scheme built on Chebyshev polynomials.

Keywords: Pseudospectral Methods, Trajectory Optimization, 4DTrajectories

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Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Awais Adnan, Muhammad Ali, Amir Hanif Dar

Abstract:

Image Searching was always a problem specially when these images are not properly managed or these are distributed over different locations. Currently different techniques are used for image search. On one end, more features of the image are captured and stored to get better results. Storing and management of such features is itself a time consuming job. While on the other extreme if fewer features are stored the accuracy rate is not satisfactory. Same image stored with different visual properties can further reduce the rate of accuracy. In this paper we present a new concept of using polynomials of sorted histogram of the image. This approach need less overhead and can cope with the difference in visual features of image.

Keywords: Sorted Histogram, Polynomial Curves, feature pointsof images, Grayscale, visual properties of image.

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Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh

Abstract:

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.

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Authors: Alexander Efremov

Abstract:

A system for market identification (SMI) is presented. The resulting representations are multivariable dynamic demand models. The market specifics are analyzed. Appropriate models and identification techniques are chosen. Multivariate static and dynamic models are used to represent the market behavior. The steps of the first stage of SMI, named data preprocessing, are mentioned. Next, the second stage, which is the model estimation, is considered in more details. Stepwise linear regression (SWR) is used to determine the significant cross-effects and the orders of the model polynomials. The estimates of the model parameters are obtained by a numerically stable estimator. Real market data is used to analyze SMI performance. The main conclusion is related to the applicability of multivariate dynamic models for representation of market systems.

Keywords: market identification, dynamic models, stepwise regression.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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Authors: Abdullah A. AlShaher

Abstract:

In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2^nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.

Keywords: Shape recognition, Arabic handwritten characters, regression curves, expectation maximization algorithm.

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Authors: R. Rinkeviciene, B. Kundrotas, S. Lisauskas

Abstract:

In this paper, the authors take a look at advantages of multiphase induction motors comparing them with three phase ones and present the applications where six-phase induction motors are used. They elaborate the mathematical model of six-phase induction motor with two similar stator three phase winding, shifted by 30 degrees in space and three phase winding in rotor, in synchronous reference frame for soft starting and scalar control. The authors simulate and discuss results of speed and torque starting transients.

Keywords: Model, scalar control, six-phase induction motor.

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Authors: Panos D. Kotsas, Tony Dodd

Abstract:

The purpose of this work is to present a method for rigid registration of medical images using 1D binary projections when a part of one of the two images is missing. We use 1D binary projections and we adjust the projection limits according to the reduced image in order to perform accurate registration. We use the variance of the weighted ratio as a registration function which we have shown is able to register 2D and 3D images more accurately and robustly than mutual information methods. The function is computed explicitly for n=5 Chebyshev points in a [-9,+9] interval and it is approximated using Chebyshev polynomials for all other points. The images used are MR scans of the head. We find that the method is able to register the two images with average accuracy 0.3degrees for rotations and 0.2 pixels for translations for a y dimension of 156 with initial dimension 256. For y dimension 128/256 the accuracy decreases to 0.7 degrees for rotations and 0.6 pixels for translations.

Keywords: binary projections, image registration, reduceddimension images.

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Authors: Mohamed Othmani, Yassine Khlifi

Abstract:

This paper presents a technique for compact three dimensional (3D) object model reconstruction using wavelet networks. It consists to transform an input surface vertices into signals,and uses wavelet network parameters for signal approximations. To prove this, we use a wavelet network architecture founded on several mother wavelet families. POLYnomials WindOwed with Gaussians (POLYWOG) wavelet families are used to maximize the probability to select the best wavelets which ensure the good generalization of the network. To achieve a better reconstruction, the network is trained several iterations to optimize the wavelet network parameters until the error criterion is small enough. Experimental results will shown that our proposed technique can effectively reconstruct an irregular 3D object models when using the optimized wavelet network parameters. We will prove that an accurateness reconstruction depends on the best choice of the mother wavelets.

Keywords: 3D object, optimization, parametrization, Polywog wavelets, reconstruction, wavelet networks.

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Authors: E. Srinivasan, D. Ebenezer

Abstract:

Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.

Keywords: Image filtering, detail preservation, median filters, nonlinear filters, order statistics filtering, Rank order filtering.

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

Abstract:

The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: Eigenvalues/Eigenvectors, Latent values/vectors, Matrix fraction description, State space description.

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Authors: Sudipta Majumdar

Abstract:

This paper presents a method for identification of a linear time invariant (LTI) autonomous all pole system using singular value decomposition. The novelty of this paper is two fold: First, MUSIC algorithm for estimating complex frequencies from real measurements is proposed. Secondly, using the proposed algorithm, we can identify the coefficients of differential equation that determines the LTI system by switching off our input signal. For this purpose, we need only to switch off the input, apply our complex MUSIC algorithm and determine the coefficients as symmetric polynomials in the complex frequencies. This method can be applied to unstable system and has higher resolution as compared to time series solution when, noisy data are used. The classical performance bound, Cramer Rao bound (CRB), has been used as a basis for performance comparison of the proposed method for multiple poles estimation in noisy exponential signal.

Keywords: MUSIC algorithm, Cramer Rao bound, frequency estimation.

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Authors: Pavel Psota, Vít Lédl, Jan Václavík, Roman Doleček, Pavel Mokrý, Petr Vojtíšek

Abstract:

This paper presents advanced time average digital holography by means of frequency shift and phase modulation. This technique can measure amplitudes of vibrations at ultimate dynamic range while the amplitude distribution evaluation is done independently in every pixel. The main focus of the paper is to gain insight into behavior of the method at low amplitudes of vibrations. In order to reach that, a set of experiments was performed. Results of the experiments together with novel noise suppression show the limit of the method to be below 0.1 nm.

Keywords: Acousto-optical modulator, digital holography, low amplitudes, vibrometry.

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Authors: Prakash G L, Thejaswini M, S H Manjula, K R Venugopal, L M Patnaik

Abstract:

Wireless sensor network can be applied to both abominable and military environments. A primary goal in the design of wireless sensor networks is lifetime maximization, constrained by the energy capacity of batteries. One well-known method to reduce energy consumption in such networks is data aggregation. Providing efcient data aggregation while preserving data privacy is a challenging problem in wireless sensor networks research. In this paper, we present privacy-preserving data aggregation scheme for additive aggregation functions. The Cluster-based Private Data Aggregation (CPDA)leverages clustering protocol and algebraic properties of polynomials. It has the advantage of incurring less communication overhead. The goal of our work is to bridge the gap between collaborative data collection by wireless sensor networks and data privacy. We present simulation results of our schemes and compare their performance to a typical data aggregation scheme TAG, where no data privacy protection is provided. Results show the efficacy and efficiency of our schemes.

Keywords: Aggregation, Clustering, Query Processing.

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Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: Cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol.

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