Search results for: Wavelet basis function.

Authors: Vladimir S. Timofeev

Abstract:

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.

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Authors: M. Govindarajan

Abstract:

One of the major developments in machine learning in the past decade is the ensemble method, which finds highly accurate classifier by combining many moderately accurate component classifiers. In this research work, new ensemble classification methods are proposed with homogeneous ensemble classifier using bagging and heterogeneous ensemble classifier using arcing and their performances are analyzed in terms of accuracy. A Classifier ensemble is designed using Radial Basis Function (RBF) and Support Vector Machine (SVM) as base classifiers. The feasibility and the benefits of the proposed approaches are demonstrated by the means of standard datasets of intrusion detection. The main originality of the proposed approach is based on three main parts: preprocessing phase, classification phase, and combining phase. A wide range of comparative experiments is conducted for standard datasets of intrusion detection. The performance of the proposed homogeneous and heterogeneous ensemble classifiers are compared to the performance of other standard homogeneous and heterogeneous ensemble methods. The standard homogeneous ensemble methods include Error correcting output codes, Dagging and heterogeneous ensemble methods include majority voting, stacking. The proposed ensemble methods provide significant improvement of accuracy compared to individual classifiers and the proposed bagged RBF and SVM performs significantly better than ECOC and Dagging and the proposed hybrid RBF-SVM performs significantly better than voting and stacking. Also heterogeneous models exhibit better results than homogeneous models for standard datasets of intrusion detection. 

Keywords: Data mining, ensemble, radial basis function, support vector machine, accuracy.

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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.

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Authors: A. Jabbari, M. Shakeri, A. Nabavi

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In this paper, a tooth shape optimization method for cogging torque reduction in Permanent Magnet (PM) motors is developed by using the Reduced Basis Technique (RBT) coupled by Finite Element Analysis (FEA) and Design of Experiments (DOE) methods. The primary objective of the method is to reduce the enormous number of design variables required to define the tooth shape. RBT is a weighted combination of several basis shapes. The aim of the method is to find the best combination using the weights for each tooth shape as the design variables. A multi-level design process is developed to find suitable basis shapes or trial shapes at each level that can be used in the reduced basis technique. Each level is treated as a separated optimization problem until the required objective – minimum cogging torque – is achieved. The process is started with geometrically simple basis shapes that are defined by their shape co-ordinates. The experimental design of Taguchi method is used to build the approximation model and to perform optimization. This method is demonstrated on the tooth shape optimization of a 8-poles/12-slots PM motor.

Keywords: PM motor, cogging torque, tooth shape optimization, RBT, FEA, DOE.

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Authors: Tokuei Sako, Paul-Antoine Hervieux

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The energy-level structure of a pair of electron and positron confined in a quasi-one-dimensional nano-scale potential well has been investigated focusing on its trend in the small limit of confinement strength ω, namely, the Wigner molecular regime. An anisotropic Gaussian-type basis functions supplemented by high angular momentum functions as large as l = 19 has been used to obtain reliable full configuration interaction (FCI) wave functions. The resultant energy spectrum shows a band structure characterized by ω for the large ω regime whereas for the small ω regime it shows an energy-level pattern dominated by excitation into the in-phase motion of the two particles. The observed trend has been rationalized on the basis of the nodal patterns of the FCI wave functions. 

Keywords: Confined systems, positron, wave function, Wigner molecule, quantum dots.

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Authors: Z. 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: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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Authors: Kourosh Parand, Jamal Amani Rad

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In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

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In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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Authors: Xiaolei Hu, Enrico Ferrera, Riccardo Tomasi, Claudio Pastrone

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Load Forecasting plays a key role in making today's and future's Smart Energy Grids sustainable and reliable. Accurate power consumption prediction allows utilities to organize in advance their resources or to execute Demand Response strategies more effectively, which enables several features such as higher sustainability, better quality of service, and affordable electricity tariffs. It is easy yet effective to apply Load Forecasting at larger geographic scale, i.e. Smart Micro Grids, wherein the lower available grid flexibility makes accurate prediction more critical in Demand Response applications. This paper analyses the application of short-term load forecasting in a concrete scenario, proposed within the EU-funded GreenCom project, which collect load data from single loads and households belonging to a Smart Micro Grid. Three short-term load forecasting techniques, i.e. linear regression, artificial neural networks, and radial basis function network, are considered, compared, and evaluated through absolute forecast errors and training time. The influence of weather conditions in Load Forecasting is also evaluated. A new definition of Gain is introduced in this paper, which innovatively serves as an indicator of short-term prediction capabilities of time spam consistency. Two models, 24- and 1-hour-ahead forecasting, are built to comprehensively compare these three techniques.

Keywords: Short-term load forecasting, smart micro grid, linear regression, artificial neural networks, radial basis function network, Gain.

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Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh

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Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties

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Authors: Shin Je Lee, Go Bong Choi, Jeong Cheol Seo, Jong Min Lee, Gibaek Lee

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Water pipe network is installed underground and once equipped, it is difficult to recognize the state of pipes when the leak or burst happens. Accordingly, post management is often delayed after the fault occurs. Therefore, the systematic fault management system of water pipe network is required to prevent the accident and minimize the loss. In this work, we develop online fault detection system of water pipe network using data of pipes such as flow rate or pressure. The transient model describing water flow in pipelines is presented and simulated using MATLAB. The fault situations such as the leak or burst can be also simulated and flow rate or pressure data when the fault happens are collected. Faults are detected using statistical methods of fast Fourier transform and discrete wavelet transform, and they are compared to find which method shows the better fault detection performance.

Keywords: fault detection, water pipeline model, fast Fourier transform, discrete wavelet transform.

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Authors: Aleksandra Aleksandrovna Filimonova, Lev Sergeevich Kazarinov, Tatyana Aleksandrovna Barbasova

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A method of effective planning and control of industrial facility energy consumption is offered. The method allows optimally arranging the management and full control of complex production facilities in accordance with the criteria of minimal technical and economic losses at the forecasting control. The method is based on the optimal construction of the power efficiency characteristics with the prescribed accuracy. The problem of optimal designing of the forecasting model is solved on the basis of three criteria: maximizing the weighted sum of the points of forecasting with the prescribed accuracy; the solving of the problem by the standard principles at the incomplete statistic data on the basis of minimization of the regularized function; minimizing the technical and economic losses due to the forecasting errors.

Keywords: Energy consumption, energy efficiency, energy management system, forecasting model, power efficiency characteristics.

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Authors: I. R. Farah, I. B. Ismail, M. B. Ahmed

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The huge development of new technologies and the apparition of open communication system more and more sophisticated create a new challenge to protect digital content from piracy. Digital watermarking is a recent research axis and a new technique suggested as a solution to these problems. This technique consists in inserting identification information (watermark) into digital data (audio, video, image, databases...) in an invisible and indelible manner and in such a way not to degrade original medium-s quality. Moreover, we must be able to correctly extract the watermark despite the deterioration of the watermarked medium (i.e attacks). In this paper we propose a system for watermarking satellite images. We chose to embed the watermark into frequency domain, precisely the discrete wavelet transform (DWT). We applied our algorithm on satellite images of Tunisian center. The experiments show satisfying results. In addition, our algorithm showed an important resistance facing different attacks, notably the compression (JEPG, JPEG2000), the filtering, the histogram-s manipulation and geometric distortions such as rotation, cropping, scaling.

Keywords: Digital data watermarking, Spatial Database, Satellite images, Discrete Wavelets Transform (DWT).

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: Pallav Roxy, Durga Toshniwal

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Clustering unstructured text documents is an important issue in data mining community and has a number of applications such as document archive filtering, document organization and topic detection and subject tracing. In the real world, some of the already clustered documents may not be of importance while new documents of more significance may evolve. Most of the work done so far in clustering unstructured text documents overlooks this aspect of clustering. This paper, addresses this issue by using the Fading Function. The unstructured text documents are clustered. And for each cluster a statistics structure called Cluster Profile (CP) is implemented. The cluster profile incorporates the Fading Function. This Fading Function keeps an account of the time-dependent importance of the cluster. The work proposes a novel algorithm Clustering n-ary Merge Algorithm (CnMA) for unstructured text documents, that uses Cluster Profile and Fading Function. Experimental results illustrating the effectiveness of the proposed technique are also included.

Keywords: Clustering, Text Mining, Unstructured TextDocuments, Fading Function.

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Authors: Saleem Z. Ramadan, Gürsel A. Süer

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In this paper a genetic algorithm (GA) with dual-fitness function is proposed and applied to solve the deterministic identical machine scheduling problem. The mating fitness function value was used to determine the mating for chromosomes, while the selection fitness function value was used to determine their survivals. The performance of this algorithm was tested on deterministic identical machine scheduling using simulated data. The results obtained from the proposed GA were compared with classical GA and integer programming (IP). Results showed that dual-fitness function GA outperformed the classical single-fitness function GA with statistical significance for large problems and was competitive to IP, particularly when large size problems were used.

Keywords: Machine scheduling, Genetic algorithms, Due dates, Number of tardy jobs, Number of early jobs, Integer programming, Dual Fitness functions.

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Authors: V. Veeraprathap, G. S. Harish, G. Narendra Kumar

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Uncontrolled growth of abnormal cells in the lung in the form of tumor can be either benign (non-cancerous) or malignant (cancerous). Patients with Lung Cancer (LC) have an average of five years life span expectancy provided diagnosis, detection and prediction, which reduces many treatment options to risk of invasive surgery increasing survival rate. Computed Tomography (CT), Positron Emission Tomography (PET), and Magnetic Resonance Imaging (MRI) for earlier detection of cancer are common. Gaussian filter along with median filter used for smoothing and noise removal, Histogram Equalization (HE) for image enhancement gives the best results without inviting further opinions. Lung cavities are extracted and the background portion other than two lung cavities is completely removed with right and left lungs segmented separately. Region properties measurements area, perimeter, diameter, centroid and eccentricity measured for the tumor segmented image, while texture is characterized by Gray-Level Co-occurrence Matrix (GLCM) functions, feature extraction provides Region of Interest (ROI) given as input to classifier. Two levels of classifications, K-Nearest Neighbor (KNN) is used for determining patient condition as normal or abnormal, while Artificial Neural Networks (ANN) is used for identifying the cancer stage is employed. Discrete Wavelet Transform (DWT) algorithm is used for the main feature extraction leading to best efficiency. The developed technology finds encouraging results for real time information and on line detection for future research.

Keywords: ANN, DWT, GLCM, KNN, ROI, artificial neural networks, discrete wavelet transform, gray-level co-occurrence matrix, k-nearest neighbor, region of interest.

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Authors: Minh T. N. Le, Cathleen Teh, Ng Shyh-Chang, Vladimir Korzh, Harvey F. Lodish, Bing Lim

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MicroRNAs are an important class of gene expression regulators that are involved in many biological processes including embryogenesis. miR-125b is a conserved microRNA that is enriched in the nervous system. We have previously reported the function of miR-125b in neuronal differentiation of human cell lines. We also discovered the function of miR-125b in regulating p53 in human and zebrafish. Here we further characterize the brain defects in zebrafish embryos injected with morpholinos against miR-125b. Our data confirm the essential role of miR-125b in brain morphogenesis particularly in maintaining the balance between proliferation, cell death and differentiation. We identified lunatic fringe (lfng) as an additional target of miR-125b in human and zebrafish and suggest that lfng may mediate the function of miR-125b in neurogenesis. Together, this report reveals new insights into the function of miR- 125b during neural development of zebrafish.

Keywords: microRNA, miR-125b, neurogenesis, zebrafish.

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Authors: Yuan Zheng

Abstract:

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.

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Authors: Y. Bhatt, N. Ghosh, N. Tiwari

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Acreage response function are modeled taking account of expected harvest prices, weather related variables and other non-price variables allowing for partial adjustment possibility. At the outset, based on the literature on price expectation formation, we explored suitable formulations for estimating the farmer’s expected prices. Assuming that farmers form expectations rationally, the prices of food and biofuel crops are modeled using time-series methods for possible ARCH/GARCH effects to account for volatility. The prices projected on the basis of the models are then inserted to proxy for the expected prices in the acreage response functions. Food crop acreages in different growing states are found sensitive to their prices relative to those of one or more of the biofuel crops considered. The required percentage improvement in food crop yields is worked to offset the acreage loss.

Keywords: Acreage response function, biofuel, food security, sustainable development.

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Authors: Ying-Han Pang, Andrew Teoh Beng Jin, David Ngo Chek Ling

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A cancelable palmprint authentication system proposed in this paper is specifically designed to overcome the limitations of the contemporary biometric authentication system. In this proposed system, Geometric and pseudo Zernike moments are employed as feature extractors to transform palmprint image into a lower dimensional compact feature representation. Before moment computation, wavelet transform is adopted to decompose palmprint image into lower resolution and dimensional frequency subbands. This reduces the computational load of moment calculation drastically. The generated wavelet-moment based feature representation is used to generate cancelable verification key with a set of random data. This private binary key can be canceled and replaced. Besides that, this key also possesses high data capture offset tolerance, with highly correlated bit strings for intra-class population. This property allows a clear separation of the genuine and imposter populations, as well as zero Equal Error Rate achievement, which is hardly gained in the conventional biometric based authentication system.

Keywords: Cancelable biometric authenticator, Discrete- Hashing, Moments, Palmprint.

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

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Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant.

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Authors: M. Sedighizadeh, A. Rezazadeh

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Movable power sources of proton exchange membrane fuel cells (PEMFC) are the important research done in the current fuel cells (FC) field. The PEMFC system control influences the cell performance greatly and it is a control system for industrial complex problems, due to the imprecision, uncertainty and partial truth and intrinsic nonlinear characteristics of PEMFCs. In this paper an adaptive PI control strategy using neural network adaptive Morlet wavelet for control is proposed. It is based on a single layer feed forward neural networks with hidden nodes of adaptive morlet wavelet functions controller and an infinite impulse response (IIR) recurrent structure. The IIR is combined by cascading to the network to provide double local structure resulting in improving speed of learning. The proposed method is applied to a typical 1 KW PEMFC system and the results show the proposed method has more accuracy against to MLP (Multi Layer Perceptron) method.

Keywords: Adaptive Control, Morlet Wavelets, PEMFC.

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Authors: Takashi Mitsuishi, Koji Saigusa

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This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Keywords: Defuzzification, periodic membership function, polar coordinates transformation.

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Authors: Ethar H. Khalil, Bahaa I. Kazem

Abstract:

In this work a software simulation model has been proposed for two driven wheels mobile robot path planning; that can navigate in dynamic environment with static distributed obstacles. The work involves utilizing Bezier curve method in a proposed N order matrix form; for engineering the mobile robot path. The Bezier curve drawbacks in this field have been diagnosed. Two directions: Up and Right function has been proposed; Probability Recursive Function (PRF) to overcome those drawbacks. PRF functionality has been developed through a proposed; obstacle detection function, optimization function which has the capability of prediction the optimum path without comparison between all feasible paths, and N order Bezier curve function that ensures the drawing of the obtained path. The simulation results that have been taken showed; the mobile robot travels successfully from starting point and reaching its goal point. All obstacles that are located in its way have been avoided. This navigation is being done successfully using the proposed PRF techniques.

Keywords: Mobile robot, path planning, Bezier curve.

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Authors: Khalid A. Kaabneh

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This paper introduces and studies new indexing techniques for content-based queries in images databases. Indexing is the key to providing sophisticated, accurate and fast searches for queries in image data. This research describes a new indexing approach, which depends on linear modeling of signals, using bases for modeling. A basis is a set of chosen images, and modeling an image is a least-squares approximation of the image as a linear combination of the basis images. The coefficients of the basis images are taken together to serve as index for that image. The paper describes the implementation of the indexing scheme, and presents the findings of our extensive evaluation that was conducted to optimize (1) the choice of the basis matrix (B), and (2) the size of the index A (N). Furthermore, we compare the performance of our indexing scheme with other schemes. Our results show that our scheme has significantly higher performance.

Keywords: Axial Projection, images, indexing, multimedia database, searching.

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Authors: Mohammed Rziza, Mohamed El Aroussi, Mohammed El Hassouni, Sanaa Ghouzali, Driss Aboutajdine

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In this paper, an efficient local appearance feature extraction method based the multi-resolution Curvelet transform is proposed in order to further enhance the performance of the well known Linear Discriminant Analysis(LDA) method when applied to face recognition. Each face is described by a subset of band filtered images containing block-based Curvelet coefficients. These coefficients characterize the face texture and a set of simple statistical measures allows us to form compact and meaningful feature vectors. The proposed method is compared with some related feature extraction methods such as Principal component analysis (PCA), as well as Linear Discriminant Analysis LDA, and independent component Analysis (ICA). Two different muti-resolution transforms, Wavelet (DWT) and Contourlet, were also compared against the Block Based Curvelet-LDA algorithm. Experimental results on ORL, YALE and FERET face databases convince us that the proposed method provides a better representation of the class information and obtains much higher recognition accuracies.

Keywords: Curvelet, Linear Discriminant Analysis (LDA) , Contourlet, Discreet Wavelet Transform, DWT, Block-based analysis, face recognition (FR).

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Authors: Seung-Won Jung, Hye-Soo Kim, Le Thanh Ha, Seung-Jin Baek, Sung-Jea Ko

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In this paper, a novel deinterlacing algorithm is proposed. The proposed algorithm approximates the distribution of the luminance into a polynomial function. Instead of using one polynomial function for all pixels, different polynomial functions are used for the uniform, texture, and directional edge regions. The function coefficients for each region are computed by matrix multiplications. Experimental results demonstrate that the proposed method performs better than the conventional algorithms.

Keywords: Deinterlacing, polynomial interpolation.

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Authors: Inese Bula

Abstract:

Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.

Keywords: Infinite symbol space, prefix metric, chaotic mapping, generator function, jump mapping.

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

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

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

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