Chebyshev Polynomial
ON THE CHEBYSHEV POLYNOMIAL COEFFICIENT PROBLEM OF BI-BAZILEVI C FUNCTIONS
... Abstract. A function said to be bi-Bazilevi˘ c in the open unit disk U if both the function and its inverse are Bazilevi˘ c there. In this paper, we will study a newly constructed class of bi-Bazilevi˘ c functions. ...
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A new kind of double Chebyshev polynomial approximation on unbounded domains
... of Chebyshev polynomials can appear in the solution of differential ...example, Chebyshev polynomial approximations have been used to solve ordinary differ- ential equations with boundary conditions in ...
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On The Numerical Solution of Urysohn Integral Equation Using Chebyshev Polynomial
... is called an Urysohn equation of the second kind. The main objective of this paper is to solve the Urysohn type Fredholm integral equation Eq. (1). This method is based on replacement of the unknown function by the ...
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SYNTHESIS OF NON UNIFORM LINEAR ARRAYS USING DOLPH – CHEBYSHEV POLYNOMIAL BY REDUCING SIDE LOBE LEVEL BASED ON MODULATING PARAMETER ARRAY FACTOR
... In this paper a new approach to reduce the first side lobe level of an antenna array, without disturbing the main beam width using doplh – chebyshev array. There are number of Techniques used to reduce Side Lobe ...
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A family of doubly stochastic matrices involving Chebyshev polynomials
... A normalized Chebyshev polynomial is a Chebyshev polynomial divided by the coefficient of its leading term.. So, the leading term of a normalized Chebyshev polynomial is always 1.[r] ...
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Graph convolutional networks: a comprehensive review
... CNN: convolution neural network; ChebNet: Chebyshev polynomial based graph convolution (model proposed in [ 34 ]); GCN: graph convolutional network (model proposed in [ 37 ]); FastGCN: [r] ...
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Numerical Solution of Linear Second Order Ordinary Differential Equations with Mixed Boundary Conditions by Galerkin Method
... approximating polynomial defined for x ∈ − [ 1,1] the given BVP defined on arbitrary interval [a, b] must be converted into an equivalent BVP defined on [-1, ...approximating polynomial should be defined on ...
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Patch-based models and algorithms for image denoising: a comparative review between patch-based images denoising methods for additive noise reduction
... CPA: Chebyshev polynomial approximation; DL: Dictionary learning; EPLL: Extend patch log likelihood; HSI: Hyperspectral image; HT: Hard thresholding; It-PPB: Iterative probabilistic patch-based; K-SVD: ...
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Powder study of (R) 1 phenylethylammonium (R) 2 phenylbutyrate form 2
... Only H-atom coordinates refined Weighting scheme based on measured s.u.'s 1/σYobs2 Δ/σmax = 0.005 Background function: Chebyshev polynomial Preferred orientation correction: A spherical [r] ...
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1 Methyl 2 (4 nitrophenyl)imidazo[1,2 a]pyridinium perchlorate: a powder study
... 220 restraints 36 constraints H-atom parameters constrained Weighting scheme based on measured s.u.'s Δ/σmax = 0.023 Background function: Chebyshev polynomial up to the 5th order Preferr[r] ...
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The Lanczos Chebyshev Pseudospectral Method for Solution of Differential Equations
... f x = x − ≤ ≤ x (13) It has been found that, at least, a 10 th -order Chebyshev polynomial series is required for this function to be represented with sufficient accuracy [23]. We test the series expansion ...
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Design of Even-Order Symmetric Bandpass Filter with Chebyshev Response
... The Chebyshev polynomial is often used as a synthesis method of the filter design [12, ...with Chebyshev response is presented in [12], and the Chebyshev lowpass prototype is used in its ...
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Total characters and Chebyshev polynomials
... Proof. The first half follows easily by an inductive argument on n and by using the recursive relation mentioned above. For divisibility of the coeffi- cients, observe that the result is true for n = 1 and n = 2. Now assume ...
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Accurate splitting approach to characterize the solution set of boundary layer problems
... shifted Chebyshev polynomial of the first ...shifted Chebyshev polynomials. The shifted Chebyshev polynomial [3] of the first kind T n ∗ (x), with degree n in x ∈ [0, δ], is defined by the ...
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An Effective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument
... Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with ...
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Fractional Calculus for Solving generalized Abel’s Integral Equations using Chebyshev Polynomials
... Now, we collocate the roots of Chebyshev polynomial of degree in It leads to a system of linear equations. By solution of obtained system we have the approximate solution of Abel’s integral equation as For ...
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A General Algorithm for Biorthogonal Functions and Performance Analysis of Biorthogonal Scramble Modulation System
... as Chebyshev polynomial and Legendre polynomial analy- sis, have better BER performance and spectrum effi- ciency than the BOSM system based on Fourier series analysis, orthogonal MCM system or OFDM ...
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Wavelets operational methods for fractional differential equations and systems of fractional differential equations
... shifted Chebyshev polynomials of any degree in terms of shifted Chebyshev polynomials themselves, and used it together with tau and collocation spectral methods to find an approximate solutions for ...
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REPRESENTING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE FIRST KIND AND LUCAS POLYNOMIALS BY CHEBYSHEV POLYNOMIALS
... of Chebyshev polynomials of the first kind in ...of Chebyshev polynomials to find that all the coefficients involve terminating hypergeometric functions 2 F 1 ...
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A characterization of the four Chebyshev orthogonal families
... these Chebyshev weights are the Bernstein polynomials (see [3, ...of Chebyshev polynomials, with fixed length and constant coefficients (see [4, ...orthogonal polynomial sequences with respect to a ...
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