Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. In this paper, a new stable algorithm based on shifted Chebyshev polynomial approxima...

In this article, a method is presented for transforming the singular Lippmann-Schwinger integral equation to a matrix algebraic equation. This method of computing the matrix elements of the reaction and transition operators is used on the real axis and on the complex plane, respectively. By specifying the elements value of the reaction and transition matrix on the energy-shell, both phase shift...

The main purpose of this article is to solve the connection problems between (p, q)−Fibonacci polynomials and the two polynomials, namely Chebyshev polynomials of third and fourth kinds which are considered as two nonsymmetric polynomials of the Jacobi polynomials. Moreover, the inversion connection formulae for the latter formulae are given. We show that all the connection coefficients are exp...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

The aim of the present paper is to extend the classical Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system.

Absboer -Robust stability conditions for low-order Schw polynomials are obtained. In McuLu, conditions for dewe n = 2, 3, 4, and 5 are explicitly obtained. These conditions relate to &&ty of the corner points for n = 2.3 and for corner and possible supplementary points for n = 4 and 5. Two countere-ples given in the literature are fully discussed in relation to the obtained conditions. Futme re...

Caution: These polynomials are referred to as w0, w1, w2, ... in Sections 5-8 of [1]. However, beginning with Section 9 of [1], Hazewinkel uses the notations w1, w2, w3, ... for some different polynomials (the so-called big Witt polynomials, defined by formula (9.25) in [1]), which are not the same as our polynomials w1, w2, w3, ... (though they are related to them: in fact, the polynomial wk t...

Using the KOF data at the annual level, we construct ten different composite indices for comparing the extent of globalization of 131 countries for eleven years, 1999-2009. We compare the different indices of globalization among themselves and also with the Dreher-KOF index of globalization and find that among the different indices the Dreher-Chebyshev index is the most representative one. Amon...