Bjorner was the first to determine the Mobius functions of factor orders and subword orders. To determine the Mobius functions, he used involutions, shellability, and generating functions. [2][3][4] Bjorner and Stanley found an interesting relation among the subword order derived from a two point set {a, b} , symmetric groups and composition orders. [6] Factor orders, subword orders, and genera...

We show that the resultants with respect to x of certain linear forms in Chebyshev polynomials with argument x are again linear forms in Chebyshev polynomials. Their coefficients and arguments are certain rational functions of the coefficients of the original forms. We apply this to establish several related results involving resultants and discriminants of polynomials, including certain self-r...

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain a...

We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials ins...

‎we mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+p(z)f(z+c)^n=q(z)$‎, ‎which is a supplement of previous‎ ‎results in [k‎. ‎liu‎, ‎l. z‎. ‎yang and x‎. ‎l‎. ‎liu‎, ‎existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎czechoslovak math. j. 61 (2011)‎, no. 2, ‎565--576‎, and x‎. ‎g‎. ‎qi‎...

We present a criterion that provides an easy sufficient condition in order that a collection of Abelian integrals has the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could no...

We construct an hyperinterpolation formula of degree n in the three-dimensional cube, by using the numerical cubature formula for the product Chebyshev measure given by the product of a (near) minimal formula in the square with Gauss-Chebyshev-Lobatto quadrature. The underlying function is sampled at N ∼ n/2 points, whereas the hyperinterpolation polynomial is determined by its (n + 1)(n + 2)(n...

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...

ECG (Electrocardiogram) signals originating from heart muscles, generate massive volume of digital data. They need to be compressed or approximated for efficient transmission and storage. ECG signal compression is traditionally performed in three ways: direct, transform and parameter extraction. Polynomial approximation which is a form of parameter extraction method, is employed here. This pape...

In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials ...