This article provides an overview of some recent developments in quantum dynamic and spectroscopic calculations using the Chebyshev propagator. It is shown that the Chebyshev operator ( Tk (Ĥ)) can be considered as a discrete cosine type propagator ( cos(kΘ̂)), in which the angle operator ( Θ̂ = arccos Ĥ ) is a single-valued mapping of the scaled Hamiltonian ( Ĥ ) and the order (k) is an effectiv...

In this paper, we investigate the diameters, Chebyshev radii, self-radii and inner radii of a sequence sets in normed spaces. We prove that if is I -Hausdorff convergent to set, I-convergent. Similar relations are showed for sequence.

We introduce a new and eecient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the Legendre-Galerkin and Chebyshev-Galerkin methods.

For a fixed prime p, we consider the set of maps Z/pZ → Z/pZ of the form a 7→ Tn(a), where Tn(x) is the degree-n Chebyshev polynomial of the first kind. We observe that these maps form a semigroup, and we determine its size and structure.

In this paper, we set forth a new family of regularizing filters based on the magnitude response function of Chebyshev-I lowpass filter. The corresponding regularization strategies for inverse problem are constructed. The optimum asymptotic order of the regularized solution is obtained by a priori choice of the regularization parameter. Finally, numerical results are given to demonstrate the ef...

We study generating functions for the number of permutations in Sn subject to set of restrictions. One of the restrictions belongs to S3, while the others to Sk. It turns out that in a large variety of cases the answer can be expressed via continued fractions, and Chebyshev polynomials of the second kind. 2001 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 30B70 42C05

Let K be a number field with algebraic closure K, let S be a finite set of places of K containing the archimedean places, and let φ be a Chebyshev polynomial. We prove that if α ∈ K is not preperiodic, then there are only finitely many preperiodic points β ∈ K which are S-integral with respect to α.

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results to the case of comonotone functions.

An operational approach introduced by Gould and Hopper to the construction of generalized Hermite polynomials is followed in the hypercomplex context to build multidimensional generalized Hermite polynomials by the consideration of an appropriate basic set of monogenic polynomials. Directly related functions, like Chebyshev polynomials of first and second kind are constructed.