Let ψK be the Chebyshev function of a number field K. Under the Generalized Riemann Hypothesis we prove an explicit upper bound for |ψK(x)−x| in terms of the degree and the discriminant of K. The new bound improves significantly on previous known results. Math. Comp. 85(298), 889–906 (2016). Electronically published on October 7, 2015. DOI: http://dx.doi.org/10.1090/mcom3031

We study a generalized Chebyshev oscillator associated with point interaction for the discrete Schrödinger equation. Our goal is to find realization of annihilation operator this by differential operator. This can be used obtain equation corresponding polynomials.

In this paper, we propose a new method to design an observer and control the linear singular systems described by Chebyshev wavelets. The idea of the proposed approach is based on solving the generalized Sylvester equations. An example is also given to illustrate the procedure.

An algorithm for a generalized Chebyshev interpolation procedure, increasing the number of sample points more moderately than doubling, is presented. The FFT for a real sequence is incorporated into the algorithm to enhance its efficiency. Numerical comparison with other existing algorithms is given.

A generalized N-point Birkhoff–Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived. 2011 Elsevier Inc. All rights reserved.

Similarity measure is a very important problem in fuzzy soft set theory. In this paper, seven similarity measures of fuzzy soft sets are introduced, which are based on the normalized Hamming distance, the normalized Euclidean distance, the generalized normalized distance, the Type-2 generalized normalized distance, the Type-2 normalized Euclidean distance, the Hausdorff distance and the Chebysh...

Recently, Babson and Steingrimsson (see [2]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We study generating functions for the number of permutations on n letters avoiding 1-3-2 (or containing 1-3-2 exactly once) and an arbitrary generalized pattern τ on k letters, or containing τ exactly onc...