The purpose of this survey is to present some approximation and shape preserving properties of the so-called nonlinear (more exactly sublinear) and positive, max-product operators, constructed by starting from any discrete linear approximation operators, obtained in a series of recent papers jointly written with B. Bede and L. Coroianu. We will present the main results for the max-product opera...

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain delta-type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and re...

The paper shows that in the analysis of a queuing system with fixed-size batch arrivals, there emerges a set of polynomials which are a generalization of Chebyshev polynomials of the second kind. The paper uses these polynomials in assessing the transient behaviour of the overflow (equivalently call blocking) probability in the system. A key figure to note is the proportion of the overflow (or ...

In this work we consider a Generalized Bronnikov-Ellis wormhole and the tideless Morris-Thorne study propagation of massive scalar fields. We calculate quasinormal frequencies using WKB method pseudospectal Chebyshev show presence an anomalous decay rate for modes in wormhole. However, such behaviour is avoided fundamental mode background.

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful effective type of inequality. The main findings by using integrable functions generalized fractional integral operators many existing results as well iterating the Chebyshev special cases.

We explicitly calculate characteristic functions of cones of generalized polynomials corresponding to Chebyshev systems on intervals of the real line and the circle. Thus, in principle, we calculate homogeneous self-concordant barriers for this class of cones. This class includes almost all "cones of squares" considered in 5]. Our construction, however, does not use this structure and is applic...

Newton’s formula for constructing the interpolation polynomial is well–known. It makes use of divided differences. It was generalized around 1971–1973 by Mühlbach for interpolation by a linear family of functions forming a complete Chebyshev system. This generalization rests on a generalization of divided differences due to Popoviciu. In this paper, it is shown that Mühlbach’s formula is relate...

Proceeding the study of local properties of analytic functions started in [Br] we prove new dimensionless inequalities for such functions in terms of their Chebyshev degree. As a consequence we obtain the reverse Hölder inequalities for analytic functions with absolute (i.e., independent of dimension) constants. For polynomials such inequalities were recently proved by Bobkov who sharpened and ...