We generalize the notion of the Tchebyshev transform of a graded poset to a triangulation of an arbitrary simplicial complex in such a way that, at the level of the associated F -polynomials ∑ j fj−1((x − 1)/2), the triangulation induces taking the Tchebyshev transform of the first kind. We also present a related multiset of simplicial complexes whose association induces taking the Tchebyshev t...

In this paper we describe the use of multivariate Chebyshev polynomials in computing spectral derivations and Clenshaw–Curtis type quadratures. The multivariate Chebyshev polynomials give a spectrally accurate approximation of smooth multivariate functions. In particular we investigate polynomials derived from the A2 root system. We provide analytic formulas for the gradient and integral of A2 ...

and Applied Analysis 3 nonlinear term is treated with the Chebyshev collocation method. The time discretization is a classical Crank-Nicholson-leap-frog scheme. Yuan and Wu 43 extended the Legendre dual-Petrov-Galerkin method proposed by Shen 44 , further developed by Yuan et al. 45 to general fifth-order KdV-type equations with various nonlinear terms. The main aim of this paper is to propose ...

The article presents a comparative analysis of the accuracy of the distance to the observed object for geometric methods in noisy observations of bearings-only information. Algorithms for determining the parameters of the trajectories of moving objects are widely used in control systems and navigation systems, with one of the most difficult tasks is to determine the trajectory parameters for pa...

In the generalized Legendre transform construction the Kähler potential is related to a particular function. Here, the form of this function appropriate to the k-monopole metric is calculated from the known twistor theory of monopoles.

The uniaxial orientational order in a macromolecular system is usually specified using the Hermans factor which equivalent to second moment of system's orientation distribution function (ODF) expanded terms Legendre polynomials. In this work, we show that for aligned materials are two-dimensional (2D) or have measurable 2D intensity distribution, such as carbon nanotube (CNT) textiles, not appr...

Background: This paper is an improvement of a previous work on the problem recovering function or probability density from finite number its geometric moments, [1]. The worked solved with help B-Spline theory which great approach as long resulting linear system not very large. In this work, two solution algorithms based approximate representation target distribution via orthogonal expansion are...

Orthogonal Legendre moments are used in several pattern recognition and image processing applications. Translation and scale Legendre moment invariants were expressed as a combination of the approximate original Legendre moments. The shifted and scaled Legendre polynomials were expressed in terms of the original Legendre polynomials according to complicated and time-consuming algebraic relation...