Ahstracr -The present paper investigates the recursive realization of a rational generalized transfer function (GTF) as a linear time-variant (LTV) difference equation. We develop a relationship between a GTF and a time-variant difference equation. The unique realizability of a GTF as a LTV difference equation is discussed. Procedures for determining a timevariant difference equation from a giv...

We study the kernel Kn,s(z) of the remainder term Rn,s( f ) of Gauss–Turán–Kronrod quadrature rules with respect to one of the generalized Chebyshev weight functions for analytic functions. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L∞-error bounds of Gauss–Turán–Kronrod quadratures. Following Kronrod,...

This talk will present an effort to formalize Taylor Models in the Coq proof assistant. Machinecheckable correctness proofs are facilitated by an abstract viewpoint: Taylor models can be generalized to balls in the Chebyshev metric. Extensions of elementary functions are then explained as compositions of such balls. This approach also accommodates other polynomial approximation methods than Tay...

Horadam [7], in a recent article, defined two sequences of polynomials Jn(x) and j„(x), the Jacobsthal and Jacobsthal-Lucas polynomials, respectively, and studied their properties. In the same article, he also defined and studied the properties of the rising and descending polynomials i^(x), rn(x), Dn(x)y and dn(x), which are fashioned in a manner similar to those for Chebyshev, Fermat, and oth...

Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or po...

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...

In this paper we construct two types of Hessenberg matrices with the property that every weighted isobaric polynomial (WIP) appears as a determinant of one of them, and as the permanent of the other. Every integer sequence which is linearly recurrent is representable by (an evaluation of) some linearly recurrent sequence of WIPs. WIPs are symmetric polynomials written in the elementary symmetri...

Abstract We consider solitary-wave solutions of the generalized Burger’s-Fisher equation ∂Ψ ∂t + αΨ δ ∂Ψ ∂x − ∂ 2Ψ ∂x2 = βΨ(1 − Ψδ). In this paper, we present a new method for solving of the generalized Burger’s-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation met...

We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N . This definition generalizes a very large class of Extended Complete Chebyshev systems in the one-dimensional case. This is the first of a series of papers in this area, which solves the longstanding problem of finding a satisfactory mul...

Based on probability density evolution method (PDEM) and Bayes’ law, a new filter strategy is proposed, in which the prior of system state interest predicted by solving generalized equation (GDEE), posterior then updated terms Bayesian formula. Furthermore, Chebyshev polynomial-based collocation developed to obtain numerical solutions probability. Three illustrative examples are finally present...