Equivalence of differentiable functions, rational functions and polynomials

Computer Algebra of Polynomials and Rational Functions

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Generalized Α-variation and Lebesgue Equivalence to Differentiable Functions

We find an equivalent condition for a real function f : [a, b] → R to be Lebesgue equivalent to an n-times differentiable function (n ≥ 2); a simple solution in the case n = 2 appeared in an earlier paper. For that purpose, we introduce the notions of CBV G1/n and SBV G1/n functions, which play analogous rôles for the n-th order differentiability as the classical notion of a V BG∗ function for ...

Faber Polynomials for Rational Mapping Functions

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

gH-differentiable of the 2th-order functions interpolating

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...