Abstract In this paper we consider generalized monomial functions $$f, g:{\mathbb {F}}\rightarrow {\mathbb {C}}$$ f , g : F → C (of possibly different degree) that also fulfill $$\begin...

The aim of the paper is to find polynomial parametric equations rectifying Salkowski curves in Minkowski 3-space, via a serial approach. These are characterized by according their curvature; particular those with constant curvature functions and linear harmonic fully characterized. Then, obtained as solutions differential third-order coefficients.

It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton’s identities. In this work, by further exploring Newton’s identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power...

Recently it was found [1] that polynomial solutions of differential equations are connected to finite-dimensional representations of the algebra sl2 of firstorder differential operators. In this Talk it will be shown that there also exists a connection between polynomial solutions of finite-difference equations (like Hahn, Charlier and Meixner polynomials) and unusual finitedimensional represen...

All isolated solutions of the cyclic-n polynomial equations are not known for larger dimensions than 8 except the dimensions 10 and 11. We exploit two types of symmetric structures in the cyclic-n polynomial to compute all isolated nonsingular solutions of the equations efficiently by the polyhedral homotopy continuation method and to verify the correctness of the generated approximate solution...

In this paper, we present and analyse fourth order method for finding simultaneously multiple zeros of polynomial equations. S. M. Ilič and L. Rančič modified cubically convergent Ehrlich Aberth method to fourth order for the simultaneous determination of simple zeros [5]. We generalize this method to the case of multiple zeros of complex polynomial equations. It is proved that the method has f...

In this paper, we present some efficient numerical algorithm for solving system of fuzzy polynomial equations based on Newton's method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms.