rational functions are of great interest to engineers and geoscientists. the rational polynomial coefficient (rpc) model as a generalized sensor model has been introduced as an alternative for the rigorous sensor model of the satellite imaging. numerical instability of normal equations is the only single obstacle to the implementation of these functions. practically, estimating rational functio...

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.

This paper presents a formula expressing Macaulay constants of numerical polynomial through its minimizing coefficients. From this, we obtain that Kolchin dimension polynomials do not decrease. For the minimal differential $$ {\omega}_{\mathcal{G}/\mathcal{F}} (this concept was introduced by W. Sitt) will prove criterion for to be equal. In this case, as our example shows, there are no bounds f...

We prove that the question of whether a given linear partial differential or difference equation with polynomial coefficients has non-zero polynomial solutions is algorithmically undecidable. However, for equations with constant coefficients this question can be decided very easily since such an equation has a non-zero polynomial solution iff its constant term is zero. We give a simple combinat...