1 citations · 2 across the 15 of their papers we have counts for
16 papers
A Boolean polynomial operator for the Collatz problem
Mario DeFranco
We define a reformulation of the Collatz map which allows us to express it as an operator on the set of sequences of Boolean polynomials. We express this operator in terms o…
Multi-point variants of the Newton-Raphson-Simpson method arising from organizing a formal zero according to a function
Mario DeFranco
Fix an integer , and a function with . We define a multi-point variant of the Newt…
On Boolean polynomials and the Union-Closed Conjecture
Mario DeFranco
For a set of subsets of a universe set of size , we construct a Boolean polynomial such that the Union-Closed Conjecture is true for this and …
Verification of the Jacobian Conjecture for -linear maps in two variables
Mario DeFranco
For any integer , we verify the Jacobian Conjecture for a -linear map in two variables. We prove that almost all the coefficients of the formal inverse are in the idea…
On the Jacobian Conjecture and ideal membership for degree -linear maps
Mario DeFranco
We consider polynomial maps, which we call degree -linear maps, that satisfy the Jacobian condition. We prove that certain infinite families of elements, which appear in the coe…
On Taylor series of zeros with general base function
Mario DeFranco
We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simpl…