4 citations · 7 across the 8 of their papers we have counts for
9 papers
Gravilon: Applications of a New Gradient Descent Method to Machine Learning
Chad Kelterborn, Marcin Mazur, Bogdan V. Petrenko
Gradient descent algorithms have been used in countless applications since the inception of Newton's method. The explosion in the number of applications of neural networks has re-e…
Some properties of coefficients of cyclotomic polynomials
Marcin Mazur, Bogdan V. Petrenko
This paper investigates coefficients of cyclotomic polynomials theoretically and experimentally. We prove the following result. {{\em If where are odd prime…
Generators of maximal orders
Rostyslav V. Kravchenko, Marcin Mazur, Bogdan V. Petrenko
Let R be the ring of algebraic integers in a number field K and let L be a maximal order in a semisimple K-algebra B. Building on our previous work, we compute the smallest number…
Representations of analytic functions as infinite products and their application to numerical computations
Marcin Mazur, Bogdan V. Petrenko
Let be an open disk of radius in , and let be a sequence of . We prove that for every analytic function without zeros in…
On the conjectures of Atiyah and Sutcliffe
Marcin Mazur, Bogdan V. Petrenko
Motivated by certain questions in physics, Atiyah defined a determinant function which to any set of distinct points in assigns a complex number $D…
On the smallest number of generators and the probability of generating an algebra
Rostyslav V. Kravchenko, Marcin Mazur, Bogdan V. Petrenko
In this paper we study algebraic and asymptotic properties of generating sets of algebras over orders in number fields. Let be an associative algebra over an order in an al…