Journal of Integer Sequences, 2022
In this paper, we investigate the dynamical system of higher order of arithmetic partial derivatives. We show that there are infinitely many numbers with exactly n anti-partial derivatives for any nonnegative integer n. This is a joint work with Brad Emmons.
MAA Press: An Imprint of the American Mathematical Society, 2022
This is a real analysis textbook for future secondary teachers and general undergraudate mathematics major. This is a joint work with David M. Clark.
Transactions of the American Mathematical Society, 2021
In this paper, we develop a combinatorial formual to calculate the dimension of the automorphism group of F-cyclic F-crystal over an algebraically close dfield at some finite level. This is a joint work with Zeyu Ding.
Pi Mu Epsilon Journal, 2018
In this paper, we determine the size of a Radon-Kaczmarz Puzzle so that it has a unique solution when give a fixed set of clues. This is a joint work with Steven Rossi.
Mathematische Nachrichten, 2017
In this paper, we generalize minimal p‐divisible groups to minimal F-crystals. Using minimal heights, we give an estimate of isomorphism number of isosimple F-crystals.
Journal of Ramanujan Mathematical Society, 2014
In this paper, we prove Vasiu’s conjecture that the isomorphism number of an F-crystal is equal to its level torsion.
Journal of Number Theory, 2012
In this paper, we use the level torions to compute isomorphism numbers of various F-crystals.