Notes on Number Theory and Discrete Mathematics, 2024
In this paper, we generalize the arithmetic partial derivative to local fields like the p-adic fields, and the arithmetic derivative to global fields like the number fields.
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.
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.
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.