Minimizing the Moral Remainder

The Chinese Remainder Theorem

k-Remainder Cordial Graphs

In this paper we generalize the remainder cordial labeling, called $k$-remainder cordial labeling and investigate the $4$-remainder cordial labeling behavior of certain graphs.

Moral Repair and the Moral Saints Problem

This article explores the forms of moral repair that the wrongdoer has to perform in an attempt to make amends for her past wrongdoing, with a focus on the issues of interpersonal moral repair; that is, what a wrongdoer can do to merit her victim‘s forgiveness and achieve reconciliation with her community. The article argues against the very general demands of atonement that amount to an obliga...

Taylor’s Formula with Remainder

In this paper, we present a proof in ACL2(r) of Taylor’s formula with remainder. This important theorem allows a function f with n + 1 derivatives on the interval [a, b] to be approximated with a Taylor series of n terms centered at a. Moreover, the formula allows the error in the approximation to be bounded by a term involving the (n + 1)st derivative of f on (a, b). The results in this paper ...

On Polynomial Remainder Codes

Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work. We explicitly allow the code symbols to be polynomials of different degrees, which leads to two different notions of weight and distance. Algebraic decoding ...