Long Division, Remainder 1

Chromosomal Diseases in Humans (1): Cell Division

This article has no abstract.

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.

The Chinese Remainder Theorem

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 ...