Counterintuitive in nature, the Mpemba effect asserts that hot liquid freezes faster than cold liquid. While noted throughout history by scientific minds like Aristotle, the phenomenon remains in contention with varying hypotheses for the effect proposed alongside the effect’s rise in popularity. Contributing to the research efforts surrounding the Mpemba effect, the authors in this article explore the effect in different liquids ranging in physical properties and intermolecular forces to determine potential parameters attributable to producing the Mpemba effect.

In this study, the authors sought to find out how many mathematical solutions there were to the Indian mathematician Ramanujan's formula, which is a³ + b³ + c³ = d³, and also quantify the densities its solutions. They wrote their own computer program to do so and kept values of a, b, and c less than 10,000. While conducting the analysis, they were also looking for perfect power taxicab numbers and their frequency. They were able to find solutions and densities for the equation. Additionally, while they found that most perfect cube taxicab numbers had a frequency of 2 or 3, they also found on number with a frequency of 42!

In this study, the authors investigate the relationship between iron/hydrogen ratio [Fe/H] of a type of variable stars commonly used as reference points RR Lyrae stars and their light curves to see if one can determine the composition of these stars solely by measuring their light curve characteristics.