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An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

Grewal et al. | Oct 05, 2020

An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

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!

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Racial and gender disparities in the portrayal of lawyers and physicians on television

Asadi et al. | Nov 18, 2022

Racial and gender disparities in the portrayal of lawyers and physicians on television

Powered by the sociological framework that exposure to television bleeds into social biases, limiting media representation of women and minority groups may lead to real-world implications and manifestations of racial and gender disparities. To address this phenomenon, the researchers in this article take a look at primetime fictional representation of minorities and women as lawyers and physicians and compare television representation to census data of the same groups within real-world legal and medical occupations. The authors maintain the hypothesis that representation of female and minority groups as television lawyers and doctors is lower than that of their white male counterparts relative to population demographics - a trend that they expect to also be reflected in actual practice. With fictional racial and gender inequalities and corresponding real-world trends highlighted within this article, the researchers call for address towards representation biases that reinforce each other in both fictional and non-fictional spheres.

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