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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!

Middle school math forms the basis for advanced mathematical courses leading up to the university level. Large language models (LLMs) have the potential to power next-generation educational technologies, acting as digital tutors to students. The main objective of this study was to determine whether LLMs like ChatGPT, Bard, and Llama 2 can serve as reliable middle school math tutoring assistants on three tutoring tasks: hint generation, comprehensive solution, and exercise creation.

Though current strategies in counterterrorism are somewhat effective, the Simultaneous Attack/Persistent Pursuit (SAPP) Theory may be superior alternative to current methods. The authors simulated five attack strategies (1 SAPP and 4 non-SAPP), and concluded that the SAPP model was significantly more effective in reducing the final number of terrorist attacks. This demonstrates the comparative advantage of utilizing the SAPP model, which may prove to be critical in future efforts in counterterrorism.

Cancer is often caused by improper function of a few proteins, and sometimes it takes only a few proteins to malfunction to cause drastic changes in cells. Here the authors look at the genes that were mutated in patients with a type of pancreatic cancer to identify proteins that are important in causing cancer. They also determined which proteins currently lack effective treatment, and suggest that certain proteins (named KRAS, CDKN2A, and RBBP8) are the most important candidates for developing drugs to treat pancreatic cancer.

The authors looked at potential downstream effects of raising the minimum wage. Specifically they focused on taxable wages, employment, and firm counts.

In this study, the impact of fluorination of heterocyclic drug Allopurinol on its stability and other chemical properties is investigated.

In this study, we developed an algorithm to estimate the contact rate and the average infectious period of influenza using a Susceptible, Infected, and Recovered (SIR) epidemic model. The parameters in this model were estimated using data on infected Greek individuals collected from the National Public Health Organization. Our model labeled influenza as an epidemic with a basic reproduction value greater than one.

The authors looked at how molarity impacts the degree to which ionic compounds dissociate in solution. They found that lower molarities led to decreased conductivity of solutions in a manner that did not follow the theoretical predictions.

The authors use the unique movements of the jumping gall wasp to study momentum transfer with potential applications in robotics and extraterrestrial research.

The authors looked at using genetic algorithms to look at the Indian labor market and what features might best explain any variation seen. They found that features such as economic growth and household consumption, among others, best explained variation.