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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!

This study's goal was to identify the Mach numbers for which electrostatic drag and heat transfer manipulation would be most applicable inside the stratosphere. The experiments were conducted using computational fluid dynamics software. The study demonstrated that, on average, higher Mach speeds resulted in a considerably higher potential decrease in density. The study highlights that further research on the surface charge method is warranted to explore higher hypersonic speeds within the stratosphere.

In a 10-year period in the early 2000’s, hospital-based (nosocomial) infections increased by 123%, and this number is increasing as time goes on. The purpose of this experiment was to use hyaluronic acid, silver nanoparticles, and a bacteriophage cocktail to create a hydrogel that promotes wound healing by increasing cell proliferation while simultaneously disrupting biofilm formation and breaking down Staphylococcus aureus and Pseudomonas aeruginosa, which are two strains of bacteria that attribute to nosocomial infections and are increasing in antibiotic resistance.

This study explored the use of graphite's conductivity for circuit boards by creating a conductive paste through exfoliation with organic solvents and sonication. The combination of acetone and sonication was found to be the most effective, producing a high-conductivity paste with desirable properties such as a low boiling point. While not a replacement for wires, this conductive paste has potential applications in electronics and infrastructure, provided that key engineering challenges are addressed.

The authors looked at how a student's own background influence their attitude towards integration of diverse cultures and ethnicities. While overall students viewed other groups positively, the authors found that groups still indicated they felt judged by their peers.

One-third of the world's people do not have access to clean drinking water. Nadella and Nadella tackle this issue by testing a low-cost filtration system for removing heavy metal and bacteria from water.

Using the European Space Agency’s Gaia dataset, the authors analyzed the relationship between white dwarfs’ magnitudes and proper motions. They hypothesized that older white dwarf stars may have different velocities than younger ones, possibly that stars slow down as they age. They found that the white dwarfs in the dataset were substantially redder and higher magnitude (traits traditionally associated with older stars) as compared to their non-fast counterparts.

Enzyme chemotaxis is a thermodynamic phenomenon in which enzymes move along a substrate concentration gradient towards regions with higher substrate concentrations and can be used to steer nanovehicles towards targets along natural substrate concentrations. In patients with Alzheimer’s disease, a gradient of tau protein forms in the bloodstream. Tau protein is a substrate of the enzyme CDK5, which catalyzes the phosphorylation of tau protein and can travel using chemotaxis along tau protein gradients to increasing concentrations of tau and amyloid-beta proteins. The authors hypothesized that CDK5 would be able to overcome these barriers of Brownian motion and developed a quantitative model using Michaelis-Menten kinetics to define the necessary parameters to confirm and characterize CDK5’s chemotactic behavior to establish its utility in drug delivery and other applications.

Do different physical traits affect teenagers’ initial trust of an unknown person? Would they give greater trust to women and people of similar ethnicity? To test these hypotheses, the authors developed a survey to determine the sets of physical characteristics that affect a person's trustworthiness. They found that gender and expression were the main physical traits associated with how trustworthy an individual looks, while ethnicity was also important.

In many areas of the world’s oceans, diatoms such as Thalassiosira pseudonana are limited in growth by the availability of iron (Fe), which is an essential nutrient for diatoms. The authors of this study examined if Fe-limitation makes a significant difference in the proteins expressed within the chloroplast, the power source for diatoms, utilizing a new plastid isolation technique specific to diatoms and completing 14 mass spectrometry experiments.