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!

The authors use the Lanczos algorithm to computationally solve the Schrodinger equation for 2D potentials with a Python program

The energy of an atom is extremely useful in nuclear physics and reaction mechanism pathway determination but is challenging to compute. This work aimed to synthesize regression models for Pople Gaussian expansions of Slater-type Orbitals (STO-nG) atomic energy vs. atomic number scatter plots to allow for easy approximation of atomic energies without using computational chemistry methods. The data indicated that of the regressions, sinusoidal regressions most aptly modeled the scatter plots.

In this experiment, the authors modify the heat equation to account for imperfect insulation during heat transfer and compare it to experimental data to determine which is more accurate.

Here, the authors sought to investigate the efficiency, cost, and environmental impact of several possible propellants that are or could be used for space flight. By deriving three novel equations, they identified harm, energy, and cost scores for each fuel, suggesting that considering each factor will be essential to the ongoing growth of the space industry.

Here based on an interest in fractals, the authors used a Julia Set Generator to consider a specific point on the Mandelbrot set with an associated coordinate. In this manner, they found that the complexity of the Mandelbrot and Julia Sets are governed by relatively simple rules, revealing that the intricate patterns of fractals can be defined by defined by simple rules and patterns.

In our modern age, the burgeoning use of radios and radars has resulted in competition for electromagnetic spectrum resources. With recent research highlighting solutions to radio and radar mutual interference, there is a desperate need for a cost-effective configuration that permits a radar-radio joint system. In this study, the authors have set out to determine the feasibility of using single-tone continuous-wave radars in a radar-joint system. With this system, they aim to facilitate cost-effective near-field target detection by way of the popularized 2.4-GHz industrial, scientific, and medical (ISM) band.

Here, seeking to develop an understanding of the properties that determine the viability of piezoelectric flexible materials for applications in electro-mechanical sensors, the authors investigated the effects of the inclusion BaTiO₃ nanoparticles in electrospun Polyvinyledene Fluoride. They found the voltage generated had a piecewise linear dependence on the applied force at a few temperatures.

In this article, the authors look into what is already known about the factor affecting longevity and determine the importance of behavioral factors including alcohol consumption, smoking, and obesity on longevity. The authors quantify data from over 150 countries and, interestingly, find that the impact each factor has on longevity is at least in part dependent on the country's economic development status. Overall, they conclude that an average person’s life expectancy can increase by more than 3 years if smoking and alcohol consumption is reduced by a half and weight is decreased by 10%.

There are complex interactions between water and outside forces such as magnetic fields. This study aims to examine the effects of magnetic forces on the flow rate of water. The alteration of flow rate by magnets could have exciting applications in many fields.