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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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A 3D printed triboelectric nanogenerator for bridge vibration energy harvesting and sensing

Walavalkar et al. | Jul 19, 2026

A 3D printed triboelectric nanogenerator for bridge vibration energy harvesting and sensing
Image credit: Jakub Żerdzicki

This study strongly illustrates that optimizing 3D printing parameters would enhance a triboelectric nanogenerator's performance. The design improvements substantiate the potential of optimized, 3D-printed TENGs for developing scalable, cost-effective solutions for powering low-energy electronics, particularly in applications such as structural health monitoring.

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Eye color, visual acuity and photophobia: How eye color affects light sensitivity

Spencer et al. | May 20, 2026

Eye color, visual acuity and photophobia: How eye color affects light sensitivity

This study examined whether eye color affects photophobia and vision in elementary school students and staff, finding no significant relationship between eye color, light sensitivity, or visual acuity. However, photophobia was common across age groups, highlighting the need for greater awareness of light sensitivity in learning environments.

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