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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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The Effect of Different Concentrations of Iron on the Growth of Egeria (Elodea) Densa

Hu et al. | Jan 08, 2015

The Effect of Different Concentrations of Iron on the Growth of <em>Egeria (Elodea) Densa</em>

Minerals such as iron are essential for life, but too much of a good thing can be poisonous. Here the authors investigate the effect of iron concentrations on the growth of an aquatic plant and find that supplementing small amounts of iron can help, but adding too much can be bad for the plant. These results should help inform decisions on allowable iron concentrations in the environment, aquatic farming, and even home aquariums.

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Androgen Diffusion Patterns in Soil: Potential Watershed Impacts

Corson et al. | Jan 24, 2019

Androgen Diffusion Patterns in Soil: Potential Watershed Impacts

Androgens are natural or synthetic steroid hormones that control secondary male sex characteristics. Androgens are excreted in cattle urine and feces, and can run off or seep into nearby waters, negatively impacting aquatic life and potentially polluting human water sources. Here, the authors investigated the effectiveness of soil as a natural barrier against androgen flow into vulnerable waterways. Their results, obtained by testing diffusion patterns of luminol, an androgen chemical analog, indicated that soil is a poor barrier to androgen diffusion.

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Comparative Gamma Radiation Analysis by Geographic Region

Zadan et al. | Jul 20, 2015

Comparative Gamma Radiation Analysis by Geographic Region

Gamma radiation can be produced by both natural and man-made sources and abnormally high exposure levels could lead to an increase in cell damage. In this study, gamma radiation was measured at different locations and any correlation with various geographic factors, such as distance from a city center, elevation and proximity to the nearest nuclear reactor, was determined.

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