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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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Income mobility and government spending in the United States

Datta et al. | Nov 04, 2023

Income mobility and government spending in the United States
Image credit: CDC via Unsplash

Recent research suggests that the "American Dream" of income mobility may be becoming increasingly hard to obtain. Datta and Schmitz explore the role of government spending in socioeconomic opportunity by determining which state government spending components are associated with increased income mobility.

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The Effect of Cooking Method on the Amount of Fat in an Egg

Srinivasan et al. | Dec 01, 2014

The Effect of Cooking Method on the Amount of Fat in an Egg

Fat can be chemically altered during cooking through a process called lipid oxidation, which can have a negative impact on health. In this study, the authors measured the extracted fat in raw, fried and hard-boiled eggs and found that cooking eggs to a higher temperature resulted in a lower amount of extracted fat, indicating a greater amount of oxidized fat.

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A novel approach for early detection of Alzheimer’s disease using deep neural networks with magnetic resonance imaging

Ganesh et al. | Mar 20, 2022

A novel approach for early detection of Alzheimer’s disease using deep neural networks with magnetic resonance imaging

In the battle against Alzheimer's disease, early detection is critical to mitigating symptoms in patients. Here, the authors use a collection of MRI scans, layering with deep learning computer modeling, to investigate early stages of AD which can be hard to catch by human eye. Their model is successful, able to outperform previous models, and detected regions of interest in the brain for further consideration.

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The optical possibilities of gelatin

Parikh et al. | Mar 28, 2024

The optical possibilities of gelatin
Image credit: Lensabl

Here the authors investigated the optical possibilities of gelatin and acrylic in regards to potential implementations at soft contact lenses. They fabricated lenses of different shapes and evaluated the refraction of laser light finding that gelatin needed to be thickened or increased in curvature to account for its lower refractive index compared to plastics, or used in a mixture to strengthen the lens.

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Reimagize – a digital card-based roleplaying game to improve adolescent girls’ body image

Kumar et al. | Oct 04, 2021

Reimagize – a digital card-based roleplaying game to improve adolescent girls’ body image

Reimagize, a role-playing with decision-making, was conjured, implementing social psychological concepts like counter-stereotyping and perspective-taking. As the game works implicitly to influence body image, it even counters image issues beyond personal body dissatisfaction. This study explored whether a digital role-playing card game, incorporating some of the most common prejudices of body image (like size prejudice, prejudices from the media, etc.) as identified by a digital survey/questionnaire completed by Indian girls aged 11-21, could counter these issues and reduce personal body dissatisfaction.

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