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Analysis of Patterns in the Harmonics of a String with Artificially Enforced Nodes

Jain et al. | Jan 28, 2021

Analysis of Patterns in the Harmonics of a String with Artificially Enforced Nodes

This study examines the higher harmonics in an oscillating string by analyzing the sound produced by a guitar with a spectrum analyzer. The authors mathematically hypothesized that the higher harmonics in the series of the directly excited 2nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2nd, 3rd, and 4th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

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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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Development of selective RAC1/KLRN inhibitors

Kubrat Neczaj-Hruzewicz et al. | Nov 04, 2024

Development of selective RAC1/KLRN inhibitors

Kalirin is a guanine nucleotide exchange factor (GEF) for the GTPase RAC1, linked to schizophrenia and Alzheimer’s Disease. It plays a crucial role in synaptic plasticity by regulating dendritic spine formation and actin cytoskeleton remodeling, which are essential for creating new synapses. Authors developed two novel compounds targeting kalirin, confirming that predictive modeling can indicate biological activity.

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