![Estimating the liquid jet breakdown height using dimensional analysis with experimental evidence](/rails/active_storage/representations/proxy/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaHBBak1PIiwiZXhwIjpudWxsLCJwdXIiOiJibG9iX2lkIn19--c696b56c608ccfd730963c3a362f71c24c4f14f7/eyJfcmFpbHMiOnsibWVzc2FnZSI6IkJBaDdCem9MWm05eWJXRjBTU0lJY0c1bkJqb0dSVlE2QzNKbGMybDZaVWtpRFRZd01IZzJNREErQmpzR1ZBPT0iLCJleHAiOm51bGwsInB1ciI6InZhcmlhdGlvbiJ9fQ==--33b2b080106a274a4ca568f8742d366d42f20c14/Screen%20Shot%202023-06-20%20at%203.23.51%20PM.png)
These authors mathematically deduce a model that explains the interesting (and unintuitive) physical phenomenon that occurs when water falls.
Read More...Estimating the liquid jet breakdown height using dimensional analysis with experimental evidence
These authors mathematically deduce a model that explains the interesting (and unintuitive) physical phenomenon that occurs when water falls.
Read More...Formation and sticking of air bubbles in water in d-block containers
Bubbles! In this study, the authors investigate the effects that different materials, temperature, and distance have on the formation of water bubbles on the surface of copper and steel. They calculated mathematical relations based on the outcomes to better understand whether interstitial hydrogen present in the d-block metals form hydrogen bonds with the water bubbles to account for the structural and mechanical stability.
Read More...Population Forecasting by Population Growth Models based on MATLAB Simulation
In this work, the authors investigate the accuracy with which two different population growth models can predict population growth over time. They apply the Malthusian law or Logistic law to US population from 1951 until 2019. To assess how closely the growth model fits actual population data, a least-squared curve fit was applied and revealed that the Logistic law of population growth resulted in smaller sum of squared residuals. These findings are important for ensuring optimal population growth models are implemented to data as population forecasting affects a country's economic and social structure.
Read More...Fractal dimensions of crumpled paper
Here, beginning from an interest in fractals, infinitely complex shapes. The authors investigated the fractal object that results from crumpling a sheet of paper. They determined its fractal dimension using continuous Chi-squared analysis, thereby testing and validating their model against the more conventional least squares analysis.
Read More...Comparison of three large language models as middle school math tutoring assistants
Middle school math forms the basis for advanced mathematical courses leading up to the university level. Large language models (LLMs) have the potential to power next-generation educational technologies, acting as digital tutors to students. The main objective of this study was to determine whether LLMs like ChatGPT, Bard, and Llama 2 can serve as reliable middle school math tutoring assistants on three tutoring tasks: hint generation, comprehensive solution, and exercise creation.
Read More...Comparative analysis of CO2 emissions of electric ride-hailing vehicles over conventional gasoline personal vehicles
While some believe that ride-hailing services offer reduced CO2 emissions compared to individual driving, studies have found that driving without passengers on ride-hailing trips or "deadheading" prevents this. Here, with a mathematical model, the authors investigated if the use of electric vehicles as ride-hailing vehicles could offer reduced CO2 emissions. They found that the improved vehicle efficiency and cleaner generation could in fact lower emissions compared to the use of personal gas vehicles.
Read More...Optimizing Interplanetary Travel Using a Genetic Algorithm
In this work, the authors develop an algorithm that solves the problem of efficient space travel between planets. This is a problem that could soon be of relevance as mankind continues to expand its exploration of outer space, and potentially attempt to inhabit it.
Read More...Optimizing airfoil shape for small, low speed, unmanned gliders: A homemade investigation
Here, the authors sought to identify a method to optimize the lift generated by an airfoil based solely on its shape. By beginning with a Bernoullian model to predict an optimized wing shape, the authors then tested their model against other possible shapes by constructing them from Styrofoam and testing them in a small wind tunnel. Contrary to their hypothesis, they found their expected optimal airfoil shape did not result in the greatest lift generation. They attributed this to a variety of confounding variables and concluded that their results pointed to a correlation between airfoil shape and lift generation.
Read More...The effect of activation function choice on the performance of convolutional neural networks
With the advance of technology, artificial intelligence (AI) is now applied widely in society. In the study of AI, machine learning (ML) is a subfield in which a machine learns to be better at performing certain tasks through experience. This work focuses on the convolutional neural network (CNN), a framework of ML, applied to an image classification task. Specifically, we analyzed the performance of the CNN as the type of neural activation function changes.
Read More...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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