This is the personal website of Jason Zhang.
All research can be found here.
Category: Mathematics (multisets, infinity, cardinality)
We investigate an alternative perspective to the cardinality of multisets introduced by Velev (2024), opting to define “m-cardinality” via equivalence classes of bijective functions on multisets instead of the classical sum of multiplicities. This paper aims to formalize this concept into an exact hierarchy and to investigate specific properties of this hierarchy such as the order theoretic structure. We show that the class of m-cardinals is equivalent to a special subset of non-decreasing sequences of cardinals and that the m-cardinals form a lattice.
Category: Computer Science (Remote Sensing, Machine Learning)
Since the early 2000s, Ashburn, a satellite city to DC, has urbanized rapidly and has turned into a “Data Center Alley.” Approximately 70 % of internet traffic passes through the region. The data centers have led to an increase in the Urban Heat Island (UHI) effect, which impacts the local environment. This study aims to quantify the extent of the UHI effect and the key causes of the side effects. Satellite data was analyzed through various statistical methods and comparisons and various regions of interest were considered. Additionally, machine learning techniques were applied for downscaling the Land Surface Temperature (LST) data for the purpose of understanding the temperature distribution in a finer detail. The analysis yields that there has been a significant increase in LST, particularly in areas near data centers. This research highlights the urgent need to regulate urbanization and data centers for environmental sustainability. The environmental impact of recent technological innovation and urban development has raised temperatures and destroyed crucial green land that helps combat climate change.
Currently, I am working on investigating the untyped \(\lambda\)-calculus. Specifically, I am working towards developing an interactive theorem prover for the \(\lambda\)-calculus and investigating the \(\lambda\)-calculus’ various models (e.g., Scott’s \(D^{\infty}\) model).