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Full-Text Articles in Physical Sciences and Mathematics
Eigenvalues And Approximation Numbers, Ryan Chakmak
Eigenvalues And Approximation Numbers, Ryan Chakmak
CMC Senior Theses
While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.
An Overview Of Computational Mathematical Physics: A Deep Dive On Gauge Theories, Andre Simoneau
An Overview Of Computational Mathematical Physics: A Deep Dive On Gauge Theories, Andre Simoneau
CMC Senior Theses
Over the course of a college mathematics degree, students are inevitably exposed to elementary physics. The derivation of the equations of motion are the classic examples of applications of derivatives and integrals. These equations of motion are easy to understand, however they can be expressed in other ways that students aren't often exposed to. Using the Lagrangian and the Hamiltonian, we can capture the same governing dynamics of Newtonian mechanics with equations that emphasize physical quantities other than position, velocity, and acceleration like Newton's equations do. Building o of these alternate interpretations of mechanics and understanding gauge transformations, we begin …
Bayesian Hierarchical Meta-Analysis Of Asymptomatic Ebola Seroprevalence, Peter Brody-Moore
Bayesian Hierarchical Meta-Analysis Of Asymptomatic Ebola Seroprevalence, Peter Brody-Moore
CMC Senior Theses
The continued study of asymptomatic Ebolavirus infection is necessary to develop a more complete understanding of Ebola transmission dynamics. This paper conducts a meta-analysis of eight studies that measure seroprevalence (the number of subjects that test positive for anti-Ebolavirus antibodies in their blood) in subjects with household exposure or known case-contact with Ebola, but that have shown no symptoms. In our two random effects Bayesian hierarchical models, we find estimated seroprevalences of 8.76% and 9.72%, significantly higher than the 3.3% found by a previous meta-analysis of these eight studies. We also produce a variation of this meta-analysis where we exclude …