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Full-Text Articles in Physical Sciences and Mathematics
Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost
Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost
All Dissertations
In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …
Exploring The Structure Of Partial Difference Sets With Denniston Parameters, Nicolas Ferree
Exploring The Structure Of Partial Difference Sets With Denniston Parameters, Nicolas Ferree
Honors Theses
In this work, we investigate the structure of particular partial difference sets (PDS) of size 70 with Denniston parameters in an elementary abelian group and in a nonelementary abelian group. We will make extensive use of character theory in our investigation and ultimately seek to understand the nature of difference sets with these parameters. To begin, we will cover some basic definitions and examples of difference sets and partial difference sets. We will then move on to some basic theorems about partial difference sets before introducing a group ring formalism and using it to explore several important constructions of partial …
The Sharp Bounds Of A Quasi-Isometry Of P-Adic Numbers In A Subset Real Plane, Kathleen Zopff
The Sharp Bounds Of A Quasi-Isometry Of P-Adic Numbers In A Subset Real Plane, Kathleen Zopff
Undergraduate Theses
P-adic numbers are numbers valued by their divisibility by high powers of some prime, p. These numbers are an important concept in number theory that are used in major ideas such as the Reimann Hypothesis and Andrew Wiles’ proof of Fermat’s last theorem, and also have applications in cryptography. In this project, we will explore various visualizations of p-adic numbers. In particular, we will look at a mapping of p-adic numbers into the real plane which constructs a fractal similar to a Sierpinski p-gon. We discuss the properties of this map and give formulas for the sharp bounds of its …
Geometric Dissections, Daniel Robert Martin
Geometric Dissections, Daniel Robert Martin
MSU Graduate Theses
In the study of geometry, the notion of dissection and its mechanics are occasionally over-looked. We consider and trace the history and theorems surrounding geometric dissections in both recreational and academic mathematics. We explore the important advancements in this particular topic from antiquity through the nineteenth and early twentieth centuries. We conclude with an exploration of the Banach-Tarski paradox