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Boundary Behavior Of Laplace Transforms, Timothy Ferguson
Boundary Behavior Of Laplace Transforms, Timothy Ferguson
Honors Theses
In this thesis, we examine the boundary behavior of Laplace transforms (as analytic functions on the right and left half planes) of certain bounded functions. The types of bounded functions we consider are Fourier transforms of measures and almost periodic functions.
On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens
On Conway's Generalization Of The 3x + 1 Problem, Robin M. Givens
Honors Theses
This thesis considers a variation of the 3x+1, or Collatz, Problem involving a function we call the Conway function. The Conway function is defined by letting C3(n)=2k for n=3k and C3(n)=4k±1 for n=3k±1, where n is an integer. The iterates of this function generate a few 'short' cycles, but the s' tructural dynamics are otherwise unknown. We investigate properties of the Conway function and other related functions. We also discuss the possibility of using the Conway function to generate keys for cryptographic use based on a fast, efficient binary implemenation of the function. Questions related to the conjectured tree-like structure …