It is well known that the Fibonacci numbers can be expressed in the
form Round {1/√5 λ₀[superscript n]} where λ₀ = (1 + √5)/2. [Knu75] We look at integer sequences which are solutions to non-negative difference equations and show that if the equation is 1-Bounded then the solution can be...
Arising from an investigation in Hydrodynamics, the Korteweg-de Vries equation demonstrates existence of nonlinear waves that resume their profile after interaction. In this thesis, the classical equations governing wave motion are the starting point for the development of an analogue of the KdV that describes the evolution of a wave...
The recursive and stochastic representation of solutions to the Fourier transformed Navier-Stokes equations, as introduced by [34], is extended in several ways. First, associated families of functions known as majorizing kernels are analyzed, in light of their apparently essential role in the representation. Second, the theory is put on a...
Revised Universal Soil Loss Equation (RUSLE) is a standard for estimating soil loss caused by rainfall and overland flow. The current software tool that implements this standard is RUSLE 1.06b, which is a stand-alone DOS application. In this project, we converted the DOS application to a Web application, which we...
The fractal dimension of measured ocean wave profiles is found to be in the range of 1.5-1.8. This non-integer dimension indicates the fractal nature of the waves. Standard formulations to analyze waves are based on a differential approach. Since fractals are non-differentiable, this formulation fails for waves with fractal characteristics....
The existence of generalized symmetries of Maxwell's equations in Gödel's Universe is investigated. It is shown that their existence is in turn tied to the existence of certain spinorial objects called Killing spinors.
The conformal algebra, corresponding to valence (1; 1) Killing spinors, for Gödel's Universe is discussed in detail....
In this dissertation, we investigate three numerical methods for inverting the Laplace transform. These methods are all based on the trapezoidal-type approximations to the Bromwich integral. The first method is the direct integration method: It is a straightforward application of the trapezoidal rule to the Bromwich integral, followed by convergence...
Missing data can lead to biased and inefficient estimation if the missing mechanism is not taken into account in the analysis. In this dissertation we propose two estimators that, under fairly general conditions, are asymptotically unbiased. The first proposed estimator assume the data are missing at random (MAR) and does...
The micropolar equations of motion are developed, in a very general form, for a
mixture of fluid and solid particles. The fluid is allowed to move differently than the solids,
and the solids are modeled as a micropolar continuum. That is, the solid particles have an
additional degree of freedom...