The focus of this grounded theory research was to investigate the problems that those groups closest to students placed in mathematics classes by mathematics ability have and how those parties work to resolve the problems. The main problem found was a conflict between educators and parents over which students deserve...
An analytical model is developed to address the question of how different disturbance
regimes affect the mean and variance of landscape carbon storage in forest ecosystems. Total landscape carbon is divided into five pools based on the processes from which they are derived and based on their temporal dynamics. Formulae...
This thesis considers one of the classical problems in the actuarial mathematics literature, the decay of the probability of ruin in the collective risk model. The
claim number process N(t) is assumed to be a renewal process, the resulting model
being referred as the Sparre Andersen risk model. The inter-claim...
Water is one of the most biologically and economically important substances on Earth. A significant portion of Earth's water subsists in the subsurface. Our ability to monitor the flow and transport of water and other fluids through this unseen environment is crucial for a myriad of reasons.
One difficulty we...
In this paper we develop an upscaling technique for non-Darcy flow in porous media. Non-Darcy model of flow applies to flow in porous media when large velocities occur. The well-posedness results for theory of quasilinear elliptic partial differential equations. To discretize the model we used lowest order Raviart-Thomas mixed finite...
This thesis contains three manuscripts addressing the application of stochastic processes to the analysis and solution of partial differential equations (PDEs) in mathematical physics.
In the first manuscript, one dimensional diffusion and Burgers equation are considered. The Fourier transform of the solution to each PDE is represented as the expected...
Cellular sets in the Hilbert cube are the intersection of nested sequences of normal
cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert
cube into cellular sets and using a quotient map. By using a cellular decomposition of the
Hilbert cube, an example...
This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutations e.g., transpositions and 3-cycles.
The generalized variational principle of Herglotz defines the functional whose extrema are sought by a differential equation rather than an integral. It reduces to the classical variational principle under classical conditions. The Noether theorems are not applicable to functionals defined by differential equations. For a system of differential equations derivable...
A fundamental question related to any Lie algebra is to know its subalgebras. This is
particularly true in the case of E6, an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question...