Physical Sciences and Mathematics Commons^™

In Silico Investigation For The Conversion Of Methyl Oleate To Gasoline, Arkanil Roy

MSU Graduate Theses

Petroleum products are found in all walks of life. From the plastic casing on a cell phone to the gasoline that runs most vehicles, a lot is derived from petroleum. Ubiquitous use of petroleum has adversely affected the environment. Toxic substances such as SOx and NOx are released into the atmosphere during the processing and usage of petroleum products, which contributes to global warming. Inevitable oil spills cause devastating effects to marine ecosystems. The rate of regeneration of petroleum is much slower than the rate of usage that would lead to it being exhausted in the recent future. Hence, a …

School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari

Honors Scholar Theses

In this work we propose a reversible Markov chain scheme to model for the mobility of students affected by a grade school leveling policy. This model provides unified and mathematically tractable framework in which transition functions are sampled uniformly from the set of {\bf reversible} transition functions. The results from the study appear to confirm the disadvantageous effects of this school policy, on par with the of a previous model on the same policy.

Groups Generated By Automata Arising From Transformations Of The Boundaries Of Rooted Trees, Elsayed Ahmed

USF Tampa Graduate Theses and Dissertations

In this dissertation we study groups of automorphisms of rooted trees arising from the transformations of the boundaries of these trees. The boundary of every regular rooted tree can be endowed with various algebraic structures. The transformations of these algebraic structures under certain conditions induce endomorphisms or automorphisms of the tree itself that can be described using the language of Mealy automata. This connection can be used to study boundarytransformations using the propertiesof the induced endomorphisms, or vice versa.

We concentrate on two ways to interpret the boundary of the rooted d-regular tree. In the first approach discussed in detail …

Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen

Wayne State University Dissertations

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the

mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.

Assuming that the systems are in continuous times,

stemming from stochastic-differential-equation-based models and random discrete events,

switching diffusions come into being. In such systems, continuous states and discrete events

(discrete states)

coexist and interact.

A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).

When the discrete component takes a …

No-Slip Billiards, Christopher Lee Cox

Arts & Sciences Electronic Theses and Dissertations

We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. A general theory of rigid body collisions in is developed, which returns the known dimension two model as a special case but generalizes to higher dimensions. We give new results on periodicity and boundedness of orbits which suggest that a class of billiards (including all polygons) is not ergodic. Computer generated phase portraits demonstrate non-ergodic features, suggesting chaotic no-slip billiards cannot easily be constructed using the common techniques for generating chaos in standard billiards. However, …

Ergodicity Of Stochastic Switching Diffusions And Stochastic Delay Systems, Hongwei Mei

Wayne State University Dissertations

This dissertation contains two main parts. The first part focuses on numerical algorithms for approximating the ergodic means of suitable functions of solutions to stochastic differential equations with Markov regime switching. Our main effort is devoted to obtaining the convergence and rates of convergence of the approximation algorithms. The study is carried out by obtaining laws of large numbers and laws of iterated logarithms for numerical approximation to long-run averages of suitable functions of solutions to switching diffusions.

The second part is devoted to stochastic functional differential equations (SFDEs) with infinite delay. This part consists of two main themes. First, …

Asymptotic Theory Of General Multivariate Garch Models, Weibin Jiang

Electronic Thesis and Dissertation Repository

Generalized autoregressive conditional heteroscedasticity (GARCH) models are widely used in financial markets. Parameters of GARCH models are usually estimated by the quasi-maximum likelihood estimator (QMLE). In recent years, economic theory often implies equilibrium between the levels of time series, which makes the application of multivariate models a necessity. Unfortunately the asymptotic theory of the multivariate GARCH models is far from coherent since many algorithms on the univariate case do not extend to multivariate models naturally. This thesis studies the asymptotic theory of the QMLE under mild conditions. We give some counterexamples for the parameter identifiability result in Jeantheau [1998] and …

A Remark On Conservative Diffeomorphisms, Jairo Bochi, Bassam R. Fayad, Enrique Pujals

Publications and Research

Abstract:

We show that a stably ergodic diffeomorphism can be C¹ approximated by a diffeomorphism having stably non-zero Lyapunov exponents.

Résumé:

On montre qu'un difféomorphisme stablement ergodique peut être C¹ approché par un difféomorphisme ayant des exposants de Lyapunov stablement non-nuls.