acase@tulane.edu

In all that follows, D denotes a monoid whose underlying space is an n-disk, H a compact group of units of D, and A a compact group of monoid automorphisms of D. This thesis is primarily concerned with the structure of H, Z(H,D) = {d (ELEM) D (VBAR) hd = dh for all h (ELEM) H} and F(A,D) = {d (ELEM) D (VBAR) (eta) (d) = d for all (eta) (ELEM) A} for small values of n One of the primary tools that we develop for this thesis is the following theorem: If A acts effectively on D (or any monoid whose underlying space is an orientable manifold with connected boundary), then A restricts to an effective action on (PAR-DIFF)D For the case that n (LESSTHEQ) 3, we show that Z(H,D) and F(A,D) are disks and H is represented as an abelian subgroup of O(n). When n = 4, we restrict our attention to the case where H is a Lie group. We show, with the possible exception of two finite non-solvable groups, that Z(H,D) is a (generalized) disk. By studying the center of H and the Sylow subgroups of H, we derive a strong relationship between non-abelian groups of units and subgroups of O(2) and S('3) We also develop some techniques for constructing examples that complement the theory / acase@tulane.edu

acase@tulane.edu

In statistical analysis; it is very important to check the validity of model assumptions that are imposed on the data to be analyzed before drawing statistical inference based on these model assumptions. This research is motivated by a health insurance data set which captures the relation between insurance status and some covariates, such as gender, household income category, etc. Our interest lies in the effect of the covariates on the duration of the insurance coverage, which is connected to a right censored data problem. Preliminary testing suggests that an Accelerated Life Model fits the effect of gender on the length of insurance coverage. To our best knowledge, there are currently no existing methods to check the model assumption for accelerated life models with right censored data. Therefore, it is the goal of this research to construct a goodness of fit test for accelerated life models with right censored data In order to construct such a test, the Empirical Likelihood Method is used as the tool to construct the test statistic, which is based on a Cramer-von Mises type statistic, and the Maximum Likelihood Estimator (MLE) for the parameter-acceleration factor in the model. The Bootstrap Method is applied to find the critical values for the test statistic. The consistency of the MLE of the acceleration factor under the model assumption is established. In order to investigate the effectiveness of the proposed model checking method, computer simulation studies on the power of the proposed goodness of fit test and the confidence intervals for the acceleration factor are also conducted / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

Of concern are the properties of solutions of one space dimensional evolution equation utx,t=A u˙,t x,x∈ R,t>0, 0.1 where A is a nonlinear operator which is independent of the time t, maps functions of space variable · to functions of x. Examples of this include some important models such as Allen-Cahn equation, Neural network model and Ising model etc. We show that under certain assumptions on A , the solution of the rescaled version of (0.1) utx,t=A ue˙, t xe ,e>0small, will develop a 'transition layer structure', i.e. a pattern, at a predictable time and that this pattern will last for a very long time but will be eventually destroyed / acase@tulane.edu

acase@tulane.edu

In the Symposium Plato provides a forum for a confrontation between Socrates and his most important accuser, the comic poet Aristophanes. As Socrates reminds the Athenian jury at his trial, the charges against him were originally inspired by Aristophanes' Clouds, with its portrait of the philosopher who does not believe in the gods of the city and who is responsible for corrupting the city's youth. In the Symposium Plato makes Aristophanes a character in his own work. He pits the comic poet against the philosopher in a contest to determine the most qualified candidate to speak about the human situation in terms of eros, or human desire. By way of Aristophanes' memorable speech about eros, this study argues, Plato gives reason to take seriously the poet's critique of philosophy. Socrates' belief that philosophy is the sole contributor to the human good is subject to further critical assessment by the appearance, at the end of the dialogue, of the problematic Athenian statesman Alcibiades. In its interpretation of Aristophanes' and Socrates' speeches about eros, this dissertation aims to show how the rational and political orientations of human beings give rise to two potentially incompatible modes of pursuing the good. And in Alcibiades' dramatic presence at the conclusion of the Symposium, this study finds a sign of Plato's teaching, that a fuller understanding of human desire requires consideration of both the Socratic and Aristophanic perspectives / acase@tulane.edu

acase@tulane.edu