When testing individual correlations in a matrix for significance, researchers primarily use F or z tests repeatedly, thereby inflating the overall Type I error rate. Alternative approaches are to test whether the observed correlation matrix differs from the identity matrix or to test individual correlations for significance using procedures which control overall Type I error rates. Monte Carlo simulations were conducted to examine the power and general characteristics of: (a) the Bartlett, Brien et al., Kullback, and Steiger procedures, tests of the first type, and (b) the multistage Bonferroni, rank order method proposed by Stavig and Acock (1976), and a modified rank order method which is based on comparing the rank ordered Fisher z transform with its corresponding critical value on the ordered half-normal score distribution; these are tests of the second type. Critical value tables for ordered half-normal scores are found in Appendix A The Brien et al. procedure was the most powerful for testing the hypothesis that the observed correlation matrix differs from the identity matrix and yet showed stable empirical alpha values. The modified rank order method was the most powerful in assessing significance of the largest correlation in a matrix; however, the Type I error rate was slightly inflated for small sample sizes with larger numbers of variables. The multistage Bonferroni had a conservative Type I error rate and demonstrated moderate power. In terms of the number of significant correlations in a matrix, the modified rank order method controlled Type I error well, while possessing the greatest power. Both the multistage Bonferroni and rank order methods had conservative Type I error rates, especially as the number of variables increased. In testing all correlations in a matrix via a stepdown procedure or in assessing individual correlations after the Brien et al. procedure was first found significant, all methods were too conservative. The modified rank order method is recommended for testing all correlations in a matrix, although correction in Fisher's z or some other adjustment might be needed to reduce the nonconservative bias with a greater number of variables / acase@tulane.edu

acase@tulane.edu

The thesis most central to my dissertation is the claim that thinking is a spatio-temporal process, that 'knowing' is an event which, like all others, happens or occurs. It is not an original thesis. It is an implication of materialism, and just as old. However, until the last century there was no way of explaining the development of mental phenomena. Even today, the mind is usually considered different in kind from the rest of nature, as removed from the causal order of things. Such a conception is implied by metaphysical realists, and openly articulated by theists. It is the motivation for the philosophical projects of epistemology and metaphysics, continuing into the scientific age as a rationalist hope of checking the results of empiricism through non-empirical means A generation ago, Richard Rorty claimed that this conception of the mind as a 'mirror of nature' was misguided, that modeling mental activity on the transparent process of sight had outlived its usefulness and led to problems both theoretical and practical. Eliminating the visual metaphors on which traditional conceptions of the mind had depended would mean abandoning philosophical aspirations to the Truth (a way things really are apart from all belief). Unwilling to accept the notion that the mind is a physical (spatio-temporal) phenomenon, Rorty's work was largely disparaged as relativistic, since it made objectivity a matter of intersubjective agreement Such a democratic approach was what the Sophists had advocated, what Plato sought to refute, and what the tradition of philosophy was designed to replace. However, as Rorty's predecessor John Dewey pointed out, a 'spectator theory of knowledge' requires a subject which is detached from the world he observes, a subject beyond the constraints of space and time. It is therefore necessary to choose between the truth of philosophy and the consequences of pragmatism: the view that the mind, like everything else in nature, is a product of space and time The present dissertation is a defense of Rorty's position. It claims that the bulk of that position is not original with him, but is indicative of pragmatism generally, and that in turn the tenets of pragmatism are consequences of Darwinism. That is, the pragmatist claims Rorty makes are nothing other than what Dewey called 'the influence of Darwin on philosophy'. As a result, any effective refutation of Rorty's position will require either a refutation of Darwinism or an explanation as to why the constraints of space and time do not apply to the human ability to think / acase@tulane.edu

The initial value problem$$\eqalign{u\sb{t} &= \Delta u - u + H(u-a),\cr u(x,0) &= u\sb0(x),\cr}$$for $x\in \IR\sp2$ and $t > 0$ is studied in this work. We prove existence of traveling wave solutions by studying the behavior of the level curves $u = a$ as t increases. In Chapter 3 it is shown that traveling wa e solutions with radially symmetric initial values have velocity 0, using this fact we give these solutions using Bessel functions and then we prove that these solutions are unstable. Finally, in the last chapter we present some results which were obtained using numerical approximations / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu