Thesis (Ph.D.)--University of Delaware, 2006. / Principal faculty advisor: Daniel S. Weile, Dept. of Electrical and Computer Engineering. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 95).

Thesis (Ph. D.)--University of Chicago, 1916. / Vita. "A Private Edition Distributed by the University of Chicago Libraries." "Reprinted from Transactions of the American mathematical society, vol. 18, no. 2, April, 1917." Includes bibliographical references. Also available on the Internet.

Thèse--Universit́e de Paris.

Thesis (Ph. D.)--Oregon State University, 1980. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (Ph D.)--University of Chicago. / A Dissertation, submitted to the Faculty of the Ogden Graduate School of Science, in Candidacy for the Degree of Doctor of Philosophy. Department of Astronomy. Vita. Includes bibliographical references. Also available on the Internet. Also issued online.

In order to introduce the study undertaken in this thesis, let us consider the differential equationz2 (μ 2 - 2μ zm + z2m) d2y/dz2 + z (b0 + b1zm + b2z2m) dy/dz+ (c0 + c1zm + c2z2m) y = 0The variable z and he coefficients μ, bi, ci (i = 0, 1, 2) are regarded as complex and m is an arbitrary positive integer. It is also assumed that b0 + b1u + b2p2 = 0 and that the difference of the two roots of the indicial equation about z = 0 is not congruent to zero modulo m.

The subject of this work is functional equations with direction towards linear functional equations. The .rst part describes function sets where iterates of the functions converge to a .xed point. In the second part the convergence property is used to provide solutions to linear functional equations by de.ning solutions as in.nite sums. Furthermore, this work contains some transforms to linear form, examples of functions that belong to di¤erent classes and corresponding linear functional equations. We use Mathematica to generate solutions and solve itera- tively equations.

Controlling and understanding the propagation of optical pulses through dispersive media forms the basis for optical communication, medical imaging, and other modern technological advances. Integral to this control and understanding is the ability to describe the transients which occur immediately after the onset of a signal. This thesis examines the transients of such a system when a unit step function is applied. The electromagnetic field is described by an integral resulting from Maxwell’s Equations. It was previously believed that optical precursors, a specific transient effect, existed only for only a few optical cycles and contributed only small magnitudes to the field. The main results of this thesis show that the transients arising from this integral are entirely precursors and that they may exist on longer time scales and contribute larger magnitudes to the field. The experimental detection of precursors has previously been recognized only through success comparison to the transient field resulting from an application of the method of steepest descent to that field integral. For any parameter regime where steepest descents may be applied, this work gives iterative methods to determine saddle points which are both more accurate than the accepted results and to extend into regimes where the current theory has failed. Furthermore, asymptotic formulae have been derived for regions where previous attempts at steepest descent have failed. Theory is also presented which evaluates the applicability of steepest descents in the represention of precursor behavior for any set of parameters. Lastly, the existence of other theoretical models for precursor behavior who may operate beyond the reach of steepest descent is validated through successful comparisons of the transient prediction of those methods to the steepest descent based results of this work. / Dissertation

Despite our intuition, birds are no smaller than mammals when the constraints of a flying body plan are taken into account. Nevertheless, the largest mammals are ten times the mass of the largest birds. Allometric equations generated for anseriforms and ratites suggest mid-shaft femur circumference is the best measure to use in estimating avian body mass. The small sample size of extant ratites makes mass estimate extrapolation to larger extinct species inaccurate. The division of ratites into cursorial and graviportal groups is supported. Aepyornithids do not show atypical femoral shaft asymmetry. New and more accurate estimates of egg masses, and separate male and female body masses for sexually-dimorphic ratites are generated. Egg mass scaling exponents for individual bird orders differ from that Aves as a whole, probably due to between-taxa effects. Ratite egg mass does not scale with the same exponent as other avian orders, whether kiwi are included or excluded. Total clutch mass in ratites, however, scales similarly to egg mass in other birds, perhaps as a consequence of the extreme variation in ratite clutch size. Kiwi and elephant bird eggs are consistent with the allometric trend for ratites as a whole, taking clutch size into account. Thus kiwi egg mass is probably an adaptation for a precocial life history, not a side effect of their being a dwarfed descendant of a moa-sized ancestor. Relatively small body size in ancestral kiwis is consistent with a trans-oceanic dispersal to New Zealand in the Tertiary, as suggested by recent molecular trees. This implies multiple loss of flight in Tertiary ratite lineages, which is supported by biogeographic, molecular, paleontological, and osteological evidence, but which is not the currently prevailing hypothesis. / Dissertation